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GEORGE BARBASTATHIS:
Hi, everyone.

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OK, Yeah, so let me tell
you my vision of what SMA is

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00:00:31,940 --> 00:00:34,290
and what we're supposed to do.

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Oh, before I do that, let
me do one more introduction.

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00:00:36,540 --> 00:00:39,940
This is Professor Colin Sheppard
sitting on the other side.

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00:00:39,940 --> 00:00:43,470
So he's the instructor
on the Singapore side.

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00:00:43,470 --> 00:00:46,430
So basically, the four of us
are the team of instructors--

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00:00:46,430 --> 00:00:51,470
Professor Shepherd, Se
Baek, Pepe, and myself.

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00:00:51,470 --> 00:00:55,420
And the class is not
quite an SMA class.

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00:00:55,420 --> 00:00:58,790
It is not quite part of
the Singapore-MIT Alliance.

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00:00:58,790 --> 00:01:00,290
It is part of
something else called

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00:01:00,290 --> 00:01:04,819
Singapore-MIT Alliance for
Research and Technology, SMART.

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00:01:04,819 --> 00:01:09,830
And there is a very complicated
description of what SMART is

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00:01:09,830 --> 00:01:11,570
and why we're
teaching the class.

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00:01:11,570 --> 00:01:14,360
But the bottom line is
that this is more or less

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the same class of optics
that has been taught

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at MIT for the last 10 years.

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00:01:19,590 --> 00:01:22,010
It's actually an improved
version of the class.

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00:01:22,010 --> 00:01:23,930
And it is being
broadcast to Singapore

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00:01:23,930 --> 00:01:26,510
at a very inconvenient time
for everybody involved,

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00:01:26,510 --> 00:01:28,500
both in Singapore and for us.

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So I think it is fair.

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00:01:31,610 --> 00:01:35,900
And so this is a summary,
a little bit of what I just

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said about the instructors.

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00:01:37,780 --> 00:01:39,310
We also have the two assistants.

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00:01:39,310 --> 00:01:41,900
Primarily, you'll be
dealing with Kate,

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00:01:41,900 --> 00:01:43,440
those of you who are here.

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00:01:43,440 --> 00:01:45,080
She's my assistant at MIT.

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00:01:45,080 --> 00:01:47,390
And for those of
you in Singapore,

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00:01:47,390 --> 00:01:49,610
if you need sometimes
to turn in assignments,

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00:01:49,610 --> 00:01:52,240
or desperately get hold
of me, or whatever,

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00:01:52,240 --> 00:01:53,430
[? Deana ?] is your contact.

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00:01:53,430 --> 00:01:55,940
She's in block S16.

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00:01:59,290 --> 00:02:02,660
But anyway, Singapore
uses English

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00:02:02,660 --> 00:02:04,520
as an official
language, but as you

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00:02:04,520 --> 00:02:06,050
will notice
throughout the class,

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00:02:06,050 --> 00:02:07,110
there's some differences.

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00:02:07,110 --> 00:02:09,235
For example, in Singapore,
we don't say "building."

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00:02:09,235 --> 00:02:10,340
We say "block."

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00:02:10,340 --> 00:02:12,950
So there's also some
other subtle differences

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in Singapore English.

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00:02:15,700 --> 00:02:20,440
OK, we will seldom give
any handouts in the class.

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00:02:20,440 --> 00:02:22,280
Everything you need
is in the website.

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00:02:22,280 --> 00:02:24,960
I have listed there
link over here.

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00:02:24,960 --> 00:02:27,820
And when you log in there, you
will hit two, three things,

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00:02:27,820 --> 00:02:28,320
actually.

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You'll see the syllabus
has been posted,

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a set of policies
has been posted,

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00:02:34,180 --> 00:02:37,020
which says some obvious
things like don't copy,

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don't cheat on exams,
and stuff like that.

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00:02:39,490 --> 00:02:44,372
And also, the first lecture
has also been posted.

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And I will tell you a little
bit about how we deal with the

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posted lectures and so on.

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And these are some
administrative details here

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that I'm not sure if I want
to spend any time on those.

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For those of you
who are Course 2,

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if you're
undergraduate, graduate,

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it meets your restricted
elective requirement.

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If you're graduate,
it prepares you

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for one of the qualifying exams
offered in the department.

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And a little bit about
what the class covers.

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So the class is
very introductory

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about light phenomena and how
we design optical systems.

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And so this is a
bunch of pictures

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I stole from various websites.

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It shows a rainbow.

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It shows the galaxy
that we can capture

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with advanced telescopes.

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It shows-- do I have a pointer?

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I'd better just
use this for now.

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Well, I guess I cannot use.

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Anyway, so it shows
a cell over here

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captured with a microscope--

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which, I believe, is a
confocal microscopes.

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So it is Professor
Sheppard's expertise.

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And this is the picture of the
esophagus of a person captured

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with an endoscopy.

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So they basically lower
the fiber bundle inside,

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down someone's throat.

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00:04:06,120 --> 00:04:09,060
And using a technique called
optical coherence tomography--

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it is an optical
imaging technique--

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00:04:11,310 --> 00:04:15,020
they capture the esophagus.

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00:04:15,020 --> 00:04:18,329
And so finally,
what you see here

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is, of course, an optical
disk, if you're not

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00:04:20,250 --> 00:04:21,510
familiar with those.

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00:04:21,510 --> 00:04:24,530
And over here I believe
that's a holographic setup.

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00:04:24,530 --> 00:04:27,360
It is a diffusion
screen, and this

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00:04:27,360 --> 00:04:32,010
is supposed to be a setup for
a three-dimensional display.

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00:04:32,010 --> 00:04:34,320
When you look at it,
it creates the illusion

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00:04:34,320 --> 00:04:37,410
of a three-dimensional
projection.

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00:04:37,410 --> 00:04:39,510
So if we had this, for
example, in Singapore,

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00:04:39,510 --> 00:04:41,130
then I would, in
principle, appear

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00:04:41,130 --> 00:04:42,660
as if I'm standing over there.

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00:04:42,660 --> 00:04:45,770
This, of course, is still at
the science fiction stage,

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00:04:45,770 --> 00:04:48,340
but a lot of people
are working on it.

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And in fact, nowadays,
some companies,

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they offer a three
dimensional television

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00:04:53,850 --> 00:04:57,282
sets that you can buy for
a small additional amount.

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00:04:57,282 --> 00:04:58,740
I think it's a few
hundred dollars.

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00:04:58,740 --> 00:05:01,710
Samsung offers a 3D TV set.

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00:05:01,710 --> 00:05:05,370
Anyway, so the
point of this slide

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00:05:05,370 --> 00:05:09,240
is that there's many
applications of optics that

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00:05:09,240 --> 00:05:11,430
are interesting in engineering.

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00:05:11,430 --> 00:05:14,520
And, of course,
light phenomena are

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00:05:14,520 --> 00:05:16,630
interesting in their own right.

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00:05:16,630 --> 00:05:22,475
So the class will try to
balance curiosity-based,

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00:05:22,475 --> 00:05:23,850
more of a science
approach, where

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00:05:23,850 --> 00:05:27,060
we learn basic facts
about how light behaves,

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00:05:27,060 --> 00:05:29,790
how it propagates, how
it interacts with matter,

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00:05:29,790 --> 00:05:32,270
and we'll balance those with
engineering applications that

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00:05:32,270 --> 00:05:36,760
are, presumably, of
interest to many of you.

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00:05:36,760 --> 00:05:39,730
And for issues that have to
do with the expertise of both

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00:05:39,730 --> 00:05:43,090
of us, both of the
instructors, we

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00:05:43,090 --> 00:05:46,400
will concentrate most of
the applications on imaging.

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00:05:46,400 --> 00:05:49,150
So we'll be dealing a lot
with things like microscopes

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00:05:49,150 --> 00:05:51,260
and telescopes primarily.

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00:05:51,260 --> 00:05:56,500
These the major
imaging instruments.

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00:05:56,500 --> 00:05:58,630
But we'll also cover some
other things for fun.

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00:05:58,630 --> 00:06:01,060
For example, we'll talk
about the human eye.

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00:06:01,060 --> 00:06:05,510
We'll describe its structure,
its biology, how it works--

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00:06:05,510 --> 00:06:07,510
not in great detail,
because this is, after all,

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00:06:07,510 --> 00:06:09,220
not a biology class.

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00:06:09,220 --> 00:06:11,590
But just for fun,
because of the human eye

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turns out to have some very
interesting optics inside it.

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00:06:15,130 --> 00:06:17,380
And also, we'll
discuss very briefly

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the eyes of insects, which, as
you can see from the picture

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00:06:20,830 --> 00:06:23,740
and you may already
know, they're very

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different than the human eye.

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And we'll discuss a little
bit why they're different

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00:06:28,820 --> 00:06:31,490
and how each one
of them operates.

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And finally, some other
optical imaging systems that

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look very surprising.

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00:06:35,770 --> 00:06:38,770
This picture over
here is an instrument

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called the Very Large
Array telescope, or VLA.

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00:06:41,920 --> 00:06:46,410
It is located in Socorro, New
Mexico, here in the States.

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00:06:46,410 --> 00:06:50,470
And it is composed
of 27 antennas.

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00:06:50,470 --> 00:06:53,350
Each one of these little
white things is an antenna.

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00:06:53,350 --> 00:06:58,280
It's about 27 meters tall, and
the diameter of the instrument,

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00:06:58,280 --> 00:07:01,930
this branch over here,
is approximately--

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00:07:01,930 --> 00:07:02,740
well, it varies.

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00:07:02,740 --> 00:07:05,080
I don't know what it was
when this picture was taken.

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00:07:05,080 --> 00:07:07,520
But it can between 3 miles--

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00:07:07,520 --> 00:07:11,080
the diameter that is the size
of Cambridge, Massachusetts--

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00:07:11,080 --> 00:07:15,040
and 15 miles-- that is the
size of Washington, DC.

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00:07:15,040 --> 00:07:16,210
So that is an instrument.

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00:07:16,210 --> 00:07:18,085
An optical instrument,
if you can believe it,

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00:07:18,085 --> 00:07:21,580
has the size of an
entire state in the US.

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00:07:21,580 --> 00:07:25,450
And it is used to observe
very remote galaxies

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with high resolution.

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00:07:27,310 --> 00:07:29,650
So it falls a little bit
outside the scope of the class,

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00:07:29,650 --> 00:07:34,690
because it uses it uses
statistical optics, which

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we don't cover over here,
but we may mention it

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00:07:37,390 --> 00:07:40,720
in passing a little bit later.

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00:07:40,720 --> 00:07:44,320
So this is, of course,
among other things

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that you may have seen.

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00:07:46,780 --> 00:07:48,730
But actually, it cannot be done.

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00:07:48,730 --> 00:07:49,930
This is Luke Skywalker.

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00:07:49,930 --> 00:07:52,180
I'm old enough to
have been around when

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this movie came out, Star Wars.

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00:07:54,700 --> 00:07:57,940
And I just want to point out
that a lightsaber can actually

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00:07:57,940 --> 00:07:59,020
not be made.

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00:07:59,020 --> 00:08:00,530
It is one of these
impossible things

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00:08:00,530 --> 00:08:03,390
that you can see
in science fiction,

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00:08:03,390 --> 00:08:05,920
but it violates some
physical principles.

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00:08:05,920 --> 00:08:08,470
So unfortunately, it
cannot be made, but anyway,

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00:08:08,470 --> 00:08:13,050
it is still fun to think about.

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00:08:13,050 --> 00:08:16,460
OK, so I think I covered
the class objectives.

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00:08:16,460 --> 00:08:20,740
And we have to balance
here physical intuition

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with engineering
understanding and design.

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00:08:27,080 --> 00:08:31,300
So we'll cover the fundamentals
in pretty good detail,

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00:08:31,300 --> 00:08:33,100
and we'll also cover
some applications

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00:08:33,100 --> 00:08:35,710
in pretty good detail to
the degree that we can

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00:08:35,710 --> 00:08:38,620
within the scope of a semester.

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00:08:38,620 --> 00:08:42,100
So we'll try to be to be
very careful about that,

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how we balance the two.

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00:08:43,348 --> 00:08:44,890
Sometimes the two
can compete, right?

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00:08:44,890 --> 00:08:47,140
So we'll try to balance the
competition between basics

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and application.

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00:08:49,870 --> 00:08:54,190
And also, we'll cover
some applications.

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00:08:54,190 --> 00:08:56,170
And I mentioned,
primarily, we'll

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deal with microscopy and, also,
some topics such as telescopes.

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00:09:01,540 --> 00:09:03,820
There are some other topics
that I will not really

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00:09:03,820 --> 00:09:07,030
cover in class, like
optical data storage.

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00:09:07,030 --> 00:09:10,060
But as I will
mention in a second,

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00:09:10,060 --> 00:09:14,380
there is class projects that
are like mini research projects

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00:09:14,380 --> 00:09:16,850
that you will do
later in the semester.

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00:09:16,850 --> 00:09:18,640
So you're welcome
to pick topics out

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00:09:18,640 --> 00:09:21,480
of those if you are interested.

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00:09:21,480 --> 00:09:24,810
Some basics about the
sort of prerequisites.

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00:09:24,810 --> 00:09:28,890
This is the basic math
and physics that you need.

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00:09:28,890 --> 00:09:32,640
I think most of you have
covered these topics in your--

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00:09:32,640 --> 00:09:35,310
at least on the MIT side,
you covered those in places

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00:09:35,310 --> 00:09:40,470
like 18.03, and 2.004, and 8.02.

201
00:09:40,470 --> 00:09:44,258
So I assume that all of
you who are undergraduates

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00:09:44,258 --> 00:09:45,300
have taken those classes.

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00:09:49,170 --> 00:09:52,370
And there is it two textbooks.

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00:09:52,370 --> 00:09:54,790
So the class is a little bit
expensive, sorry about that.

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00:09:54,790 --> 00:09:58,170
There's two textbooks,
[? Hecht ?] and Goodman.

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00:09:58,170 --> 00:10:01,290
We'll be using,
throughout the first half

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00:10:01,290 --> 00:10:03,840
of the semester,
mostly [? Hecht, ?]

208
00:10:03,840 --> 00:10:06,540
and then, throughout the
second half, mostly Goodman.

209
00:10:06,540 --> 00:10:10,170
But the textbooks--
we did not really

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00:10:10,170 --> 00:10:12,330
cover the sequence
of the textbooks.

211
00:10:12,330 --> 00:10:15,810
You should use them
primarily as a reference.

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00:10:15,810 --> 00:10:18,370
All of this stuff is posted,
by the way, on the website.

213
00:10:18,370 --> 00:10:23,300
So you don't need to
write down the book names.

214
00:10:23,300 --> 00:10:26,570
But anyway, so the
textbooks are reference.

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00:10:26,570 --> 00:10:29,870
Your primary sources are the
notes and what you do in class.

216
00:10:29,870 --> 00:10:31,880
And then you can go
back and read them.

217
00:10:31,880 --> 00:10:34,550
And there some
other texts that are

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00:10:34,550 --> 00:10:37,590
useful if you have access
to them through the library,

219
00:10:37,590 --> 00:10:38,728
and so on.

220
00:10:38,728 --> 00:10:40,145
Some other
administrative details.

221
00:10:43,310 --> 00:10:45,830
This is the grade distribution
for the undergraduate class,

222
00:10:45,830 --> 00:10:47,620
2.71--

223
00:10:47,620 --> 00:10:50,740
30 homeworks, 30
quizzes, 40 final.

224
00:10:50,740 --> 00:10:52,360
We have eight homeworks.

225
00:10:56,700 --> 00:10:58,860
And the homeworks are due--

226
00:10:58,860 --> 00:11:03,540
actually, they are due nine
days after they're posted.

227
00:11:03,540 --> 00:11:05,970
So you have plenty of
time to work on them.

228
00:11:05,970 --> 00:11:08,250
And also, Pepe
will strategically

229
00:11:08,250 --> 00:11:12,780
schedule his office hours so
that you can ask questions

230
00:11:12,780 --> 00:11:14,430
before the homework.

231
00:11:14,430 --> 00:11:19,600
And we'll see how to do the
office hours for the Singapore

232
00:11:19,600 --> 00:11:20,100
students.

233
00:11:20,100 --> 00:11:23,800
We'll work something
out when I get there.

234
00:11:23,800 --> 00:11:27,510
Anyway, the first homework
is not due until February 18,

235
00:11:27,510 --> 00:11:31,410
so there's no need to
panic about that yet.

236
00:11:31,410 --> 00:11:35,940
And the homeworks will also
be posted on their website.

237
00:11:35,940 --> 00:11:38,610
And the 7.10 is very
similar, but the 7.10,

238
00:11:38,610 --> 00:11:41,230
the graduate version,
also has a project.

239
00:11:41,230 --> 00:11:44,430
So the project also counts
for a significant portion

240
00:11:44,430 --> 00:11:45,095
of the grade.

241
00:11:45,095 --> 00:11:46,470
And I think I
already mentioned--

242
00:11:46,470 --> 00:11:48,678
this is like a mini research
project where you either

243
00:11:48,678 --> 00:11:53,760
give a short lecture on a
hot topic in current optics

244
00:11:53,760 --> 00:11:59,190
research, or you
pick your own topic,

245
00:11:59,190 --> 00:12:03,150
and you do a little
bit of calculation

246
00:12:03,150 --> 00:12:08,040
or some simple thinking.

247
00:12:08,040 --> 00:12:10,750
It's supposed to
be a class topic.

248
00:12:10,750 --> 00:12:13,020
It's not a [INAUDIBLE] or
anything, but like a mini

249
00:12:13,020 --> 00:12:14,410
research topic.

250
00:12:14,410 --> 00:12:16,950
In fact, there are a couple
of people already asking me

251
00:12:16,950 --> 00:12:20,830
if they can do something related
to their current research.

252
00:12:20,830 --> 00:12:23,310
And that's perfectly fine,
but you have to sell it,

253
00:12:23,310 --> 00:12:25,890
because this is a
team project, right?

254
00:12:25,890 --> 00:12:28,410
So if you want to do something
related to you research,

255
00:12:28,410 --> 00:12:31,100
you need to recruit
two, three, four,

256
00:12:31,100 --> 00:12:33,810
other colleagues from the class
and form a team around it.

257
00:12:33,810 --> 00:12:34,560
So it's up to you.

258
00:12:34,560 --> 00:12:38,160
And I certainly
encourage, actually,

259
00:12:38,160 --> 00:12:42,070
research-related
projects in the class.

260
00:12:42,070 --> 00:12:43,860
So this is only for 710.

261
00:12:43,860 --> 00:12:47,190
If you are enrolled in 701
and would like to be involved

262
00:12:47,190 --> 00:12:52,530
in this, you are welcome
to do it, but to be fair,

263
00:12:52,530 --> 00:12:54,060
you cannot get credit.

264
00:12:54,060 --> 00:12:55,890
However, you can
be undergraduate

265
00:12:55,890 --> 00:12:59,380
and enroll in the graduate
version of the class.

266
00:12:59,380 --> 00:13:01,680
So for example, if
you are planning

267
00:13:01,680 --> 00:13:04,440
to stay on at MIT
for graduate school,

268
00:13:04,440 --> 00:13:06,660
that's not a bad idea,
because the class is H-level,

269
00:13:06,660 --> 00:13:10,470
so it will already count you
towards some of your credits

270
00:13:10,470 --> 00:13:11,280
later.

271
00:13:11,280 --> 00:13:14,225
So anyway, that's something
that we can discuss separately,

272
00:13:14,225 --> 00:13:16,610
if you like.

273
00:13:16,610 --> 00:13:19,538
And finally, the ugly side,
we do have quizzes, and exams,

274
00:13:19,538 --> 00:13:20,330
and all this stuff.

275
00:13:20,330 --> 00:13:21,350
I hate them myself.

276
00:13:21,350 --> 00:13:22,790
I hated them when
I was a student.

277
00:13:22,790 --> 00:13:24,710
But it's a little bit
like the dentist, right?

278
00:13:24,710 --> 00:13:27,920
In You hate it, but
you have to do it.

279
00:13:27,920 --> 00:13:32,030
So this is the distribution
of the quizzes and the final.

280
00:13:34,610 --> 00:13:37,790
One important thing I would
like to emphasize, which is,

281
00:13:37,790 --> 00:13:41,120
I always deliver a small
sermon when I start a class,

282
00:13:41,120 --> 00:13:44,720
and that has to do with
asking the question.

283
00:13:44,720 --> 00:13:48,590
I really think that you get the
most benefit not from listening

284
00:13:48,590 --> 00:13:52,610
to me while I lecture,
especially at 7:00 AM,

285
00:13:52,610 --> 00:13:55,507
you know, when, including
me, you're all sleepy.

286
00:13:55,507 --> 00:13:57,132
And I will be sleepy
in Singapore, too,

287
00:13:57,132 --> 00:13:58,460
because it's going to be late.

288
00:13:58,460 --> 00:14:00,710
Anyway, so you don't get the
most benefit out of that.

289
00:14:00,710 --> 00:14:03,470
You don't get the most benefit
by reading your book alone

290
00:14:03,470 --> 00:14:07,010
at home in your bed and so on.

291
00:14:07,010 --> 00:14:08,840
The most benefit
you get is actually

292
00:14:08,840 --> 00:14:12,800
from participating in
discussions in the classroom--

293
00:14:12,800 --> 00:14:19,310
with your peers, with the
instructors, everybody.

294
00:14:19,310 --> 00:14:23,330
So I would like to encourage you
to not hesitate for any reason

295
00:14:23,330 --> 00:14:24,700
whatsoever.

296
00:14:24,700 --> 00:14:26,540
If there's something
that bothers you,

297
00:14:26,540 --> 00:14:29,060
some question, something
you're not understanding,

298
00:14:29,060 --> 00:14:34,280
something you're uncertain,
or whatever, please do ask.

299
00:14:34,280 --> 00:14:39,050
There's no reason to be shy.

300
00:14:39,050 --> 00:14:45,017
Very often people--
myself included--

301
00:14:45,017 --> 00:14:47,100
if you're in a big audience,
you may be reluctant.

302
00:14:47,100 --> 00:14:51,090
Because you say well, gee, what
if my question is not good,

303
00:14:51,090 --> 00:14:53,460
or what if I embarrass myself?

304
00:14:53,460 --> 00:14:55,620
So there is no such thing, OK?

305
00:14:55,620 --> 00:14:58,710
If a question pops
up in your mind,

306
00:14:58,710 --> 00:15:01,890
the probability is very high
that someone else in the class

307
00:15:01,890 --> 00:15:03,880
has the exact same question.

308
00:15:03,880 --> 00:15:06,960
And this person is
equally shy as you

309
00:15:06,960 --> 00:15:08,700
are to ask that question.

310
00:15:08,700 --> 00:15:10,350
So you do yourself
a favor, and you

311
00:15:10,350 --> 00:15:12,780
do many of your other
classmates a favor,

312
00:15:12,780 --> 00:15:16,620
if you just interrupt me and ask
a question so please do that.

313
00:15:16,620 --> 00:15:21,090
And also, on my side, I will
treat all questions equally,

314
00:15:21,090 --> 00:15:24,450
and I will do my best to
answer every possible question.

315
00:15:24,450 --> 00:15:26,460
Sometimes I might
not answer a question

316
00:15:26,460 --> 00:15:27,910
if I don't know
the answer myself.

317
00:15:27,910 --> 00:15:29,640
This happens very
often in my classes

318
00:15:29,640 --> 00:15:31,530
and, I think, in
everybody's classes.

319
00:15:31,530 --> 00:15:34,012
Always, someone can
come up with a question

320
00:15:34,012 --> 00:15:35,220
that I don't know the answer.

321
00:15:35,220 --> 00:15:38,280
If that happens I'll tell you,
sorry, I'll get back to you

322
00:15:38,280 --> 00:15:40,530
in the next lecture, right?

323
00:15:40,530 --> 00:15:44,640
Anyway I think, it will
take a few lectures.

324
00:15:44,640 --> 00:15:48,110
Usually, in my classes, it takes
a few lectures for the students

325
00:15:48,110 --> 00:15:49,618
to overcome the threshold.

326
00:15:49,618 --> 00:15:51,660
But I think it becomes
very productive, actually,

327
00:15:51,660 --> 00:15:54,670
when you engage in
discussions in the class.

328
00:15:54,670 --> 00:15:57,660
And yeah, don't worry
about falling behind

329
00:15:57,660 --> 00:15:59,160
on the syllabus or anything.

330
00:15:59,160 --> 00:16:01,980
It is much more important
that we learn well what

331
00:16:01,980 --> 00:16:05,320
we do learn than that we
cover a lot of material

332
00:16:05,320 --> 00:16:08,100
and, in the end, nothing
has been left in your minds.

333
00:16:08,100 --> 00:16:10,320
So one of the benefit of
discussions, especially

334
00:16:10,320 --> 00:16:12,940
arguments, if we get into
an argument about something,

335
00:16:12,940 --> 00:16:15,180
then everybody will
remember, right?

336
00:16:15,180 --> 00:16:18,210
Because it's kind of fun to
watch people argue a topic.

337
00:16:18,210 --> 00:16:22,950
So yeah, by all means,
please interrupt and ask.

338
00:16:22,950 --> 00:16:26,040
And we don't have recitations,
but as you noticed,

339
00:16:26,040 --> 00:16:28,800
the class has a slightly
unusual schedule.

340
00:16:28,800 --> 00:16:30,840
You have a two-hour
lecture on Wednesday

341
00:16:30,840 --> 00:16:32,910
and one hour on Monday.

342
00:16:32,910 --> 00:16:36,510
So we'll structure the syllabus
so that most of the material

343
00:16:36,510 --> 00:16:41,190
is covered on Wednesday and most
of the examples, and practice,

344
00:16:41,190 --> 00:16:44,460
and so on, they
happen on Mondays.

345
00:16:44,460 --> 00:16:47,790
So this is how we deal
with the recitation issue.

346
00:16:47,790 --> 00:16:50,250
And, of course, there's
also the office hours.

347
00:16:50,250 --> 00:17:00,050
And-- oh, yeah,
and sometimes, we

348
00:17:00,050 --> 00:17:02,930
cover some mathematical
topics that some of you

349
00:17:02,930 --> 00:17:07,790
may have forgotten or may
not be very up to speed with,

350
00:17:07,790 --> 00:17:09,770
especially Fourier transforms.

351
00:17:09,770 --> 00:17:15,310
So when the time comes, we
might do a special lecture

352
00:17:15,310 --> 00:17:17,790
in the evening, MIT time.

353
00:17:17,790 --> 00:17:19,700
And if we need to do
that in Singapore,

354
00:17:19,700 --> 00:17:22,210
we'll do it, actually,
individually with me,

355
00:17:22,210 --> 00:17:24,290
sort of in my office
or something like that.

356
00:17:24,290 --> 00:17:25,790
Those of you at
MIT, you'll probably

357
00:17:25,790 --> 00:17:30,680
do it with Se Baek or Pepe, come
back one evening after 7:00 PM,

358
00:17:30,680 --> 00:17:35,578
so we obey Institute policies,
and do a math review.

359
00:17:35,578 --> 00:17:37,620
So this may happen once
or twice in the semester,

360
00:17:37,620 --> 00:17:39,980
especially when it comes
to Fourier transforms.

361
00:17:39,980 --> 00:17:43,700
Because my experience.

362
00:17:43,700 --> 00:17:46,100
You need the
logistics of Fourier

363
00:17:46,100 --> 00:17:49,010
transforms in order to
follow a significant fraction

364
00:17:49,010 --> 00:17:50,190
of the class.

365
00:17:50,190 --> 00:17:55,750
So if you are not really up to
speed with your basic Fourier

366
00:17:55,750 --> 00:18:01,480
from wherever you learned things
18.03 or 2.671, and so on,

367
00:18:01,480 --> 00:18:02,550
we'll do that for you.

368
00:18:05,200 --> 00:18:11,150
OK, this is a list of topics
that we'll cover in the class.

369
00:18:11,150 --> 00:18:12,970
You can browse them
in the website.

370
00:18:12,970 --> 00:18:15,590
I will not go through
each topic now,

371
00:18:15,590 --> 00:18:18,640
because I don't want
to give it away.

372
00:18:18,640 --> 00:18:22,060
I want to leave an
element of surprise.

373
00:18:22,060 --> 00:18:25,270
But basically, the class is
divided into geometrical optics

374
00:18:25,270 --> 00:18:27,250
and wave optics.

375
00:18:27,250 --> 00:18:32,570
And we'll start with geometrical
optics for about four weeks,

376
00:18:32,570 --> 00:18:35,270
and then we'll move
to wave optics.

377
00:18:35,270 --> 00:18:38,050
So the difference, it really
has to do with approximations

378
00:18:38,050 --> 00:18:42,703
of when we deal with
light phenomena,

379
00:18:42,703 --> 00:18:44,120
it's actually very
complicated how

380
00:18:44,120 --> 00:18:47,000
light interacts with matter,
and how it propagates, and so.

381
00:18:47,000 --> 00:18:49,640
It is really a
horrendous problem.

382
00:18:49,640 --> 00:18:51,950
But over the years--
over the centuries,

383
00:18:51,950 --> 00:18:55,030
actually-- people have come up
with different approximations

384
00:18:55,030 --> 00:18:56,800
of progressive accuracy.

385
00:18:56,800 --> 00:18:59,330
So geometrical optics is
the simplest approximation

386
00:18:59,330 --> 00:19:03,170
that gives you very simple
formulas, very simple math,

387
00:19:03,170 --> 00:19:07,280
and actually describes light
quite well up to a point.

388
00:19:07,280 --> 00:19:09,710
So we'll do that
first, and then we'll

389
00:19:09,710 --> 00:19:13,160
graduate to wave optics,
which is a little bit more

390
00:19:13,160 --> 00:19:15,800
involved mathematically,
but it also

391
00:19:15,800 --> 00:19:21,380
gives better approximations
about the propagation of light.

392
00:19:21,380 --> 00:19:24,750
And then, finally, in
the very last few--

393
00:19:24,750 --> 00:19:27,590
probably in the last lecture,
and only if we have time--

394
00:19:27,590 --> 00:19:31,070
we'll cover a topic called
sub-wavelength optics, which is

395
00:19:31,070 --> 00:19:32,510
an even better approximation.

396
00:19:32,510 --> 00:19:37,790
But that is actually pretty much
impossible to do analytically.

397
00:19:37,790 --> 00:19:39,890
So one has to go onto
a computer and do

398
00:19:39,890 --> 00:19:44,090
numerical solution of a nasty
set of coupled differential

399
00:19:44,090 --> 00:19:45,000
equations.

400
00:19:45,000 --> 00:19:48,230
So we'll do that not in
the computational way,

401
00:19:48,230 --> 00:19:50,840
but we'll cover some of
the related phenomena

402
00:19:50,840 --> 00:19:54,170
and what this
approximation gives.

403
00:19:54,170 --> 00:19:57,650
But roughly, anyway, the
class is structured according

404
00:19:57,650 --> 00:20:01,490
to these approximations.

405
00:20:01,490 --> 00:20:03,020
Any questions so far?

406
00:20:14,700 --> 00:20:17,910
And if think of a question, you
can also interrupt me, right?

407
00:20:17,910 --> 00:20:18,998
You're always welcome.

408
00:20:18,998 --> 00:20:20,040
Well, and one more thing.

409
00:20:20,040 --> 00:20:22,560
Yes, I'll tell you the one
more thing, perhaps, later.

410
00:20:26,810 --> 00:20:29,798
Let me start with a
little bit of history.

411
00:20:29,798 --> 00:20:31,840
This, of course, is not
the subject of the class,

412
00:20:31,840 --> 00:20:33,790
but it's kind of fun to do.

413
00:20:33,790 --> 00:20:37,320
I used to start my classes with
a joke that not everybody got.

414
00:20:37,320 --> 00:20:40,090
I used to start by
saying that optics

415
00:20:40,090 --> 00:20:41,800
is the most ancient science.

416
00:20:41,800 --> 00:20:43,240
Not the most
ancient profession--

417
00:20:43,240 --> 00:20:44,480
that's something else--

418
00:20:44,480 --> 00:20:45,820
but is the most ancient science.

419
00:20:48,830 --> 00:20:52,420
And I think the reason
is because humans

420
00:20:52,420 --> 00:20:55,330
are very visual animals.

421
00:20:55,330 --> 00:21:00,160
Our vision, for those of us who
are lucky enough to have it,

422
00:21:00,160 --> 00:21:03,460
our vision is one of them
most dominant census.

423
00:21:03,460 --> 00:21:07,240
So people got interested in
phenomena involving light

424
00:21:07,240 --> 00:21:11,440
relatively early on
in the early ages.

425
00:21:11,440 --> 00:21:13,870
And this probably happened
across civilizations--

426
00:21:13,870 --> 00:21:19,340
Chinese, Egyptian,
Western Greek, and so on.

427
00:21:19,340 --> 00:21:22,960
But as it happens, the Greeks
were the only ones to publish.

428
00:21:22,960 --> 00:21:25,510
They were open about what
they were discovering.

429
00:21:25,510 --> 00:21:28,060
The Egyptians and the
Chinese, the priests

430
00:21:28,060 --> 00:21:30,690
kept everything under control.

431
00:21:30,690 --> 00:21:32,440
So we don't know much
about what they did.

432
00:21:32,440 --> 00:21:35,560
But from what we've
discovered, archaeologists

433
00:21:35,560 --> 00:21:38,710
have discovered in ancient
tombs and so on, they also

434
00:21:38,710 --> 00:21:39,940
knew quite a bit about light.

435
00:21:43,630 --> 00:21:46,300
Of course, the Greeks
made the major mistake--

436
00:21:46,300 --> 00:21:49,570
so Greek science
was very interesting

437
00:21:49,570 --> 00:21:52,730
because it was the flip
side of modern science.

438
00:21:52,730 --> 00:22:01,570
The Greeks had the attitude
that you can understand nature

439
00:22:01,570 --> 00:22:03,970
just by thinking.

440
00:22:03,970 --> 00:22:07,950
So the Greeks actually
discouraged experiment.

441
00:22:07,950 --> 00:22:12,450
Strangely enough, this tradition
has followed the Greek psyche,

442
00:22:12,450 --> 00:22:13,950
because if you
look at the faculty

443
00:22:13,950 --> 00:22:16,110
in the mechanical
engineering department,

444
00:22:16,110 --> 00:22:21,030
there's a lot of Greeks, or
professors of Greek origin,

445
00:22:21,030 --> 00:22:22,870
and lots of them
are theoreticians.

446
00:22:22,870 --> 00:22:25,590
Anyway, I'm just joking.

447
00:22:25,590 --> 00:22:27,480
But anyway, the
ancient Greeks, they

448
00:22:27,480 --> 00:22:30,110
have this attitude that you
don't need to do experiment.

449
00:22:30,110 --> 00:22:32,070
In fact, you must
not do experiment.

450
00:22:32,070 --> 00:22:36,790
You have to understand
everything by thought.

451
00:22:36,790 --> 00:22:39,383
So because of that, they came
up with some strange ideas.

452
00:22:39,383 --> 00:22:41,050
So for example, the
Greeks, they thought

453
00:22:41,050 --> 00:22:46,210
that when you look at something,
your eyes emit some substance,

454
00:22:46,210 --> 00:22:49,090
which they called simulacra.

455
00:22:49,090 --> 00:22:54,940
And this absence is their
thought of what light is.

456
00:22:54,940 --> 00:22:57,610
So I look at you, I
transmit a substance.

457
00:22:57,610 --> 00:23:00,610
The substance comes back to
me, and that's how I see you.

458
00:23:00,610 --> 00:23:02,930
Which is, of course, a
very bizarre, bizarre way

459
00:23:02,930 --> 00:23:03,430
of thinking.

460
00:23:03,430 --> 00:23:05,500
But anyway, that's
what they thought.

461
00:23:05,500 --> 00:23:11,050
And it was the Arabs, much
later in the 10th century or so,

462
00:23:11,050 --> 00:23:13,917
who read the Greek script.

463
00:23:13,917 --> 00:23:16,250
And they said, well, that
doesn't make any sense at all.

464
00:23:16,250 --> 00:23:17,625
So the Arabs, for
the first time,

465
00:23:17,625 --> 00:23:19,840
thought, well, it must
be the other way around.

466
00:23:19,840 --> 00:23:23,620
There must be light sources,
like the sun, or a fire, or--

467
00:23:23,620 --> 00:23:24,900
that's about it at the time.

468
00:23:24,900 --> 00:23:28,090
They didn't have
light bulbs yet.

469
00:23:28,090 --> 00:23:32,590
So it must be that they emit
something that is called light,

470
00:23:32,590 --> 00:23:34,156
and that's how we see.

471
00:23:34,156 --> 00:23:36,920
So it took us about
1,000 years, I guess,

472
00:23:36,920 --> 00:23:40,520
to resolve that question.

473
00:23:40,520 --> 00:23:44,100
And also, the Arabs did a lot
of the very first basic work

474
00:23:44,100 --> 00:23:44,600
in optics.

475
00:23:44,600 --> 00:23:47,810
For example, Snell's Law,
the law of refraction

476
00:23:47,810 --> 00:23:50,030
that I will cover
in a little bit,

477
00:23:50,030 --> 00:23:53,740
the Arabs discovered it first.

478
00:23:53,740 --> 00:23:59,470
And then, much later,
another 400 years later,

479
00:23:59,470 --> 00:24:03,010
Descartes, he did two things.

480
00:24:03,010 --> 00:24:06,110
He put the basic
foundations of science--

481
00:24:06,110 --> 00:24:11,300
Descartes, you may
know this, Descartes

482
00:24:11,300 --> 00:24:14,000
was the first
philosopher, I should say,

483
00:24:14,000 --> 00:24:16,890
who flipped the
Greek point of view.

484
00:24:16,890 --> 00:24:19,160
And he said that it's
actually the other way around.

485
00:24:19,160 --> 00:24:22,070
Science must follow experiment.

486
00:24:22,070 --> 00:24:24,800
Instead of just thinking about
nature and explaining it,

487
00:24:24,800 --> 00:24:26,570
he said that it's the
other way around--

488
00:24:26,570 --> 00:24:29,000
science must be
driven by observation.

489
00:24:29,000 --> 00:24:32,060
So we observe something, we
create experimental conditions

490
00:24:32,060 --> 00:24:36,080
to test it, and then we
come up with a theory

491
00:24:36,080 --> 00:24:39,050
that tries to explain the
observation-- not the other way

492
00:24:39,050 --> 00:24:39,750
around.

493
00:24:39,750 --> 00:24:46,067
And of course, modern science
still follows that principle.

494
00:24:46,067 --> 00:24:47,150
At least hopefully, right?

495
00:24:47,150 --> 00:24:49,910
Because there have
been occasions

496
00:24:49,910 --> 00:24:51,560
of cheating and so on.

497
00:24:51,560 --> 00:24:54,170
You probably see
those in newspapers.

498
00:24:54,170 --> 00:24:56,060
I think there was
a guy who invented,

499
00:24:56,060 --> 00:24:58,930
who sort of created
data at HP Labs.

500
00:24:58,930 --> 00:25:01,180
Was it HP Labs?

501
00:25:01,180 --> 00:25:03,730
Anyway, so there are some
people who violated principle.

502
00:25:03,730 --> 00:25:07,500
But hopefully, 99.9999%
of us will actually

503
00:25:07,500 --> 00:25:08,500
follow Descartes, right?

504
00:25:08,500 --> 00:25:12,820
We make an observation,
we report it faithfully,

505
00:25:12,820 --> 00:25:15,440
and then we try to explain
it to the best we can

506
00:25:15,440 --> 00:25:17,020
and in the simplest
way that we can.

507
00:25:17,020 --> 00:25:21,290
That's the scientific method.

508
00:25:21,290 --> 00:25:23,650
But also, Descartes, as it
turns out, worked on optics.

509
00:25:23,650 --> 00:25:27,370
And he also derived
Snell's Law in his own way.

510
00:25:27,370 --> 00:25:30,550
And there's something called
the Descartes Sphere, which

511
00:25:30,550 --> 00:25:32,650
was invented
independently by the Arabs

512
00:25:32,650 --> 00:25:35,260
in the 11th century
or 12th, I forget--

513
00:25:35,260 --> 00:25:41,050
Ninth, actually--
and then Descartes

514
00:25:41,050 --> 00:25:46,710
reinvented it about
400 or 500 years later.

515
00:25:46,710 --> 00:25:49,635
Then, the next major advance
in optics came from Newton--

516
00:25:52,530 --> 00:25:54,720
actually, Newton and
Huygens, who tried to explain

517
00:25:54,720 --> 00:25:56,790
light in two different ways.

518
00:25:56,790 --> 00:25:58,650
Newton was of the
opinion that light

519
00:25:58,650 --> 00:26:02,970
is a bunch of particles
that travel in air.

520
00:26:02,970 --> 00:26:07,890
And he tried to explain various
phenomena like refraction

521
00:26:07,890 --> 00:26:11,790
from a prism, and so
on, based on this idea.

522
00:26:11,790 --> 00:26:13,830
Huygens thought that
light is a wave very

523
00:26:13,830 --> 00:26:15,380
similar to water waves.

524
00:26:15,380 --> 00:26:16,690
They did not know about--

525
00:26:16,690 --> 00:26:21,042
I believe Newton also
postulated that sound is a wave.

526
00:26:21,042 --> 00:26:22,500
But for some reason,
Newton thought

527
00:26:22,500 --> 00:26:24,550
that light is not a wave.

528
00:26:24,550 --> 00:26:25,950
In fact, the two of them fought.

529
00:26:25,950 --> 00:26:30,780
I don't know if the fought over
it, but they disagreed over it.

530
00:26:30,780 --> 00:26:33,960
But I guess because
Newton was more famous--

531
00:26:33,960 --> 00:26:39,090
he was a professor, a Lucasian
professor at Cambridge--

532
00:26:39,090 --> 00:26:43,060
so Newton's view
actually prevailed

533
00:26:43,060 --> 00:26:46,470
for several years, prevailed.

534
00:26:46,470 --> 00:26:49,080
And the particle
theory of light was

535
00:26:49,080 --> 00:26:52,590
dominant until about
a century later

536
00:26:52,590 --> 00:26:55,410
when people experimentally--

537
00:26:55,410 --> 00:26:57,540
again, here comes the
scientific method--

538
00:26:57,540 --> 00:27:01,620
people experimentally observed
phenomena like interference

539
00:27:01,620 --> 00:27:06,900
that would only be described
if light were a wave.

540
00:27:06,900 --> 00:27:09,240
So the particle theory
got a big hit then,

541
00:27:09,240 --> 00:27:13,290
because it could not explain
diffraction, interference,

542
00:27:13,290 --> 00:27:14,370
and so on, and so forth.

543
00:27:14,370 --> 00:27:17,760
But yet, people were observing
them in the laboratory.

544
00:27:17,760 --> 00:27:20,620
Of course, now, after
one more century, people

545
00:27:20,620 --> 00:27:22,230
discovered that, guess what?

546
00:27:22,230 --> 00:27:23,790
Both theories are correct.

547
00:27:23,790 --> 00:27:26,520
With quantum mechanics,
light can be thought of as

548
00:27:26,520 --> 00:27:29,490
both as particle and as a wave.

549
00:27:29,490 --> 00:27:32,640
And in fact, Einstein and
some other scientists--

550
00:27:32,640 --> 00:27:34,480
Schrodinger, Planck, and so on--

551
00:27:34,480 --> 00:27:39,520
they reconciled the
two points of view.

552
00:27:39,520 --> 00:27:41,940
Not perfectly-- there
still some puzzling aspects

553
00:27:41,940 --> 00:27:44,770
of the quantum theory of light.

554
00:27:44,770 --> 00:27:46,330
But I think
nowadays, most people

555
00:27:46,330 --> 00:27:48,010
are comfortable with
the idea that you

556
00:27:48,010 --> 00:27:51,940
can use both approaches to
describe light phenomena.

557
00:27:51,940 --> 00:27:54,340
You simply select
the ones that best

558
00:27:54,340 --> 00:27:57,670
suits your approximations
and your conditions

559
00:27:57,670 --> 00:27:58,970
at any given moment.

560
00:27:58,970 --> 00:28:01,420
So for example, if
a particle approach

561
00:28:01,420 --> 00:28:04,730
is sufficient to describe the
phenomenon, then you use it.

562
00:28:04,730 --> 00:28:07,570
And of course, there's also,
typically-- or, not typically,

563
00:28:07,570 --> 00:28:09,730
always--

564
00:28:09,730 --> 00:28:10,660
let me restate.

565
00:28:10,660 --> 00:28:15,100
There had better be an
equivalent wave description

566
00:28:15,100 --> 00:28:17,620
of whatever phenomenon
you're describing,

567
00:28:17,620 --> 00:28:19,320
but it may be more
complicated, right?

568
00:28:19,320 --> 00:28:21,980
So in that case, you
use particle theory.

569
00:28:21,980 --> 00:28:22,980
Or the other way around.

570
00:28:22,980 --> 00:28:26,410
If it is easier to describe
something as a wave,

571
00:28:26,410 --> 00:28:30,513
you opt for the
wave description.

572
00:28:30,513 --> 00:28:32,930
So of course, in this class,
we don't cover quantum optics

573
00:28:32,930 --> 00:28:33,430
at all.

574
00:28:33,430 --> 00:28:36,050
Professor Shapiro in the
electrical engineering

575
00:28:36,050 --> 00:28:39,110
department offers a
class in quantum optics.

576
00:28:39,110 --> 00:28:41,630
And I suppose that there
is also a quantum optics

577
00:28:41,630 --> 00:28:45,080
glass for those of you
who are interested.

578
00:28:45,080 --> 00:28:46,250
It's a very elegant topic.

579
00:28:49,050 --> 00:28:54,260
So the other major
advance in optics

580
00:28:54,260 --> 00:28:58,700
came in the middle
of the last century,

581
00:28:58,700 --> 00:29:04,160
when the laser was
invented and the technique

582
00:29:04,160 --> 00:29:07,780
called holography called
holographic was invented.

583
00:29:07,780 --> 00:29:11,420
Not because holography is
somehow dominant in practice.

584
00:29:11,420 --> 00:29:14,345
I mean, you see holograms
typically in museums.

585
00:29:14,345 --> 00:29:15,640
It's no big deal.

586
00:29:15,640 --> 00:29:18,530
But holography turned out
to be a very interesting

587
00:29:18,530 --> 00:29:21,800
mathematical way of
looking at optics.

588
00:29:21,800 --> 00:29:23,510
Now, that really
had a major impact

589
00:29:23,510 --> 00:29:28,520
in the subsequent development
of optical science.

590
00:29:28,520 --> 00:29:30,800
So for this reason,
both of these inventions

591
00:29:30,800 --> 00:29:33,260
led to Nobel prizes.

592
00:29:33,260 --> 00:29:37,320
They were very major advances
in the field of light.

593
00:29:37,320 --> 00:29:43,150
And especially after the
invention of the laser,

594
00:29:43,150 --> 00:29:45,460
optical science
had a huge impact

595
00:29:45,460 --> 00:29:46,630
on everyday applications.

596
00:29:46,630 --> 00:29:48,070
If you think about
devices you use

597
00:29:48,070 --> 00:29:52,750
in your everyday life, every
time you pick up a telephone

598
00:29:52,750 --> 00:29:56,262
or you use the internet,
there's typically-- especially

599
00:29:56,262 --> 00:29:58,720
if you use it long-distance--
there's some optics involved.

600
00:29:58,720 --> 00:30:03,040
Because the signals propagate
through optical fibers,

601
00:30:03,040 --> 00:30:08,530
at least in part of the
telecommunications network.

602
00:30:08,530 --> 00:30:10,950
If you're unlucky
enough to have surgery,

603
00:30:10,950 --> 00:30:14,560
there's many kinds
of laser surgery.

604
00:30:14,560 --> 00:30:17,470
Lots of clinical
medical diagnosis

605
00:30:17,470 --> 00:30:19,840
is done using
high-end microscopes,

606
00:30:19,840 --> 00:30:22,840
including confocal microscopes,
optical coherence tomographers,

607
00:30:22,840 --> 00:30:23,920
and so on, and so forth.

608
00:30:23,920 --> 00:30:26,700
These are all
commercial instruments.

609
00:30:26,700 --> 00:30:28,620
There's applications
in industry--

610
00:30:28,620 --> 00:30:32,820
for example, laser cutting,
laser welding, laser metrology

611
00:30:32,820 --> 00:30:39,990
that is used in high-end
precision engineering

612
00:30:39,990 --> 00:30:41,010
applications.

613
00:30:41,010 --> 00:30:44,040
And of course, finally, every
time you pick up a computer,

614
00:30:44,040 --> 00:30:47,520
the chips that are all made
using optical lithography,

615
00:30:47,520 --> 00:30:52,590
which is a really highly
sophisticated form of optical

616
00:30:52,590 --> 00:30:53,580
imagine.

617
00:30:53,580 --> 00:30:57,000
And I use the term "optical"
here in a very general way.

618
00:30:57,000 --> 00:30:58,440
Most of it is really optical.

619
00:30:58,440 --> 00:30:59,670
We use light.

620
00:30:59,670 --> 00:31:02,430
In some really extreme,
high-end applications,

621
00:31:02,430 --> 00:31:04,290
they use electron lithography.

622
00:31:04,290 --> 00:31:08,940
But still electrons, behave like
light when it comes to this,

623
00:31:08,940 --> 00:31:10,500
to this scale.

624
00:31:10,500 --> 00:31:14,740
So basically, the same equations
that we use to describe light,

625
00:31:14,740 --> 00:31:19,050
they use them to describe
imaging by electrons.

626
00:31:19,050 --> 00:31:26,930
So that is really a huge, huge,
huge domain of application.

627
00:31:26,930 --> 00:31:30,450
It still remains a very
active scientific field.

628
00:31:30,450 --> 00:31:32,340
So if you look at the
list of Nobel Prizes--

629
00:31:32,340 --> 00:31:36,080
this is a very incomplete list
that I compiled from the Nobel

630
00:31:36,080 --> 00:31:37,970
website--

631
00:31:37,970 --> 00:31:42,320
even that latest Nobel
Prize that was awarded--

632
00:31:42,320 --> 00:31:45,740
in chemistry, actually; it
was in the field of optics--

633
00:31:45,740 --> 00:31:49,010
these fellows, they
invented something,

634
00:31:49,010 --> 00:31:53,675
green fluorescent
protein, which is--

635
00:31:53,675 --> 00:31:55,880
I may embarrass myself
now, because I don't

636
00:31:55,880 --> 00:31:57,200
understand the biology of it,

637
00:31:57,200 --> 00:32:00,020
But my very simple
understanding is

638
00:32:00,020 --> 00:32:03,920
that they can genetically
program this protein

639
00:32:03,920 --> 00:32:07,020
to get into some animals' DNA.

640
00:32:07,020 --> 00:32:10,430
So they basically create animals
that have this protein embedded

641
00:32:10,430 --> 00:32:13,340
in their genes, and
then these proteins

642
00:32:13,340 --> 00:32:18,655
can also be designed to turn
itself on or off depending

643
00:32:18,655 --> 00:32:19,780
on happens with the animal.

644
00:32:19,780 --> 00:32:22,610
For example, if the animal
is exposed to a disease,

645
00:32:22,610 --> 00:32:25,550
or if it is exposed to a
certain chemical agent,

646
00:32:25,550 --> 00:32:28,100
or anyway, whatever
is of interest

647
00:32:28,100 --> 00:32:31,790
to the particular
biological experiment,

648
00:32:31,790 --> 00:32:35,330
it sounds kind of funny, but
the animal becomes fluorescent.

649
00:32:35,330 --> 00:32:38,330
Or more interestingly,
certain parts

650
00:32:38,330 --> 00:32:40,110
of the tissue of the
animal-- for example,

651
00:32:40,110 --> 00:32:44,510
the liver, or some tissue of
interest-- becomes fluorescent.

652
00:32:44,510 --> 00:32:48,230
So then you can pump the
animal with a laser beam,

653
00:32:48,230 --> 00:32:50,660
you can measure the
fluorescence that is coming out

654
00:32:50,660 --> 00:32:52,670
of the animal's
tissue, and then you

655
00:32:52,670 --> 00:32:55,940
can derive conclusions about
what happened to the animal.

656
00:32:55,940 --> 00:33:00,830
So this is a fantastic way of
studying genetics, studying

657
00:33:00,830 --> 00:33:05,960
diseases, studying a number of
different and very important

658
00:33:05,960 --> 00:33:07,400
biological phenomena.

659
00:33:07,400 --> 00:33:08,780
So for that reason,
these fellows

660
00:33:08,780 --> 00:33:11,810
were awarded the Nobel Prize.

661
00:33:11,810 --> 00:33:14,600
And actually, many
people, including myself--

662
00:33:14,600 --> 00:33:19,210
at least not yet, but I'm
sure in Colin's lab, already,

663
00:33:19,210 --> 00:33:24,860
we'll use animals
that are genetically

664
00:33:24,860 --> 00:33:25,940
modified with this--

665
00:33:25,940 --> 00:33:28,700
It's called GFC, green
fluorescent protein--

666
00:33:28,700 --> 00:33:30,980
to study various
biological phenomena.

667
00:33:30,980 --> 00:33:34,550
Now it is a very commonly
used technique in microscopy.

668
00:33:34,550 --> 00:33:38,780
So this was the most recent
optics-related Nobel Prize.

669
00:33:38,780 --> 00:33:41,810
There's a bunch of others.

670
00:33:41,810 --> 00:33:43,825
My favorite is actually--

671
00:33:43,825 --> 00:33:44,900
where is it?

672
00:33:44,900 --> 00:33:46,430
This one.

673
00:33:46,430 --> 00:33:51,010
In 1997, this was a
given for optical traps.

674
00:33:51,010 --> 00:33:52,640
So an optical trap
is actually a way

675
00:33:52,640 --> 00:33:54,860
to move particles
by using light.

676
00:33:54,860 --> 00:33:58,370
It's a very surprising
thing, because none

677
00:33:58,370 --> 00:34:02,210
of us in everyday life will
experience mechanical force

678
00:34:02,210 --> 00:34:03,680
from a light beam.

679
00:34:03,680 --> 00:34:05,027
But in actuality, there is one.

680
00:34:05,027 --> 00:34:06,860
If you are sitting in
the back of the light,

681
00:34:06,860 --> 00:34:08,090
you are feeling the force.

682
00:34:08,090 --> 00:34:09,100
This once is very weak.

683
00:34:09,100 --> 00:34:11,370
It's in the range of
femtonewtons, typically--

684
00:34:11,370 --> 00:34:14,550
a really tiny, tiny force.

685
00:34:14,550 --> 00:34:18,020
But we're also very big, so the
force is not enough to move us.

686
00:34:18,020 --> 00:34:20,300
But if you're really tiny--
like a cell, for example--

687
00:34:20,300 --> 00:34:22,730
the force, especially if
you design the optical right

688
00:34:22,730 --> 00:34:24,860
with a very highly
focused beam, you

689
00:34:24,860 --> 00:34:26,860
can boost that
force to the range

690
00:34:26,860 --> 00:34:28,770
of, perhaps, a few piconewtons.

691
00:34:28,770 --> 00:34:31,010
Not really that's a very
high force, but anyway,

692
00:34:31,010 --> 00:34:32,989
in that order of
magnitude, it can

693
00:34:32,989 --> 00:34:35,690
be enough to actually
move a particle.

694
00:34:35,690 --> 00:34:41,520
So you can make, you can apply
mechanical forces using light.

695
00:34:41,520 --> 00:34:44,719
So this was another Nobel Prize.

696
00:34:44,719 --> 00:34:48,110
So anyway, the reason
I'm bringing this up

697
00:34:48,110 --> 00:34:50,270
is because this is a
very exciting field.

698
00:34:50,270 --> 00:34:52,469
At least-- well, I'm partial,
because I work on it,

699
00:34:52,469 --> 00:34:54,380
but it's a very exciting field.

700
00:34:54,380 --> 00:34:58,970
People come up with clever,
crazy inventions all the time.

701
00:34:58,970 --> 00:35:02,810
And many, many of
these inventions have--

702
00:35:02,810 --> 00:35:05,570
usually, they have
a very high impact.

703
00:35:05,570 --> 00:35:11,450
And so it is interesting to
see both sides of the coin,

704
00:35:11,450 --> 00:35:13,730
both the science
side of the coin

705
00:35:13,730 --> 00:35:16,820
that is purely
curiosity-driven, and very often

706
00:35:16,820 --> 00:35:19,190
people in government
question it,

707
00:35:19,190 --> 00:35:21,410
because they say, well,
why are you guys doing

708
00:35:21,410 --> 00:35:22,940
all this crazy stuff?

709
00:35:22,940 --> 00:35:25,100
Who cares about optical forces?

710
00:35:25,100 --> 00:35:26,900
But of course, these
people are so excited,

711
00:35:26,900 --> 00:35:31,310
because history shows
that most of the time,

712
00:35:31,310 --> 00:35:33,650
these curiosity-driven
discoveries,

713
00:35:33,650 --> 00:35:37,040
they end up having a huge
impact in everyday life.

714
00:35:37,040 --> 00:35:44,540
Some crazy persons-- they
were French, American,

715
00:35:44,540 --> 00:35:46,010
and Chinese-American, right?

716
00:35:46,010 --> 00:35:48,680
Three crazy persons
thought about focusing

717
00:35:48,680 --> 00:35:50,180
light to move particles.

718
00:35:50,180 --> 00:35:53,030
Then, all of a sudden, this
is used in biological research

719
00:35:53,030 --> 00:35:55,940
to try to understand
diseases like malaria.

720
00:35:55,940 --> 00:35:58,470
I don't know if any of Professor
Subra Suresh's students

721
00:35:58,470 --> 00:36:03,410
are here, but one of my
colleagues, Subra Suresh,

722
00:36:03,410 --> 00:36:05,840
studied malaria using
this technique that

723
00:36:05,840 --> 00:36:09,530
won the Nobel Prize in 1997.

724
00:36:09,530 --> 00:36:13,350
So it is our duty as
engineers, or scientists,

725
00:36:13,350 --> 00:36:15,650
or whatever the case
may be to emphasize

726
00:36:15,650 --> 00:36:17,750
to the people in
government and politics

727
00:36:17,750 --> 00:36:21,450
that yes, there is value
in fundamental science

728
00:36:21,450 --> 00:36:23,550
when they bash it
and they say that,

729
00:36:23,550 --> 00:36:27,820
what, you guys are playing
in laboratories, and so on.

730
00:36:27,820 --> 00:36:30,380
OK, so I went onto my tirade.

731
00:36:30,380 --> 00:36:34,288
And any questions?

732
00:36:38,212 --> 00:36:39,170
AUDIENCE: I've got one.

733
00:36:39,170 --> 00:36:40,212
GEORGE BARBASTATHIS: Yes.

734
00:36:40,212 --> 00:36:42,200
AUDIENCE: So I think I'm on.

735
00:36:42,200 --> 00:36:45,015
GEORGE BARBASTATHIS:
Yes, can you hear him?

736
00:36:45,015 --> 00:36:45,560
OK.

737
00:36:45,560 --> 00:36:47,185
AUDIENCE: It says
that you can describe

738
00:36:47,185 --> 00:36:50,640
how an electron beam images
in a similar way as optics.

739
00:36:50,640 --> 00:36:52,500
But electrons
interact with matter.

740
00:36:52,500 --> 00:36:54,428
So how does light
interact with matter?

741
00:36:54,428 --> 00:36:55,470
GEORGE BARBASTATHIS: Yes.

742
00:36:55,470 --> 00:36:56,490
So we will cover that.

743
00:36:56,490 --> 00:36:59,880
Of course, they interact in
very different ways, right?

744
00:36:59,880 --> 00:37:03,920
The fundamental difference is
that electrons are fermions,

745
00:37:03,920 --> 00:37:09,400
so they cannot really
be in the same state.

746
00:37:09,400 --> 00:37:15,090
Photons are bosons, so they can
actually be in the same state.

747
00:37:15,090 --> 00:37:17,360
So what I really should
have said-- and thank you

748
00:37:17,360 --> 00:37:20,600
for pointing it out--
is that in free space,

749
00:37:20,600 --> 00:37:22,340
they're described by
the same equations.

750
00:37:22,340 --> 00:37:24,380
Of course, when they
get inside matter,

751
00:37:24,380 --> 00:37:27,062
their behavior is
quite different.

752
00:37:27,062 --> 00:37:28,520
But again, for
example, if you look

753
00:37:28,520 --> 00:37:31,220
at the electrons that go
ballistically through matter,

754
00:37:31,220 --> 00:37:34,880
they experience an effect that
is very similar to refraction.

755
00:37:34,880 --> 00:37:36,350
So you can describe--

756
00:37:36,350 --> 00:37:38,550
you still see Snell's
Law, and so on.

757
00:37:38,550 --> 00:37:40,720
But of course, you see
these additional phenomena,

758
00:37:40,720 --> 00:37:44,930
like all the electrons, which
you don't see in light beams.

759
00:37:44,930 --> 00:37:46,100
So you're absolutely right.

760
00:37:46,100 --> 00:37:50,480
There's some
significant differences

761
00:37:50,480 --> 00:37:51,950
which are very important.

762
00:37:51,950 --> 00:37:56,260
But there's also some
very, very dominant

763
00:37:56,260 --> 00:37:57,970
and prominent commonalities.

764
00:37:57,970 --> 00:38:00,100
The same goes for
light and sound.

765
00:38:00,100 --> 00:38:06,585
And our department recently
merged with ocean engineering.

766
00:38:06,585 --> 00:38:07,960
And in ocean
engineering, there's

767
00:38:07,960 --> 00:38:10,270
a lot of professors
who do acoustics.

768
00:38:10,270 --> 00:38:12,620
So as a result, I
started sitting in--

769
00:38:12,620 --> 00:38:14,110
at the beginning,
out of curiosity,

770
00:38:14,110 --> 00:38:16,360
I started sitting in a couple
of the acoustic classes.

771
00:38:16,360 --> 00:38:21,580
And also, this year, I sat in
the doctoral exam in acoustics.

772
00:38:21,580 --> 00:38:23,730
And I was surprised to
see the same terms--

773
00:38:23,730 --> 00:38:28,420
diffraction, refraction,
Snell's law, waveguiding,

774
00:38:28,420 --> 00:38:31,000
all of these things, they
happen in acoustics as well.

775
00:38:31,000 --> 00:38:33,220
So you could say the
same thing about sound.

776
00:38:33,220 --> 00:38:36,130
To some approximation,
sound effects

777
00:38:36,130 --> 00:38:40,120
are identical to optics,
identical to light diffraction.

778
00:38:40,120 --> 00:38:43,120
But there's also cases of
interaction between sound

779
00:38:43,120 --> 00:38:46,120
and matter that is radically
different than interaction

780
00:38:46,120 --> 00:38:47,710
between light and matter.

781
00:38:47,710 --> 00:38:50,535
For example, I think it
is impossible for sound

782
00:38:50,535 --> 00:38:52,000
to ionize matter.

783
00:38:52,000 --> 00:38:53,650
Light can ionize matter.

784
00:38:53,650 --> 00:38:57,460
I think sound has to be pretty
darn strong to ionize, right?

785
00:38:57,460 --> 00:39:02,230
So there are significant
differences, but also some very

786
00:39:02,230 --> 00:39:03,690
convenient commonalities.

787
00:39:03,690 --> 00:39:06,800
So all of a sudden, by studying
one field, all of a sudden,

788
00:39:06,800 --> 00:39:09,100
you discover that you can
understand quite a bit

789
00:39:09,100 --> 00:39:10,608
about a different field.

790
00:39:10,608 --> 00:39:11,650
So that's kind of useful.

791
00:39:14,480 --> 00:39:15,765
Any other questions?

792
00:39:22,900 --> 00:39:27,960
Let's start by saying a few
things about what is light.

793
00:39:27,960 --> 00:39:30,260
So light is actually
a form of energy.

794
00:39:30,260 --> 00:39:34,235
Really that's the simplest--
that's the only correct way

795
00:39:34,235 --> 00:39:35,450
to describe it.

796
00:39:35,450 --> 00:39:37,820
It is a form of energy
that is transmitted

797
00:39:37,820 --> 00:39:40,160
as an electromagnetic wave.

798
00:39:40,160 --> 00:39:43,170
That's a quite
correct description.

799
00:39:43,170 --> 00:39:46,490
But as I said before, you can
think of it either as particles

800
00:39:46,490 --> 00:39:48,360
or as waves.

801
00:39:48,360 --> 00:39:53,220
So the particles are
officially called photons.

802
00:39:53,220 --> 00:39:58,940
And what is a photon is actually
not an easy thing to describe.

803
00:39:58,940 --> 00:40:01,070
Various scientists
over the centuries

804
00:40:01,070 --> 00:40:03,860
fought over the
definition of a photon.

805
00:40:03,860 --> 00:40:05,930
And we certainly don't
want to go into quantum

806
00:40:05,930 --> 00:40:07,880
optics in this class.

807
00:40:07,880 --> 00:40:11,150
So we'll think of photons
in a very simple-minded way,

808
00:40:11,150 --> 00:40:14,120
as bullets that carry energy--

809
00:40:14,120 --> 00:40:20,630
a very small amount of energy,
as we'll see in a second--

810
00:40:20,630 --> 00:40:25,020
and they follow
certain trajectories.

811
00:40:25,020 --> 00:40:27,860
So the trajectories
we'll call rays.

812
00:40:27,860 --> 00:40:32,250
And I will describe these
rays a little bit later.

813
00:40:32,250 --> 00:40:36,380
Now, the photon, one thing that
the photons do have in common

814
00:40:36,380 --> 00:40:37,340
is their speed.

815
00:40:37,340 --> 00:40:40,310
It is, of course, the speed
of light, which, in a vacuum,

816
00:40:40,310 --> 00:40:46,080
is the familiar 3 times 10
to the 8 meters per second.

817
00:40:46,080 --> 00:40:48,060
How much energy they carry?

818
00:40:48,060 --> 00:40:53,230
Well, the amount of energy is
given by Planck's constant,

819
00:40:53,230 --> 00:41:00,360
which is a very small amount of
6.6 10 to the minus 34 joules

820
00:41:00,360 --> 00:41:03,920
times second, and then
multiplied by a frequency.

821
00:41:03,920 --> 00:41:06,490
OK, so the frequency
is, of course, hertz.

822
00:41:06,490 --> 00:41:07,710
So the units work out.

823
00:41:07,710 --> 00:41:12,570
The product over
there is energy.

824
00:41:12,570 --> 00:41:13,680
What is the frequency?

825
00:41:13,680 --> 00:41:15,380
Where does it come about?

826
00:41:15,380 --> 00:41:18,900
Well, to really justify the
presence of a frequency there,

827
00:41:18,900 --> 00:41:20,130
I have to see it.

828
00:41:20,130 --> 00:41:22,500
I have to go, actually,
to the other way

829
00:41:22,500 --> 00:41:26,430
of describing light, which is
as an electromagnetic wave.

830
00:41:26,430 --> 00:41:31,200
And of course, the name
"wave" implies some sort

831
00:41:31,200 --> 00:41:34,120
of oscillatory motion.

832
00:41:34,120 --> 00:41:36,420
So the horizontal axis
here is the direction

833
00:41:36,420 --> 00:41:38,050
of the propagation of the light.

834
00:41:38,050 --> 00:41:41,550
So the light is propagating
from the left to the right.

835
00:41:41,550 --> 00:41:43,140
What is the vertical axis?

836
00:41:43,140 --> 00:41:46,050
The vertical axis is an
electric field, actually.

837
00:41:46,050 --> 00:41:48,870
It is the same spot that you
have in a capacitor where

838
00:41:48,870 --> 00:41:50,460
you charge it.

839
00:41:50,460 --> 00:41:53,020
So it is convenient to describe
it as an electric field.

840
00:41:53,020 --> 00:41:55,920
You can also describe
it is a magnetic field--

841
00:41:55,920 --> 00:42:00,690
the same stuff that you see when
you have a refrigerator magnet.

842
00:42:00,690 --> 00:42:03,980
You can put either quantity
over here in the vertical axis

843
00:42:03,980 --> 00:42:07,470
because there are a couple
of electromagnetic fields by,

844
00:42:07,470 --> 00:42:10,500
as the name suggests, it
is a coupled oscillation

845
00:42:10,500 --> 00:42:12,973
of electric and magnetic fields.

846
00:42:12,973 --> 00:42:14,640
For now, let's stick
to electric fields.

847
00:42:14,640 --> 00:42:18,030
In this class, I will say very
little about magnetic fields.

848
00:42:18,030 --> 00:42:22,110
When I describe light as
a wave, I will by default

849
00:42:22,110 --> 00:42:24,960
refer to an electric field, OK?

850
00:42:24,960 --> 00:42:29,270
So light is an electric
field that oscillates

851
00:42:29,270 --> 00:42:31,370
as a function of position.

852
00:42:31,370 --> 00:42:34,870
And of course, a
wave is not static.

853
00:42:34,870 --> 00:42:38,590
You, all of you, have seen
waves in the Singapore

854
00:42:38,590 --> 00:42:40,930
Harbor, the Singapore River.

855
00:42:40,930 --> 00:42:43,510
You cannot see waves on the
Charles right now because it is

856
00:42:43,510 --> 00:42:44,570
frozen.

857
00:42:44,570 --> 00:42:46,630
But during more
normal times, you

858
00:42:46,630 --> 00:42:47,910
can see waves on the Charles.

859
00:42:47,910 --> 00:42:52,660
So you know a wave implies
both a spatial structure--

860
00:42:52,660 --> 00:42:54,430
if you look at the
picture of a wave,

861
00:42:54,430 --> 00:42:58,690
you see oscillatory
in the picture--

862
00:42:58,690 --> 00:43:01,510
but also time, because
a wave travels in time.

863
00:43:01,510 --> 00:43:05,570
So in the context here,
the time valuable--

864
00:43:05,570 --> 00:43:07,540
well, OK, I'll
[INAUDIBLE] that back.

865
00:43:07,540 --> 00:43:09,880
But after some time
lapse, the wave

866
00:43:09,880 --> 00:43:13,270
will actually move a
little bit further, OK?

867
00:43:13,270 --> 00:43:17,080
So this is the sense of
the wave propagation.

868
00:43:17,080 --> 00:43:21,140
So since you have an
oscillatory quantity here,

869
00:43:21,140 --> 00:43:23,920
the period is called
the wavelength--

870
00:43:23,920 --> 00:43:25,900
the period in the space domain.

871
00:43:25,900 --> 00:43:30,820
So the distance between two
peaks of the electric field

872
00:43:30,820 --> 00:43:33,520
oscillator there would
define it as a wavelength.

873
00:43:33,520 --> 00:43:38,260
And it is related to the
frequency, this quantity that

874
00:43:38,260 --> 00:43:41,470
enters in the particle
description of light uses

875
00:43:41,470 --> 00:43:43,030
this equation here.

876
00:43:43,030 --> 00:43:45,040
The speed of light
equals the product

877
00:43:45,040 --> 00:43:48,765
of the wavelength
times the frequency.

878
00:43:48,765 --> 00:43:50,150
So we'll do the
calculation here.

879
00:43:57,625 --> 00:43:59,000
Well, before we
go calculation, I

880
00:43:59,000 --> 00:44:02,740
need to say something
about what is--

881
00:44:02,740 --> 00:44:04,990
I think I did something I
was not supposed to do here.

882
00:44:04,990 --> 00:44:09,760
But anyway, the blackboard
went up by itself.

883
00:44:09,760 --> 00:44:14,460
But this classroom
is highly automated.

884
00:44:14,460 --> 00:44:19,850
So I guess there's some
things that cannot be done.

885
00:44:19,850 --> 00:44:24,340
OK, so what are the
typical wavelengths?

886
00:44:24,340 --> 00:44:28,820
So the electromagnetic spectrum
actually spans all wavelengths

887
00:44:28,820 --> 00:44:33,580
from sort of infinitely
long, or kilometers long,

888
00:44:33,580 --> 00:44:38,270
to very, very short,
down to nanometers.

889
00:44:38,270 --> 00:44:42,560
The visible light, the light
that we see with our own eyes,

890
00:44:42,560 --> 00:44:48,860
is in this range over
here between approximately

891
00:44:48,860 --> 00:44:58,523
650 nanometers or so and
450 nanometers or so.

892
00:44:58,523 --> 00:44:59,440
So what's a nanometer?

893
00:44:59,440 --> 00:45:02,750
It's 10 to the minus 9 meters.

894
00:45:02,750 --> 00:45:04,620
So let's pick a
convenient number here.

895
00:45:04,620 --> 00:45:06,475
Let's say lambda equals--

896
00:45:09,160 --> 00:45:10,640
how about I do this here?

897
00:45:21,200 --> 00:45:24,400
OK, this is the wavelength.

898
00:45:24,400 --> 00:45:27,265
So our other question
is c equals lambda nu.

899
00:45:27,265 --> 00:45:35,580
So it means that nu equals 3
times 10 to the 8 over five

900
00:45:35,580 --> 00:45:38,220
times 10 to the minus 7.

901
00:45:38,220 --> 00:45:45,530
So this is something of the
order of 6 times 10 to the 14--

902
00:45:45,530 --> 00:45:46,470
what?

903
00:45:46,470 --> 00:45:47,570
Hertz, right?

904
00:45:47,570 --> 00:45:51,050
It's a temporal frequency.

905
00:45:51,050 --> 00:45:53,390
So this oscillation
that I showed

906
00:45:53,390 --> 00:45:57,230
before, it's a very
high-frequency oscillation.

907
00:45:57,230 --> 00:45:59,420
is in there in the
order of 10 to the 14

908
00:45:59,420 --> 00:46:03,600
had now we don't listen
to the radio anymore

909
00:46:03,600 --> 00:46:10,870
we listen to you know podcasts
or our satellite and so on.

910
00:46:10,870 --> 00:46:15,970
So we're not very familiar
with radio frequencies.

911
00:46:15,970 --> 00:46:17,950
But I'm old enough to
remember when you tuned

912
00:46:17,950 --> 00:46:22,150
your radio to 104.3 Megahertz.

913
00:46:22,150 --> 00:46:26,390
That happens to be
Boston's WBCN station.

914
00:46:26,390 --> 00:46:31,290
So OK, Boston's WBCN station
emits at 100 megahertz.

915
00:46:31,290 --> 00:46:33,380
It is actually the same stuff--

916
00:46:33,380 --> 00:46:36,590
I'm going to force the machine
to do what I want it to do,

917
00:46:36,590 --> 00:46:38,960
so I'm going to keep this down.

918
00:46:38,960 --> 00:46:42,320
OK, so let's say nu
equals 100 megahertz.

919
00:46:45,470 --> 00:46:50,570
That is 10 to the 8, correct?

920
00:46:50,570 --> 00:46:56,240
So therefore, the
wavelength now is what?

921
00:46:56,240 --> 00:46:58,700
c over the frequency
so it is 3 times

922
00:46:58,700 --> 00:47:08,040
10 to the 8 meters per second
over 10 to the 8 hertz.

923
00:47:08,040 --> 00:47:11,350
So this is now 3 meters.

924
00:47:11,350 --> 00:47:12,650
So it is still the same stuff.

925
00:47:12,650 --> 00:47:16,310
It is still light, if you wish,
but of a much, much longer

926
00:47:16,310 --> 00:47:18,770
wavelength at the
radio frequencies.

927
00:47:18,770 --> 00:47:23,120
So you can see that
electromagnetic waves can span

928
00:47:23,120 --> 00:47:25,850
a very broad range of scales.

929
00:47:25,850 --> 00:47:28,940
In this class, the
wavelengths of interest

930
00:47:28,940 --> 00:47:31,610
are in this range
between the dashed lines

931
00:47:31,610 --> 00:47:34,370
and the infrared,
which nominally

932
00:47:34,370 --> 00:47:38,390
ends at about 10 micrometers,
and the ultraviolet,

933
00:47:38,390 --> 00:47:43,470
which nominally ends
at about 30 nanometers.

934
00:47:43,470 --> 00:47:45,080
Where do the names come from?

935
00:47:45,080 --> 00:47:48,680
"Infra," in Latin,
means "below"--

936
00:47:48,680 --> 00:47:50,000
below red.

937
00:47:50,000 --> 00:47:53,160
So therefore, the term "infra"
refers to what, the frequency

938
00:47:53,160 --> 00:47:54,258
or the wavelength?

939
00:47:59,520 --> 00:48:00,830
The frequency, right?

940
00:48:00,830 --> 00:48:04,770
Infrared has longer
wavelengths than visible,

941
00:48:04,770 --> 00:48:08,490
and therefore it has
smaller frequencies.

942
00:48:08,490 --> 00:48:12,170
So it is below the
red in frequency.

943
00:48:12,170 --> 00:48:15,400
"Ultra," of course, means
higher, also in Latin,

944
00:48:15,400 --> 00:48:19,770
so "ultraviolet" means higher
frequencies than violet light.

945
00:48:19,770 --> 00:48:22,980
Not "violent" light,
but "violet" light.

946
00:48:22,980 --> 00:48:27,740
OK, and the major
difference, if you

947
00:48:27,740 --> 00:48:30,620
look at light
propagation in free space

948
00:48:30,620 --> 00:48:33,890
it doesn't really matter which
wavelength you are considering.

949
00:48:33,890 --> 00:48:35,720
But of course, the
interaction with matter

950
00:48:35,720 --> 00:48:38,900
is radically different as
you change wavelengths.

951
00:48:38,900 --> 00:48:42,500
So it is similar to the question
you asked about electrons.

952
00:48:42,500 --> 00:48:45,680
It is also true for
microwaves, or even

953
00:48:45,680 --> 00:48:47,920
for electromagnetic
waves themselves.

954
00:48:47,920 --> 00:48:51,410
The way visible light
interacts with matter

955
00:48:51,410 --> 00:48:55,730
is very different than
microwaves and RF waves,

956
00:48:55,730 --> 00:48:57,970
and it is also very
different than X-rays.

957
00:48:57,970 --> 00:49:00,920
So X-rays are actually
the next highest

958
00:49:00,920 --> 00:49:06,350
in frequency after ultraviolet,
and even higher in frequency

959
00:49:06,350 --> 00:49:07,460
are gamma rays.

960
00:49:07,460 --> 00:49:10,010
And I guess we stop there.

961
00:49:10,010 --> 00:49:11,680
But actually, we don't stop.

962
00:49:11,680 --> 00:49:13,970
The frequency can go, in
principle, all the way

963
00:49:13,970 --> 00:49:14,570
to infinity.

964
00:49:14,570 --> 00:49:19,070
But the gamma rays is the
highest that we can observe.

965
00:49:19,070 --> 00:49:21,140
Now, I promised to
do a calculation

966
00:49:21,140 --> 00:49:25,850
of the energy-- how much
energy is carried by a photon.

967
00:49:25,850 --> 00:49:29,920
So remember the
formula, equals h nu,

968
00:49:29,920 --> 00:49:35,060
where h is 6.6 times 10 to
the-- remember how much it was,

969
00:49:35,060 --> 00:49:36,880
the exponent?

970
00:49:36,880 --> 00:49:37,600
34, right?

971
00:49:42,800 --> 00:49:48,350
So let's pick one here-- let's
say this one-- which is visible

972
00:49:48,350 --> 00:49:49,610
wavelength.

973
00:49:49,610 --> 00:49:56,500
So it is six times 10 to
the 14 times inverse second.

974
00:49:56,500 --> 00:49:58,460
OK, so these
conveniently cancel.

975
00:49:58,460 --> 00:50:01,670
And 6 times 6 is--

976
00:50:01,670 --> 00:50:04,990
let's call it 10
for convenience.

977
00:50:04,990 --> 00:50:08,030
So it is 10, and this
is 14, of course.

978
00:50:08,030 --> 00:50:10,840
So this is 10 to
the minus 20 joules.

979
00:50:10,840 --> 00:50:13,220
OK, my arithmetic
is, obviously, wrong.

980
00:50:13,220 --> 00:50:18,710
OK, what is the
pedagogical message here?

981
00:50:18,710 --> 00:50:21,470
That when we do order of
magnitude calculations--

982
00:50:21,470 --> 00:50:25,498
6.6 times 6.6 times
equals 10, let's--

983
00:50:25,498 --> 00:50:26,540
actually, I got it wrong.

984
00:50:26,540 --> 00:50:27,945
I should have put "100."

985
00:50:27,945 --> 00:50:30,640
So minus 19.

986
00:50:30,640 --> 00:50:34,460
OK, so just the order
of magnitude, right?

987
00:50:34,460 --> 00:50:37,330
I'm not looking for
the exact answer here.

988
00:50:37,330 --> 00:50:39,060
Actually, it's very interesting.

989
00:50:39,060 --> 00:50:41,450
I did my graduate in Greece.

990
00:50:41,450 --> 00:50:43,500
And over there, the
professors were very careful.

991
00:50:43,500 --> 00:50:47,160
So here, they would have
written 39.6, or whatever

992
00:50:47,160 --> 00:50:48,928
it is-- the actual number.

993
00:50:48,928 --> 00:50:50,720
Then, I went to graduate
school at Caltech.

994
00:50:50,720 --> 00:50:54,970
And I took my first class
in quantum electronics

995
00:50:54,970 --> 00:50:57,020
by a fellow called
Amnom Yariv, who

996
00:50:57,020 --> 00:50:59,300
is pretty well-known
in the field of lasers.

997
00:50:59,300 --> 00:51:00,710
So we walked into
classes, and he

998
00:51:00,710 --> 00:51:03,220
started doing things like
that-- that pi equals 3,

999
00:51:03,220 --> 00:51:05,710
pi squared equals 10.

1000
00:51:05,710 --> 00:51:06,960
And at first, I was horrified.

1001
00:51:06,960 --> 00:51:10,230
But then I realized he had a
point-- that very often, it

1002
00:51:10,230 --> 00:51:13,470
is pointless to do exact
calculations if you're

1003
00:51:13,470 --> 00:51:15,420
looking for an order
of magnitude result.

1004
00:51:15,420 --> 00:51:18,082
For example, is the bullet
going to crash into a wall,

1005
00:51:18,082 --> 00:51:19,290
or is it going to go through?

1006
00:51:19,290 --> 00:51:20,820
Is it going to go back, or what?

1007
00:51:20,820 --> 00:51:22,612
For that, you don't
need the exact numbers.

1008
00:51:22,612 --> 00:51:27,193
Of course, exact numbers are
valuable in some other cases.

1009
00:51:27,193 --> 00:51:28,610
It's kind of an
interesting skill,

1010
00:51:28,610 --> 00:51:31,370
to know when to do
an half-calculation

1011
00:51:31,370 --> 00:51:34,190
and when to do an exact
calculation, and what

1012
00:51:34,190 --> 00:51:36,710
level of accuracy
you need, depending

1013
00:51:36,710 --> 00:51:39,153
on the resources that you
have, the time that you have,

1014
00:51:39,153 --> 00:51:41,320
the nature of the answer
you're looking for, and on,

1015
00:51:41,320 --> 00:51:43,560
and so forth.

1016
00:51:43,560 --> 00:51:47,680
OK, so for our purposes here
for now, 6 times 6 equals 100.

1017
00:51:47,680 --> 00:51:49,470
So we'll get a very
small energy, right?

1018
00:51:49,470 --> 00:51:52,790
It's 10 to the minus 19 joules.

1019
00:51:52,790 --> 00:51:57,710
If you go to higher frequencies,
in the range of X-rays,

1020
00:51:57,710 --> 00:52:02,390
the energy would go up by
a factor of maybe a couple

1021
00:52:02,390 --> 00:52:04,163
of orders of magnitude.

1022
00:52:04,163 --> 00:52:06,080
So in these kinds of
frequencies, of energies,

1023
00:52:06,080 --> 00:52:09,230
if you go up to 10 to the
minus 16 joules or so,

1024
00:52:09,230 --> 00:52:12,110
it becomes comparable with
the ionizing radiation.

1025
00:52:12,110 --> 00:52:16,850
So you see now why light
frequency is very important

1026
00:52:16,850 --> 00:52:19,210
when it comes to
interaction with matter.

1027
00:52:19,210 --> 00:52:21,710
Because visible
light, the photon,

1028
00:52:21,710 --> 00:52:25,190
each photon that impinges
on an atom in a material

1029
00:52:25,190 --> 00:52:27,380
has a relatively low energy.

1030
00:52:27,380 --> 00:52:29,180
It can do something
to the material--

1031
00:52:29,180 --> 00:52:30,530
we'll talk about it later--

1032
00:52:30,530 --> 00:52:31,850
but it cannot ionize it.

1033
00:52:31,850 --> 00:52:33,500
If you increase
the frequency, you

1034
00:52:33,500 --> 00:52:36,080
increase the energy of the
photon, and all of a sudden,

1035
00:52:36,080 --> 00:52:39,860
you can get ionizing effects.

1036
00:52:39,860 --> 00:52:42,140
So these sort of
calculations give you

1037
00:52:42,140 --> 00:52:44,490
an idea of what's going on.

1038
00:52:48,560 --> 00:52:52,610
And of course, if you
conclude the energy carried

1039
00:52:52,610 --> 00:52:57,620
by a microwave photon, it will
be several orders of magnitude

1040
00:52:57,620 --> 00:52:58,120
lower--

1041
00:52:58,120 --> 00:53:01,580
I think something like five
or six orders of magnitude

1042
00:53:01,580 --> 00:53:04,220
smaller.

1043
00:53:04,220 --> 00:53:06,510
OK, any questions about that?

1044
00:53:06,510 --> 00:53:07,680
About photons or--

1045
00:53:14,250 --> 00:53:17,392
Let me say a few things
about wave propagation.

1046
00:53:17,392 --> 00:53:19,850
At the beginning of the class,
we'll do geometrical optics.

1047
00:53:19,850 --> 00:53:22,610
But I want to say a
few things about waves

1048
00:53:22,610 --> 00:53:26,432
that we need before geometrical
optics begins to make sense.

1049
00:53:26,432 --> 00:53:27,890
So the first things
that we learned

1050
00:53:27,890 --> 00:53:29,540
is wavelength and
frequency, right?

1051
00:53:29,540 --> 00:53:34,140
These two things are important
even in geometrical optics.

1052
00:53:34,140 --> 00:53:36,490
The wavelength is a
very important concept.

1053
00:53:36,490 --> 00:53:39,840
The thing I want to talk about
is, a little bit, to show you

1054
00:53:39,840 --> 00:53:42,520
what the wave looks like.

1055
00:53:42,520 --> 00:53:44,760
So this is very simple,
one-dimensional wave.

1056
00:53:44,760 --> 00:53:47,350
And what I've done
is I have plotted it

1057
00:53:47,350 --> 00:53:49,150
at different snapshots in time.

1058
00:53:49,150 --> 00:53:54,150
So the horizontal axis, again,
is the propagation distance

1059
00:53:54,150 --> 00:54:00,360
that the wave is propagating,
and the vertical axis is--

1060
00:54:00,360 --> 00:54:03,410
well, this part of the
small axis is time,

1061
00:54:03,410 --> 00:54:06,750
and then I have captured
different snapshots.

1062
00:54:06,750 --> 00:54:08,950
So as you can see, there's
a sense of motion here.

1063
00:54:08,950 --> 00:54:12,600
If you latch on a
peak of the wave,

1064
00:54:12,600 --> 00:54:15,270
you will see that at
different instances,

1065
00:54:15,270 --> 00:54:18,600
the peak is moving from
the left to the right.

1066
00:54:18,600 --> 00:54:20,350
And of course, the
symbol uppercase

1067
00:54:20,350 --> 00:54:22,180
T here is the frequency.

1068
00:54:22,180 --> 00:54:24,300
I think it was defined
in an earlier slide.

1069
00:54:24,300 --> 00:54:26,650
It is simply the inverse--

1070
00:54:26,650 --> 00:54:29,370
I'm sorry, that is the
period, the temporal period,

1071
00:54:29,370 --> 00:54:33,820
the inverse of the
temporal frequency.

1072
00:54:33,820 --> 00:54:37,960
And of course,
after one full time

1073
00:54:37,960 --> 00:54:40,700
period, the wave
replicates itself.

1074
00:54:40,700 --> 00:54:43,630
So if you look carefully at
this wave from over here,

1075
00:54:43,630 --> 00:54:46,300
it is identical to the
wavefront at t equals 0

1076
00:54:46,300 --> 00:54:50,680
that I'm not tall
enough to reach.

1077
00:54:50,680 --> 00:54:52,690
So you can pick arbitrarily.

1078
00:54:52,690 --> 00:54:57,080
You can pick any
point in the wave.

1079
00:54:57,080 --> 00:54:58,690
I happened to pick a peak.

1080
00:54:58,690 --> 00:55:02,200
OK, I happened to pick a
peak, and I tracked that peak

1081
00:55:02,200 --> 00:55:03,730
as the wave propagates.

1082
00:55:03,730 --> 00:55:06,970
I could equally well have
picked a point over here

1083
00:55:06,970 --> 00:55:07,960
and tracked it.

1084
00:55:07,960 --> 00:55:11,330
It would also have
propagated the same way.

1085
00:55:11,330 --> 00:55:17,120
And so this concept of a point
in the wave, if you wish,

1086
00:55:17,120 --> 00:55:21,230
or more generally
a surface of a wave

1087
00:55:21,230 --> 00:55:26,760
that propagates with a
wave as a function of time

1088
00:55:26,760 --> 00:55:29,030
is called a wavefront.

1089
00:55:29,030 --> 00:55:32,630
And the term is very suggestive.

1090
00:55:32,630 --> 00:55:33,920
It implies motion.

1091
00:55:33,920 --> 00:55:35,673
It's like a battlefront.

1092
00:55:35,673 --> 00:55:36,590
What is a battlefront?

1093
00:55:36,590 --> 00:55:39,650
It's the people who are
unlucky enough to have

1094
00:55:39,650 --> 00:55:42,590
been picked to be at the
frontline of the battle.

1095
00:55:42,590 --> 00:55:47,780
So if you've seen all these old,
horrible movies about battles

1096
00:55:47,780 --> 00:55:49,640
in the Middle Ages,
you see all these guys

1097
00:55:49,640 --> 00:55:51,795
with their shields going ahead.

1098
00:55:51,795 --> 00:55:54,020
And that's a
battlefront, moving.

1099
00:55:54,020 --> 00:55:56,150
So a wavefront is
a similar concept.

1100
00:55:56,150 --> 00:56:01,040
You have a front that is moving
as the energy of the wave

1101
00:56:01,040 --> 00:56:04,060
is propagating.

1102
00:56:04,060 --> 00:56:06,060
So it's perhaps not a
very interesting wavefront

1103
00:56:06,060 --> 00:56:08,250
because it is
one-dimensional, right?

1104
00:56:08,250 --> 00:56:11,610
The wave is propagating
along a sort of linear axis.

1105
00:56:11,610 --> 00:56:15,780
In a second, I will show you
more interesting wavefronts

1106
00:56:15,780 --> 00:56:19,753
that are of relevance
in this class.

1107
00:56:19,753 --> 00:56:21,420
The other thing I
want to point out here

1108
00:56:21,420 --> 00:56:24,660
is, again, I want to bring up
the concept of the wavelength.

1109
00:56:24,660 --> 00:56:26,730
And we defined the
wavelength already

1110
00:56:26,730 --> 00:56:29,070
as the distance
between two peaks.

1111
00:56:29,070 --> 00:56:31,200
So if you look at
two peaks over here,

1112
00:56:31,200 --> 00:56:34,080
the distance is, by
definition, of a wavelength.

1113
00:56:34,080 --> 00:56:37,140
But also, the wavelength,
it has a different meaning.

1114
00:56:37,140 --> 00:56:39,540
If you look at it from the
point of view of propagation

1115
00:56:39,540 --> 00:56:42,150
of the wave, it is
also the distance

1116
00:56:42,150 --> 00:56:45,240
that the wave propagated in--

1117
00:56:45,240 --> 00:56:46,020
how long?

1118
00:56:46,020 --> 00:56:48,660
Well, one period, right?

1119
00:56:48,660 --> 00:56:50,400
And in fact, this is
where the equation c

1120
00:56:50,400 --> 00:56:52,140
equals lambda nu comes from.

1121
00:56:58,780 --> 00:57:00,830
I'll let you do
that as a homework.

1122
00:57:00,830 --> 00:57:04,720
But if you think about
it, if you treat the wave

1123
00:57:04,720 --> 00:57:11,030
as a particle that
took 3 seconds to move

1124
00:57:11,030 --> 00:57:15,520
lambda units of distance,
then its velocity c

1125
00:57:15,520 --> 00:57:18,520
must obey this
equation over here.

1126
00:57:18,520 --> 00:57:21,310
It's a one-line
derivation kind of thing.

1127
00:57:21,310 --> 00:57:22,910
I'll let you do
it as a homework.

1128
00:57:22,910 --> 00:57:25,630
And also, I want to
emphasize that this equation

1129
00:57:25,630 --> 00:57:30,340
that we called the spatial
relation in the previous slide,

1130
00:57:30,340 --> 00:57:33,460
it is only true if light
propagates in free space

1131
00:57:33,460 --> 00:57:35,110
or in uniform media.

1132
00:57:35,110 --> 00:57:39,268
If you put light, for
example, in a confined space,

1133
00:57:39,268 --> 00:57:41,560
this equation changes, and
it becomes a little bit more

1134
00:57:41,560 --> 00:57:43,360
complicated.

1135
00:57:43,360 --> 00:57:46,600
But in this class, we don't
deal with this phenomenon.

1136
00:57:46,600 --> 00:57:49,690
If you want to learn about
more complicated dispersion

1137
00:57:49,690 --> 00:57:52,930
relations, you will have to
take Professor Fujimoto's class

1138
00:57:52,930 --> 00:57:55,600
in electrical engineering.

1139
00:57:55,600 --> 00:57:57,780
I might mention something
like this in passing,

1140
00:57:57,780 --> 00:57:59,520
but not in great detail.

1141
00:57:59,520 --> 00:58:01,080
For this, we will
be happy enough

1142
00:58:01,080 --> 00:58:05,950
to take this as a dispersion
equation of the light.

1143
00:58:05,950 --> 00:58:07,950
But again, I want to alert
you that there's also

1144
00:58:07,950 --> 00:58:12,900
other dispersion
relations that may occur.

1145
00:58:12,900 --> 00:58:15,970
OK, the other thing that I will
not spend too much time here,

1146
00:58:15,970 --> 00:58:20,880
but it will come up later with
great force and great detail

1147
00:58:20,880 --> 00:58:23,600
is the concept of phase delay.

1148
00:58:23,600 --> 00:58:28,190
So you probably remember this
from your trigonometry class.

1149
00:58:28,190 --> 00:58:30,500
If you have a
periodic phenomenon

1150
00:58:30,500 --> 00:58:34,430
or a periodic function, you can
pick an arbitrary point in time

1151
00:58:34,430 --> 00:58:36,200
and call it your reference.

1152
00:58:36,200 --> 00:58:38,390
And then, as the
phenomenon evolves,

1153
00:58:38,390 --> 00:58:43,890
you can refer to this initial
point as if with a phase delay.

1154
00:58:43,890 --> 00:58:46,760
So the phase delay
is relative to 2pi,

1155
00:58:46,760 --> 00:58:49,310
which measures one full cycle.

1156
00:58:49,310 --> 00:58:54,590
So then you can interpret
these snapshots over here

1157
00:58:54,590 --> 00:58:58,850
as phase-delayed versions
of the original wave.

1158
00:58:58,850 --> 00:59:04,580
So for example, between
0 and 1/8 of a period,

1159
00:59:04,580 --> 00:59:08,660
your phase delay equals pi
over 4, because 2pi over 8

1160
00:59:08,660 --> 00:59:10,460
equals pi over 4.

1161
00:59:10,460 --> 00:59:13,190
So this is a concept that
will come up again, as I said,

1162
00:59:13,190 --> 00:59:14,550
in great detail.

1163
00:59:14,550 --> 00:59:19,620
I just wanted you to be a little
bit aware of it right now.

1164
00:59:19,620 --> 00:59:23,280
What I really wanted
to emphasize over here

1165
00:59:23,280 --> 00:59:26,380
is that light does not
usually propagate along

1166
00:59:26,380 --> 00:59:30,150
an exact one line, as I
showed in a previous line,

1167
00:59:30,150 --> 00:59:31,770
but it propagates in 3D space.

1168
00:59:31,770 --> 00:59:33,040
So it can expand.

1169
00:59:33,040 --> 00:59:34,040
It can contract.

1170
00:59:34,040 --> 00:59:36,450
It can do weird things, right?

1171
00:59:36,450 --> 00:59:38,340
So to do that, we
need a slightly more

1172
00:59:38,340 --> 00:59:39,360
elaborate description.

1173
00:59:39,360 --> 00:59:43,017
So this is an attempt
to plot 3D space.

1174
00:59:43,017 --> 00:59:45,100
And if you think about the
wavefront in this case,

1175
00:59:45,100 --> 00:59:48,390
it is a surface
that moves from left

1176
00:59:48,390 --> 00:59:51,240
to right as a function of time.

1177
00:59:51,240 --> 00:59:54,292
So as the wavefront propagates,
the surface is moving.

1178
00:59:54,292 --> 00:59:56,000
By the way, this is
a fictitious surface.

1179
00:59:56,000 --> 00:59:59,220
I'm not thinking of a
physical surface or anything.

1180
00:59:59,220 --> 01:00:03,680
But if you think about the
energy that the light carries,

1181
01:00:03,680 --> 01:00:07,430
the energy is actually moving
as the wave propagates.

1182
01:00:07,430 --> 01:00:09,410
This is how you can
connect the two.

1183
01:00:09,410 --> 01:00:11,200
If you go out to the Charles--

1184
01:00:11,200 --> 01:00:13,970
OK, you have to wait until
April when it unfreezes--

1185
01:00:13,970 --> 01:00:16,990
but if you look at the
waves on the water--

1186
01:00:16,990 --> 01:00:19,490
of course, you can do it at
home on your bucket or something

1187
01:00:19,490 --> 01:00:20,130
like that--

1188
01:00:20,130 --> 01:00:22,630
but if you look at the waves,
there's also a physical sense,

1189
01:00:22,630 --> 01:00:24,770
because the water
wave, there's a crest.

1190
01:00:24,770 --> 01:00:26,420
So there wavefront
of the water wave

1191
01:00:26,420 --> 01:00:30,687
is the crest that moves
as the wave propagates.

1192
01:00:33,320 --> 01:00:37,800
So these surfaces, the weapons,
they can have different shapes.

1193
01:00:37,800 --> 01:00:40,490
They cannot have arbitrary
shapes because they're governed

1194
01:00:40,490 --> 01:00:43,880
by the laws of
light propagation.

1195
01:00:43,880 --> 01:00:48,860
But certain allowable shapes
turn out to be very simple,

1196
01:00:48,860 --> 01:00:50,930
and we will be dealing
with them a lot.

1197
01:00:50,930 --> 01:00:53,480
So the simplest is
a planar wavefront

1198
01:00:53,480 --> 01:00:56,960
that, as the name
implies, is a plane.

1199
01:00:56,960 --> 01:01:00,260
And the next simple is
a spherical wavefront,

1200
01:01:00,260 --> 01:01:03,450
which, again, as the name
implies, is a sphere.

1201
01:01:03,450 --> 01:01:08,330
So you can think those as
our two major wavefronts

1202
01:01:08,330 --> 01:01:10,770
that we'll be dealing with
throughout the class--

1203
01:01:10,770 --> 01:01:12,830
the planar wavefront
and the spherical.

1204
01:01:12,830 --> 01:01:14,980
And we'll-- yes.

1205
01:01:14,980 --> 01:01:17,530
AUDIENCE: So in the last slide,
you showed the electric field

1206
01:01:17,530 --> 01:01:18,760
as being the y-axis.

1207
01:01:18,760 --> 01:01:21,070
But here, it's space, not field.

1208
01:01:24,030 --> 01:01:26,790
GEORGE BARBASTATHIS: Yes, so
that is correct, and thank you.

1209
01:01:26,790 --> 01:01:28,620
And I should relabel the slide.

1210
01:01:28,620 --> 01:01:34,380
Here, the two axes, they
correspond to x and y,

1211
01:01:34,380 --> 01:01:36,370
the space coordinates, yeah.

1212
01:01:36,370 --> 01:01:40,200
And the electric field is not
found here because I cannot

1213
01:01:40,200 --> 01:01:42,100
plot a fourth dimension.

1214
01:01:42,100 --> 01:01:45,750
So what is happening here is the
electric field is maximum at t

1215
01:01:45,750 --> 01:01:47,230
equal to 0.

1216
01:01:47,230 --> 01:01:51,690
So at t equals 0, the electric
field is maximum on this plane.

1217
01:01:51,690 --> 01:01:54,630
If you wait 1/8 of
a period, the field

1218
01:01:54,630 --> 01:01:56,220
will be maximum at this plane.

1219
01:01:56,220 --> 01:01:58,620
If you wait another
1/8 of a period,

1220
01:01:58,620 --> 01:02:00,540
the field is maximum
on this plane.

1221
01:02:00,540 --> 01:02:03,090
So the wavefront, in
this case, is the maximum

1222
01:02:03,090 --> 01:02:04,290
of the electric field--

1223
01:02:04,290 --> 01:02:06,480
the crest, if you wish,
of the electric field--

1224
01:02:06,480 --> 01:02:08,740
as it propagates through space.

1225
01:02:08,740 --> 01:02:10,790
And the same is here.

1226
01:02:10,790 --> 01:02:14,990
Again, these surfaces mean
that the field is maximum

1227
01:02:14,990 --> 01:02:17,160
on the surface at t equals 0.

1228
01:02:17,160 --> 01:02:19,340
And then, 1/8 of a
period later, the field

1229
01:02:19,340 --> 01:02:22,660
is maximum on the surface,
and so on, and so forth.

1230
01:02:22,660 --> 01:02:23,260
Thanks, yeah.

1231
01:02:23,260 --> 01:02:28,020
So that's a very
important clarification.

1232
01:02:28,020 --> 01:02:31,400
Now, what do you think
should happen to the energy

1233
01:02:31,400 --> 01:02:34,370
density in the two cases?

1234
01:02:34,370 --> 01:02:36,170
Suppose I have a
fixed amount of energy

1235
01:02:36,170 --> 01:02:40,438
that is entered in on the left.

1236
01:02:40,438 --> 01:02:41,730
Are they different in some way?

1237
01:02:41,730 --> 01:02:43,387
Yeah.

1238
01:02:43,387 --> 01:02:45,543
AUDIENCE: [INAUDIBLE]

1239
01:02:45,543 --> 01:02:46,960
GEORGE BARBASTATHIS:
That's right.

1240
01:02:46,960 --> 01:02:50,280
Can I can ask you to push
the button and repeat that?

1241
01:02:50,280 --> 01:02:52,290
Yeah.

1242
01:02:52,290 --> 01:02:55,170
AUDIENCE: The plane
wave's energy is constant,

1243
01:02:55,170 --> 01:02:58,050
energy density is constant,
and the spherical wave's energy

1244
01:02:58,050 --> 01:02:59,582
density is smaller.

1245
01:02:59,582 --> 01:03:00,790
GEORGE BARBASTATHIS: Correct.

1246
01:03:00,790 --> 01:03:01,720
AUDIENCE: As it expands.

1247
01:03:01,720 --> 01:03:03,137
GEORGE BARBASTATHIS:
Correct, yes,

1248
01:03:03,137 --> 01:03:04,990
because energy has
to be concerned.

1249
01:03:04,990 --> 01:03:10,410
So in this case, the
wavefront is invariant,

1250
01:03:10,410 --> 01:03:12,360
so the energy must
remain constant.

1251
01:03:12,360 --> 01:03:14,520
In this case, the
wavefront is expanding,

1252
01:03:14,520 --> 01:03:19,270
so the energy density will
decrease as you go away.

1253
01:03:19,270 --> 01:03:21,360
We will make this
more precise later.

1254
01:03:21,360 --> 01:03:23,590
We'll define what we
mean by energy density.

1255
01:03:23,590 --> 01:03:25,710
In fact, it is called intensity.

1256
01:03:25,710 --> 01:03:28,420
So we'll define that.

1257
01:03:28,420 --> 01:03:30,390
So basically if you
measure the energy

1258
01:03:30,390 --> 01:03:34,500
in watts per area, watts
per centimeter square,

1259
01:03:34,500 --> 01:03:36,630
in this case, it has
to decrease in order

1260
01:03:36,630 --> 01:03:38,640
to make sure that the
energy you started

1261
01:03:38,640 --> 01:03:44,190
with at the center of the
sphere is preserved throughout.

1262
01:03:44,190 --> 01:03:46,800
The next concept I would
like to define is the ray.

1263
01:03:46,800 --> 01:03:49,140
And the reason we
introduced wavefronts

1264
01:03:49,140 --> 01:03:53,550
is primarily because I wanted
to define relatively precisely,

1265
01:03:53,550 --> 01:03:56,550
now, what I mean by a ray.

1266
01:03:56,550 --> 01:04:00,470
For the next 4 weeks, we will be
talking about rays exclusively,

1267
01:04:00,470 --> 01:04:02,070
OK?

1268
01:04:02,070 --> 01:04:05,160
So a ray is basically a
normal to the wavefront.

1269
01:04:05,160 --> 01:04:08,670
That is the correct,
accurate definition of a ray.

1270
01:04:08,670 --> 01:04:11,820
You take this surfaces,
you plug the normals,

1271
01:04:11,820 --> 01:04:13,807
and these lines are the rays.

1272
01:04:13,807 --> 01:04:15,390
So in this case, the
rays are parallel

1273
01:04:15,390 --> 01:04:18,360
because all the surfaces
are parallel planes.

1274
01:04:18,360 --> 01:04:20,910
In this case, the
rays form a fan,

1275
01:04:20,910 --> 01:04:23,680
like a divergent
fan, that attaches

1276
01:04:23,680 --> 01:04:27,270
at each point on the spheres.

1277
01:04:27,270 --> 01:04:31,280
The fan components are
normal to the surfaces.

1278
01:04:31,280 --> 01:04:34,230
And you can also think
of them as trajectories

1279
01:04:34,230 --> 01:04:39,846
over which the particles
of light propagate.

1280
01:04:39,846 --> 01:04:41,590
It is not, perhaps,
very accurate

1281
01:04:41,590 --> 01:04:44,200
to think of the particles
as photons in this case.

1282
01:04:44,200 --> 01:04:47,740
So think of them as some sort
of fictitious light bullets that

1283
01:04:47,740 --> 01:04:52,370
propagate down the
ray trajectories.

1284
01:04:52,370 --> 01:04:54,020
And the rays have
several properties,

1285
01:04:54,020 --> 01:04:57,050
which I will ratify
later in the class.

1286
01:04:57,050 --> 01:04:59,800
The rays have to be continuous
in piecewise differential.

1287
01:04:59,800 --> 01:05:01,480
A ray cannot jump, for example.

1288
01:05:01,480 --> 01:05:04,430
You cannot have a ray
that looks like this.

1289
01:05:12,910 --> 01:05:14,836
That cannot happen-- forbidden.

1290
01:05:18,724 --> 01:05:26,440
A ray can have a continuous
but, perhaps, not differentiable

1291
01:05:26,440 --> 01:05:27,410
band like this.

1292
01:05:27,410 --> 01:05:28,700
So that's allowed.

1293
01:05:28,700 --> 01:05:31,150
And it can also have a
smooth, continuous path.

1294
01:05:31,150 --> 01:05:33,190
That's also allowed.

1295
01:05:33,190 --> 01:05:35,970
OK, that is, obviously,
why it is forbidden.

1296
01:05:35,970 --> 01:05:39,190
It is kind of strange to
imagine the photon disappearing

1297
01:05:39,190 --> 01:05:40,650
and appearing again
someplace else.

1298
01:05:44,260 --> 01:05:48,290
The others we will
see later in action.

1299
01:05:48,290 --> 01:05:53,670
And from our experience,
rays are straight lines.

1300
01:05:53,670 --> 01:05:55,910
And why do we say that,
from our experience?

1301
01:05:55,910 --> 01:05:58,200
Where have you seen
rays in everyday life?

1302
01:06:01,320 --> 01:06:02,820
Button.

1303
01:06:02,820 --> 01:06:03,532
AUDIENCE: Lasers.

1304
01:06:03,532 --> 01:06:04,990
GEORGE BARBASTATHIS:
Lasers is one.

1305
01:06:04,990 --> 01:06:08,460
But usually, if you have the
beam coming out of a laser,

1306
01:06:08,460 --> 01:06:12,260
it looks kind of
like a straight line.

1307
01:06:12,260 --> 01:06:15,800
Another example, perhaps,
from even more everyday life.

1308
01:06:15,800 --> 01:06:16,730
AUDIENCE: Shadows.

1309
01:06:16,730 --> 01:06:18,522
GEORGE BARBASTATHIS:
Shadows, that's right.

1310
01:06:18,522 --> 01:06:20,240
If you look at
shadows, the light

1311
01:06:20,240 --> 01:06:24,070
appears to come out
straight out of the shadows.

1312
01:06:24,070 --> 01:06:26,105
So it's a little bit
strange that I drew a ray

1313
01:06:26,105 --> 01:06:28,340
as a curved trajectory.

1314
01:06:28,340 --> 01:06:31,250
We will see a bit later, maybe
even today if we don't run out

1315
01:06:31,250 --> 01:06:36,590
of time, that light rays can
actually follow curved paths

1316
01:06:36,590 --> 01:06:38,390
under certain conditions.

1317
01:06:38,390 --> 01:06:41,810
But what is for sure, that in
free space or uniform space

1318
01:06:41,810 --> 01:06:42,940
like air--

1319
01:06:42,940 --> 01:06:44,990
we observe shadows in air.

1320
01:06:44,990 --> 01:06:51,810
So air is pretty much
uniform, and for that reason,

1321
01:06:51,810 --> 01:06:53,950
rays propagate in
straight lines.

1322
01:06:53,950 --> 01:06:56,550
By the way, you don't have
to go too far to see examples

1323
01:06:56,550 --> 01:06:59,280
of curved ray propagation.

1324
01:06:59,280 --> 01:07:01,470
The best example is flicker.

1325
01:07:01,470 --> 01:07:04,680
If you go up in the
mountains at night

1326
01:07:04,680 --> 01:07:06,753
and you look down at
the city beneath--

1327
01:07:06,753 --> 01:07:08,420
I don't think you can
do that in Boston.

1328
01:07:08,420 --> 01:07:10,210
We don't have any
mountains high enough.

1329
01:07:10,210 --> 01:07:13,140
But in Los Angeles, for
example, it's very pronounced.

1330
01:07:13,140 --> 01:07:16,020
If you go to the Hollywood Hills
and look down, you see flicker.

1331
01:07:16,020 --> 01:07:18,380
The lights in the city,
they are not steady.

1332
01:07:18,380 --> 01:07:20,940
They kind of flicker.

1333
01:07:20,940 --> 01:07:25,010
So the result of that is
because the atmosphere,

1334
01:07:25,010 --> 01:07:26,770
it is not an exactly
uniform medium.

1335
01:07:26,770 --> 01:07:31,250
You have temperature changes,
air currents, and so on.

1336
01:07:31,250 --> 01:07:35,080
And because of that, the
rays between the city lights

1337
01:07:35,080 --> 01:07:38,590
and your eye, the rays
follow a sort of curved path.

1338
01:07:38,590 --> 01:07:40,800
Very slightly curved, but
because they propagate

1339
01:07:40,800 --> 01:07:43,600
a long distance, it is enough
to result in this flicker

1340
01:07:43,600 --> 01:07:45,340
phenomenon.

1341
01:07:45,340 --> 01:07:47,270
OK, so from that--

1342
01:07:47,270 --> 01:07:50,060
it is not quite obvious
as in the shadow--

1343
01:07:50,060 --> 01:07:54,010
but from that, we have kind
of experienced, all of us,

1344
01:07:54,010 --> 01:07:57,125
that the rays might
actually not propagate along

1345
01:07:57,125 --> 01:07:58,170
a straight path.

1346
01:07:58,170 --> 01:08:00,020
And in a second,
I will define when

1347
01:08:00,020 --> 01:08:02,450
that happens-- when
a ray can propagate

1348
01:08:02,450 --> 01:08:06,650
in a curved trajectory.

1349
01:08:06,650 --> 01:08:11,770
Before I do that, I already
implied that the reason

1350
01:08:11,770 --> 01:08:14,420
rays might do strange
things, like deviate

1351
01:08:14,420 --> 01:08:16,109
from the straight and narrow--

1352
01:08:16,109 --> 01:08:18,710
I'm sorry, might deviate
from the straight path--

1353
01:08:18,710 --> 01:08:21,950
is because of interaction
with matter, right?

1354
01:08:21,950 --> 01:08:26,120
It is the non-uniformity in
air, in my earlier example,

1355
01:08:26,120 --> 01:08:29,670
that caused the rays to bend.

1356
01:08:29,670 --> 01:08:33,930
So then, the next topic is
a very simple description

1357
01:08:33,930 --> 01:08:36,240
of how light
interacts with matter.

1358
01:08:36,240 --> 01:08:38,180
And for now, I will
say it is a fairy

1359
01:08:38,180 --> 01:08:41,550
tale, because we don't know
enough electromagnetics yet.

1360
01:08:41,550 --> 01:08:44,670
I will come back to this
topic after we define light

1361
01:08:44,670 --> 01:08:47,010
as an electromagnetic wave.

1362
01:08:47,010 --> 01:08:50,490
I will come back to this topic
and tell you more rigorously

1363
01:08:50,490 --> 01:08:52,610
how light interacts with matter.

1364
01:08:52,610 --> 01:08:54,420
For now, very briefly,
I will tell you

1365
01:08:54,420 --> 01:08:58,430
that there is three
types of interaction

1366
01:08:58,430 --> 01:09:00,410
that we'll discuss
in this class--

1367
01:09:00,410 --> 01:09:03,470
absorption, refraction,
and scattering.

1368
01:09:03,470 --> 01:09:06,050
So today, I will define
absorption and refraction

1369
01:09:06,050 --> 01:09:10,600
in very simple
phenomenological terms.

1370
01:09:10,600 --> 01:09:13,939
Anybody knows what it
means, "phenomenological"?

1371
01:09:13,939 --> 01:09:16,729
I am Greek, so I have a
benefit of the language.

1372
01:09:22,410 --> 01:09:25,529
"Phenomenological" means
based on observation.

1373
01:09:25,529 --> 01:09:28,649
It means we define
this phenomenon

1374
01:09:28,649 --> 01:09:30,569
based on what we
observe, but we don't

1375
01:09:30,569 --> 01:09:34,470
try to dig any deeper
into the basic principles

1376
01:09:34,470 --> 01:09:36,149
behind this phenomenon.

1377
01:09:36,149 --> 01:09:38,290
You will see in a
second what I mean.

1378
01:09:38,290 --> 01:09:41,779
Very well, we'll define
absorption and refraction.

1379
01:09:41,779 --> 01:09:43,849
And what I want to
emphasize, also,

1380
01:09:43,849 --> 01:09:46,430
is that this is not the only
three types of interactions.

1381
01:09:46,430 --> 01:09:49,183
Light can do a lot
of other things.

1382
01:09:49,183 --> 01:09:50,600
There's fluorescence,
that you are

1383
01:09:50,600 --> 01:09:53,660
familiar if you go to nightclubs
where they use ultraviolet,

1384
01:09:53,660 --> 01:09:54,260
right?

1385
01:09:54,260 --> 01:09:55,700
People look kind of funny.

1386
01:09:55,700 --> 01:09:58,220
That is fluorescence.

1387
01:09:58,220 --> 01:10:01,420
There is non-linear phenomena.

1388
01:10:01,420 --> 01:10:03,290
There's ionization
that can happen.

1389
01:10:03,290 --> 01:10:05,360
So a lot of different
things that can happen,

1390
01:10:05,360 --> 01:10:07,290
but I will not cover
them in this class.

1391
01:10:07,290 --> 01:10:10,610
So as I say, they're outside
the scope of our interest here.

1392
01:10:15,110 --> 01:10:18,140
Going on with this, let me
define absorption first.

1393
01:10:18,140 --> 01:10:23,010
So from experience,
we know that anything

1394
01:10:23,010 --> 01:10:26,700
that travels through a
medium suffers losses.

1395
01:10:26,700 --> 01:10:28,140
Many of your
mechanical engineers,

1396
01:10:28,140 --> 01:10:33,210
you know that if you have
a mechanical disturbance

1397
01:10:33,210 --> 01:10:37,140
like sound propagating down
the medium, at the exit,

1398
01:10:37,140 --> 01:10:39,543
you see less of the
energy that you put in.

1399
01:10:39,543 --> 01:10:41,085
Some of you are
electrical engineers.

1400
01:10:41,085 --> 01:10:44,310
You know that if you run
current through a device,

1401
01:10:44,310 --> 01:10:46,230
typically, at the
exit of the device,

1402
01:10:46,230 --> 01:10:49,990
you see less current or
less electrical energy.

1403
01:10:49,990 --> 01:10:52,630
Typically, you see a
voltage drop than the energy

1404
01:10:52,630 --> 01:10:54,260
that you put in.

1405
01:10:54,260 --> 01:10:57,270
So why does this happen?

1406
01:10:57,270 --> 01:10:58,670
Well, because of--

1407
01:10:58,670 --> 01:10:59,170
Why?

1408
01:10:59,170 --> 01:10:59,962
Why does it happen?

1409
01:11:07,930 --> 01:11:08,430
Yes.

1410
01:11:13,300 --> 01:11:14,761
[LAUGHS]

1411
01:11:14,761 --> 01:11:16,222
AUDIENCE: [INAUDIBLE].

1412
01:11:16,222 --> 01:11:17,650
GEORGE BARBASTATHIS:
That's right.

1413
01:11:17,650 --> 01:11:19,770
It is conversion of
energy to heat, right?

1414
01:11:19,770 --> 01:11:22,450
And that generally is
undesirable unless--

1415
01:11:22,450 --> 01:11:24,900
anyway, we seldom heat
ourselves with-- well,

1416
01:11:24,900 --> 01:11:26,810
unless it's the sunlight
on a day like this,

1417
01:11:26,810 --> 01:11:29,080
we appreciate the heating.

1418
01:11:29,080 --> 01:11:32,980
But in Singapore, generally, we
don't appreciate the heating,

1419
01:11:32,980 --> 01:11:36,160
because the sunlight is
too intense, typically,

1420
01:11:36,160 --> 01:11:38,702
to tolerate.

1421
01:11:38,702 --> 01:11:40,160
But yeah, the fact
of the matter is

1422
01:11:40,160 --> 01:11:44,090
that there is ohmic
losses, or dissipation,

1423
01:11:44,090 --> 01:11:48,680
like you very correctly said,
that cause a decrease in power.

1424
01:11:48,680 --> 01:11:54,500
So the phenomenological law
that describes this effect

1425
01:11:54,500 --> 01:11:58,430
is exponential in the length
of propagation in matter.

1426
01:11:58,430 --> 01:12:00,800
So by "phenomenological,"
what I mean

1427
01:12:00,800 --> 01:12:03,370
is that I throw this
equation at you,

1428
01:12:03,370 --> 01:12:05,870
but I haven't told you why, OK?

1429
01:12:05,870 --> 01:12:07,010
I will tell you why later.

1430
01:12:07,010 --> 01:12:09,710
When we do electromagnetics,
I will justify

1431
01:12:09,710 --> 01:12:11,570
why this law comes about.

1432
01:12:11,570 --> 01:12:13,700
And strangely enough,
it is called Beer's Law.

1433
01:12:13,700 --> 01:12:15,050
No, it's not pronounced "beer."

1434
01:12:15,050 --> 01:12:16,400
It's pronounced "bear."

1435
01:12:16,400 --> 01:12:17,470
This fellow was German.

1436
01:12:17,470 --> 01:12:22,050
But anyway-- and light does
get absorbed by beer, actually.

1437
01:12:22,050 --> 01:12:25,680
And strangely enough, I did
see a paper at a conference

1438
01:12:25,680 --> 01:12:29,070
once where someone was measuring
the optical properties of beer.

1439
01:12:29,070 --> 01:12:31,340
And I'm not kidding, actually.

1440
01:12:31,340 --> 01:12:33,960
They had their project
funded by I don't know whom,

1441
01:12:33,960 --> 01:12:37,998
to shoot laser beams through
big containers of beer.

1442
01:12:37,998 --> 01:12:40,290
And then I don't know exactly
what they were measuring,

1443
01:12:40,290 --> 01:12:42,720
but I thought it was a very
cleverly conceived project.

1444
01:12:42,720 --> 01:12:45,180
Because after you finish the
experiment, what do you do?

1445
01:12:45,180 --> 01:12:46,660
You drink the beer, right?

1446
01:12:46,660 --> 01:12:47,160
OK.

1447
01:12:50,360 --> 01:12:55,490
So I said that the output
energy decays exponentially

1448
01:12:55,490 --> 01:12:57,620
as a function of the
length of the medium.

1449
01:12:57,620 --> 01:12:59,570
The coefficient that
goes in the exponent

1450
01:12:59,570 --> 01:13:02,090
is, again, very highly
dependent on the material

1451
01:13:02,090 --> 01:13:03,590
that the light propagates.

1452
01:13:03,590 --> 01:13:06,380
Conductors-- like
metals-- they tend

1453
01:13:06,380 --> 01:13:07,800
to have very high dissipation.

1454
01:13:07,800 --> 01:13:11,390
If you might propagate a few
microns inside the metal,

1455
01:13:11,390 --> 01:13:12,770
the light is all lost.

1456
01:13:12,770 --> 01:13:14,810
It is all converted to heat.

1457
01:13:14,810 --> 01:13:17,732
So on the other hand,
the electrics like glass,

1458
01:13:17,732 --> 01:13:19,190
they can have very
low dissipation.

1459
01:13:19,190 --> 01:13:23,780
In fact, some materials,
they use some special glasses

1460
01:13:23,780 --> 01:13:27,860
in optical fibers that
they usually transmit light

1461
01:13:27,860 --> 01:13:29,552
over very long distances.

1462
01:13:29,552 --> 01:13:31,010
In these occasions,
the dissipation

1463
01:13:31,010 --> 01:13:34,860
is in the order of a fraction
of a dB per kilometer.

1464
01:13:34,860 --> 01:13:37,460
So it is I don't know how many
orders of magnitude there,

1465
01:13:37,460 --> 01:13:41,540
around eight or nine orders of
magnitude in the dissipation

1466
01:13:41,540 --> 01:13:42,890
coefficient.

1467
01:13:42,890 --> 01:13:45,020
And again, that
depends on the way

1468
01:13:45,020 --> 01:13:46,760
light interacts with matter.

1469
01:13:46,760 --> 01:13:49,480
I will say a little bit
more about that later.

1470
01:13:49,480 --> 01:13:53,645
But for now, again,
take me to my word.

1471
01:13:53,645 --> 01:13:55,520
Never take anybody to
their word, by the way.

1472
01:13:55,520 --> 01:13:58,705
But I think for
reasons of organizing

1473
01:13:58,705 --> 01:14:00,080
the presentation
of the material,

1474
01:14:00,080 --> 01:14:05,090
sometimes I will ask you to
take my word for granted.

1475
01:14:05,090 --> 01:14:07,190
And usually, when I
ask you to do that,

1476
01:14:07,190 --> 01:14:11,140
I will come back and justify
myself perhaps a few lectures

1477
01:14:11,140 --> 01:14:13,600
later, or something like that.

1478
01:14:13,600 --> 01:14:16,960
OK, and the other thing
I want to emphasize

1479
01:14:16,960 --> 01:14:20,740
is that dissipation or
absorption depends strongly

1480
01:14:20,740 --> 01:14:21,910
on the wavelength.

1481
01:14:21,910 --> 01:14:24,490
And that, again, goes back to
what we were saying before.

1482
01:14:24,490 --> 01:14:27,430
Different wavelengths
carry different energy,

1483
01:14:27,430 --> 01:14:29,110
and different energies
of the photons,

1484
01:14:29,110 --> 01:14:31,530
they will interact with the
matter in different ways.

1485
01:14:31,530 --> 01:14:33,280
They might [INAUDIBLE]
due to oscillation.

1486
01:14:33,280 --> 01:14:36,850
They might set it into
dipole polarization.

1487
01:14:36,850 --> 01:14:40,620
They might set matter, they
might ionize it-- whatever.

1488
01:14:40,620 --> 01:14:43,490
So depending on who happens,
you get different behavior.

1489
01:14:43,490 --> 01:14:46,790
So this is the atmosphere.

1490
01:14:46,790 --> 01:14:49,140
The percent of transmission--
not exactly the alpha

1491
01:14:49,140 --> 01:14:54,210
coefficient, but a transmission,
percent transmission throughout

1492
01:14:54,210 --> 01:14:55,380
a nominal length--

1493
01:14:55,380 --> 01:15:01,030
I believe it is in the
order of over a few meters--

1494
01:15:01,030 --> 01:15:03,020
as a function of wavelength.

1495
01:15:03,020 --> 01:15:04,900
So we can see that
it varies quite a bit

1496
01:15:04,900 --> 01:15:07,180
even within the visible range.

1497
01:15:07,180 --> 01:15:09,850
The atmosphere is not
completely transparent.

1498
01:15:09,850 --> 01:15:12,340
It is a little bit
less transparent

1499
01:15:12,340 --> 01:15:17,185
at blue wavelengths.

1500
01:15:17,185 --> 01:15:20,830
It becomes, then,
almost transparent

1501
01:15:20,830 --> 01:15:22,530
at the longer wavelengths.

1502
01:15:22,530 --> 01:15:26,025
And then-- this
is infrared now--

1503
01:15:26,025 --> 01:15:27,400
in the infrared,
you see you have

1504
01:15:27,400 --> 01:15:30,735
some very strong absorption.

1505
01:15:30,735 --> 01:15:32,360
The transmission
coefficient goes down.

1506
01:15:32,360 --> 01:15:34,030
That means strong
absorption here.

1507
01:15:34,030 --> 01:15:36,680
That actually has to do
with molecular resonances.

1508
01:15:36,680 --> 01:15:40,270
And you can think of molecules
as little mass spring damper

1509
01:15:40,270 --> 01:15:41,200
systems.

1510
01:15:41,200 --> 01:15:42,790
And the photon comes
in and kicks them

1511
01:15:42,790 --> 01:15:44,868
so it sets them
into oscillation.

1512
01:15:44,868 --> 01:15:46,660
When that happens, the
energy of the photon

1513
01:15:46,660 --> 01:15:50,080
gets transformed resonantly
into the molecule,

1514
01:15:50,080 --> 01:15:51,530
and then you get loss.

1515
01:15:51,530 --> 01:15:54,760
So in this case, it is a
little bit more complicated

1516
01:15:54,760 --> 01:15:57,940
than heating, than
simple heating.

1517
01:15:57,940 --> 01:15:59,680
But the net effect
is still the same.

1518
01:15:59,680 --> 01:16:02,715
You still get heating from
the motion of these molecules.

1519
01:16:02,715 --> 01:16:04,090
But anyway, that's
the reason why

1520
01:16:04,090 --> 01:16:08,140
you get these strong
absorption maxima over here.

1521
01:16:11,800 --> 01:16:15,190
What I really wanted to
get to today so that we

1522
01:16:15,190 --> 01:16:17,110
can progress with
geometrical optics

1523
01:16:17,110 --> 01:16:20,870
is the phenomenon of refraction.

1524
01:16:20,870 --> 01:16:23,880
So refraction, is-- is
refers to, actually,

1525
01:16:23,880 --> 01:16:25,440
a rather strange
thing that, again, I

1526
01:16:25,440 --> 01:16:28,470
will ask you to take for
granted until we talk

1527
01:16:28,470 --> 01:16:30,910
in detail about polarization.

1528
01:16:30,910 --> 01:16:34,200
And that is the fact
that the speed of light

1529
01:16:34,200 --> 01:16:37,500
changes when light
enters the material.

1530
01:16:37,500 --> 01:16:40,110
In this case, we're talking
primarily about dielectrics,

1531
01:16:40,110 --> 01:16:41,957
but it's also true for metals.

1532
01:16:41,957 --> 01:16:44,290
But of course, in metals, the
light doesn't go very far.

1533
01:16:44,290 --> 01:16:47,830
So OK, the speed changes,
but it doesn't go very far.

1534
01:16:47,830 --> 01:16:51,180
In dielectrics, the
light can go quite far,

1535
01:16:51,180 --> 01:16:52,690
but its speed is different.

1536
01:16:52,690 --> 01:16:57,210
And again, phenomenologically--
without describing the physical

1537
01:16:57,210 --> 01:16:59,710
origins of why--

1538
01:16:59,710 --> 01:17:02,260
the speed is, of
course, reduced,

1539
01:17:02,260 --> 01:17:04,150
and it's used by
a constant that is

1540
01:17:04,150 --> 01:17:07,540
known as index of refraction,
or refractive index.

1541
01:17:07,540 --> 01:17:13,900
And most books use the
symbol n to denote it.

1542
01:17:13,900 --> 01:17:17,650
And the value of
n can value a lot.

1543
01:17:17,650 --> 01:17:21,400
In a vacuum, n equals exactly 1.

1544
01:17:21,400 --> 01:17:24,870
So the speed of light in
vacuum equals exactly c.

1545
01:17:24,870 --> 01:17:28,600
In air, it is close to 1,
within two significant digits.

1546
01:17:28,600 --> 01:17:32,260
It's maybe 1.005 or
something like that.

1547
01:17:32,260 --> 01:17:34,790
And it depends also on the
temperature, the pressure,

1548
01:17:34,790 --> 01:17:38,700
a number of different
properties over the air,

1549
01:17:38,700 --> 01:17:41,970
as we'll see again later.

1550
01:17:41,970 --> 01:17:44,220
And then, typical
dielectrics that we see

1551
01:17:44,220 --> 01:17:45,750
are water, of course.

1552
01:17:45,750 --> 01:17:48,840
So then, why is it
the water interesting?

1553
01:17:48,840 --> 01:17:51,120
Well, because-- well, water.

1554
01:17:51,120 --> 01:17:54,110
But also because our bodies
are composed mostly of water.

1555
01:17:54,110 --> 01:17:57,900
Our tissue is approximately
70% or 75% water.

1556
01:17:57,900 --> 01:18:00,720
So light index of
refraction in a body

1557
01:18:00,720 --> 01:18:04,050
is also equal to the
same quantity, 1.3.

1558
01:18:04,050 --> 01:18:07,140
Actually, this would
be 1.33, if you really

1559
01:18:07,140 --> 01:18:08,750
want to be more accurate.

1560
01:18:08,750 --> 01:18:11,640
And glass-- so glass
is used in pretty much

1561
01:18:11,640 --> 01:18:14,880
every optical instrument
for visible wavelengths.

1562
01:18:14,880 --> 01:18:16,470
So in glass, the
index of refraction

1563
01:18:16,470 --> 01:18:21,390
is approximately 1.5.

1564
01:18:21,390 --> 01:18:24,810
OK what does this mean now,
the speed of light changes?

1565
01:18:24,810 --> 01:18:28,490
Another way to say it is that
the wavelength of the light

1566
01:18:28,490 --> 01:18:29,320
changes.

1567
01:18:29,320 --> 01:18:32,750
And this is actually
a more proper way

1568
01:18:32,750 --> 01:18:35,030
to think of the phenomenon.

1569
01:18:35,030 --> 01:18:37,310
When we'll do
electromagnetics, we'll

1570
01:18:37,310 --> 01:18:40,850
see that the change
in speed is actually

1571
01:18:40,850 --> 01:18:44,050
derived from that observation.

1572
01:18:44,050 --> 01:18:49,940
And the way the wavelength
changes is it becomes shorter.

1573
01:18:49,940 --> 01:18:53,240
So if you have a light happily
propagating in free space,

1574
01:18:53,240 --> 01:18:54,710
and then, all of
a sudden, there's

1575
01:18:54,710 --> 01:18:58,850
an abrupt interface and
light enters a dielectric,

1576
01:18:58,850 --> 01:19:01,048
the wavelengths becomes shorter.

1577
01:19:01,048 --> 01:19:02,090
Now, what does that mean?

1578
01:19:02,090 --> 01:19:05,680
Does this mean that, for
example, if I have red light,

1579
01:19:05,680 --> 01:19:12,050
and the red light goes into
glass, the light becomes green?

1580
01:19:12,050 --> 01:19:14,980
That's actually not
what we observe, right?

1581
01:19:14,980 --> 01:19:21,040
if you observe, many
of you have seen,

1582
01:19:21,040 --> 01:19:23,140
if you put a yellow
pencil in glass,

1583
01:19:23,140 --> 01:19:24,310
the pencil remains yellow.

1584
01:19:24,310 --> 01:19:27,180
It does not turn blue, right?

1585
01:19:27,180 --> 01:19:30,650
So what is a possible-- does
anybody know the explanation?

1586
01:19:30,650 --> 01:19:32,315
Yeah.

1587
01:19:32,315 --> 01:19:33,940
AUDIENCE: The frequency
stays the same.

1588
01:19:33,940 --> 01:19:36,835
So if you see the
frequency as it comes out,

1589
01:19:36,835 --> 01:19:39,210
it's just going to be affecting
pretty much [INAUDIBLE]..

1590
01:19:39,210 --> 01:19:40,627
GEORGE BARBASTATHIS:
That's right.

1591
01:19:42,850 --> 01:19:45,940
So very correctly, he said
that the frequency of the light

1592
01:19:45,940 --> 01:19:47,350
remains the same.

1593
01:19:47,350 --> 01:19:50,320
Anybody want to guess why
the frequency of the light

1594
01:19:50,320 --> 01:19:55,600
might remain the same but
the wavelength can change?

1595
01:20:03,140 --> 01:20:04,307
AUDIENCE: The speed changes.

1596
01:20:04,307 --> 01:20:05,723
GEORGE BARBASTATHIS:
That's right.

1597
01:20:05,723 --> 01:20:06,588
The speed, yes.

1598
01:20:10,046 --> 01:20:10,750
That's right.

1599
01:20:10,750 --> 01:20:12,840
So both of you are right.

1600
01:20:12,840 --> 01:20:15,810
So first of all, they can
change simultaneously,

1601
01:20:15,810 --> 01:20:19,440
the wavelength and the speed,
because of this equation.

1602
01:20:19,440 --> 01:20:21,950
We said that the
speed of light--

1603
01:20:21,950 --> 01:20:26,720
I mean the speed of light
in vacuum, or in general--

1604
01:20:26,720 --> 01:20:31,410
well, in vacuum, it is
related to the frequency

1605
01:20:31,410 --> 01:20:33,900
of the wavelength by
this equation over here.

1606
01:20:33,900 --> 01:20:37,860
Well, you can then divide the
two sides of the equation by n,

1607
01:20:37,860 --> 01:20:39,787
and the question
remains the same.

1608
01:20:39,787 --> 01:20:40,995
But that's not very physical.

1609
01:20:40,995 --> 01:20:42,352
I did a mathematical trick.

1610
01:20:42,352 --> 01:20:43,560
What the hell does that mean?

1611
01:20:43,560 --> 01:20:45,020
I divided both sides by n.

1612
01:20:48,212 --> 01:20:50,420
That doesn't have to be
correct, and this is, indeed,

1613
01:20:50,420 --> 01:20:54,910
the dispersion relation in
a dielectrical material.

1614
01:20:54,910 --> 01:20:57,820
But you don't really know,
which one should you divide?

1615
01:20:57,820 --> 01:20:59,770
Should you divide
the wavelength by n,

1616
01:20:59,770 --> 01:21:02,200
or should you divide
the frequency by n?

1617
01:21:02,200 --> 01:21:04,840
Or maybe divide both
by square root n?

1618
01:21:04,840 --> 01:21:06,530
All of these are possibilities.

1619
01:21:06,530 --> 01:21:10,660
So the physical argument
that allows you to decide

1620
01:21:10,660 --> 01:21:12,410
whether to divide is what--

1621
01:21:12,410 --> 01:21:13,600
I'm sorry, your name?

1622
01:21:13,600 --> 01:21:14,020
AUDIENCE: Uh, Liz.

1623
01:21:14,020 --> 01:21:14,950
GEORGE BARBASTATHIS:
What Alice--

1624
01:21:14,950 --> 01:21:15,648
Alice, right?

1625
01:21:15,648 --> 01:21:16,440
AUDIENCE: Just Liz.

1626
01:21:16,440 --> 01:21:17,940
GEORGE BARBASTATHIS:
Liz, I'm sorry.

1627
01:21:17,940 --> 01:21:21,740
So the physical argument
is what Liz just said,

1628
01:21:21,740 --> 01:21:26,950
which is that the energy of
the photon cannot change.

1629
01:21:26,950 --> 01:21:29,650
Because the photon-- well,
I haven't said it yet,

1630
01:21:29,650 --> 01:21:34,110
but the photon is a fundamental
quantum mechanical particle.

1631
01:21:34,110 --> 01:21:35,920
It cannot be divided--

1632
01:21:35,920 --> 01:21:39,310
well, it can be divided
in some special cases.

1633
01:21:39,310 --> 01:21:43,120
But in the approximation
that we deal with here,

1634
01:21:43,120 --> 01:21:45,860
the photon must
maintain its energy.

1635
01:21:45,860 --> 01:21:47,860
So therefore, the
frequency of the photon

1636
01:21:47,860 --> 01:21:49,640
must remain the same.

1637
01:21:49,640 --> 01:21:53,890
New, the temporal
frequency is conserved.

1638
01:21:53,890 --> 01:21:56,890
So if the wavelength changes
because light entered

1639
01:21:56,890 --> 01:21:59,290
into matter, then
the velocity must

1640
01:21:59,290 --> 01:22:04,278
change to compensate in the
dispersion relationship.

1641
01:22:04,278 --> 01:22:08,590
OK, in our context
here, the only thing

1642
01:22:08,590 --> 01:22:13,617
that can happen to the
photon is it can disappear.

1643
01:22:13,617 --> 01:22:14,950
And it doesn't really disappear.

1644
01:22:14,950 --> 01:22:16,840
It gets converted
to heat, right?

1645
01:22:16,840 --> 01:22:19,270
So when the light
hits the material,

1646
01:22:19,270 --> 01:22:22,980
it actually heats the
material in discrete quanta.

1647
01:22:22,980 --> 01:22:27,300
Some of the photons that
come from the light source,

1648
01:22:27,300 --> 01:22:31,620
discrete quantities
that are equal to--

1649
01:22:31,620 --> 01:22:33,810
you cannot see it over
there because I erased it.

1650
01:22:33,810 --> 01:22:36,210
But discrete quantities
of approximately 10

1651
01:22:36,210 --> 01:22:40,560
to the minus 19 joules,
one of them at a time

1652
01:22:40,560 --> 01:22:43,800
can be converted to heat
and heat the material.

1653
01:22:43,800 --> 01:22:48,330
But you cannot get 60% of the
photon energy to go to heat

1654
01:22:48,330 --> 01:22:49,200
the material.

1655
01:22:49,200 --> 01:22:51,330
That's not the correct
way to think about it.

1656
01:22:51,330 --> 01:22:54,540
If 60% of the energy goes
into heating the material,

1657
01:22:54,540 --> 01:22:57,840
it means that 60% of
individual photons

1658
01:22:57,840 --> 01:23:02,580
died and gave up their energy to
the molecules of the material.

1659
01:23:02,580 --> 01:23:05,690
If you have a single photon
arriving into a material,

1660
01:23:05,690 --> 01:23:08,690
it will either survive
and go through impact,

1661
01:23:08,690 --> 01:23:10,820
or it will die and
be converted to heat.

1662
01:23:10,820 --> 01:23:13,980
You cannot have 60% of an
individual photon heating

1663
01:23:13,980 --> 01:23:15,280
the material.

1664
01:23:15,280 --> 01:23:17,220
OK, so because of this
line of reasoning,

1665
01:23:17,220 --> 01:23:18,845
that really requires
quantum mechanics.

1666
01:23:18,845 --> 01:23:22,160
So I cannot really justify
it very well without spending

1667
01:23:22,160 --> 01:23:23,710
a semester of quantum mechanics.

1668
01:23:23,710 --> 01:23:25,640
But because of this
line of reasoning,

1669
01:23:25,640 --> 01:23:28,460
the energy of the
photon is invalid.

1670
01:23:28,460 --> 01:23:31,490
Therefore, nu is invariant.

1671
01:23:31,490 --> 01:23:34,540
So believe it or not, I have
watched someone at a conference

1672
01:23:34,540 --> 01:23:37,473
stand up and say, well, doesn't
the light really become green?

1673
01:23:37,473 --> 01:23:38,890
And that was an
optics conference,

1674
01:23:38,890 --> 01:23:40,550
so it was very embarrassing.

1675
01:23:40,550 --> 01:23:42,850
But it's very
useful to remember.

1676
01:23:42,850 --> 01:23:50,120
No, light does not become
green when it enters glass.

1677
01:23:50,120 --> 01:23:52,875
And in any case, your
eyes respond to the energy

1678
01:23:52,875 --> 01:23:53,750
of the photon, right?

1679
01:23:53,750 --> 01:23:57,950
Because-- well, I haven't said
how your eyes perceive color

1680
01:23:57,950 --> 01:23:59,480
yet, but they respond
to the energy.

1681
01:23:59,480 --> 01:24:01,605
So you still perceive it
as red, because the energy

1682
01:24:01,605 --> 01:24:06,570
of the photon is still red.

1683
01:24:06,570 --> 01:24:11,030
OK, so having said
that now, having

1684
01:24:11,030 --> 01:24:13,910
said that the
index of refraction

1685
01:24:13,910 --> 01:24:17,060
is a property of the material,
I can conceive of materials

1686
01:24:17,060 --> 01:24:21,207
where the index of refraction
is a function of position.

1687
01:24:21,207 --> 01:24:22,290
And if that was the case--

1688
01:24:26,157 --> 01:24:27,615
the bad thing about
any measures is

1689
01:24:27,615 --> 01:24:29,720
you have to wait
for them to finish.

1690
01:24:29,720 --> 01:24:31,950
OK, so you can
conceive materials

1691
01:24:31,950 --> 01:24:34,140
where the index of
refraction is variable.

1692
01:24:34,140 --> 01:24:36,780
So the example I gave
before is the air, where,

1693
01:24:36,780 --> 01:24:40,480
because of temperature,
pressure, and so on,

1694
01:24:40,480 --> 01:24:41,830
the index changes.

1695
01:24:41,830 --> 01:24:43,540
So if the index is
functional position,

1696
01:24:43,540 --> 01:24:46,805
you can define a quantity that
is called the optical path

1697
01:24:46,805 --> 01:24:47,305
length.

1698
01:24:47,305 --> 01:24:50,430
So if you follow the
trajectory of the ray--

1699
01:24:50,430 --> 01:24:53,580
so here is the ray, and
that is its trajectory--

1700
01:24:53,580 --> 01:24:59,650
you can integrate the
index of refraction

1701
01:24:59,650 --> 01:25:03,190
in small, individual segments
as the light propagates

1702
01:25:03,190 --> 01:25:06,450
along the ray.

1703
01:25:06,450 --> 01:25:09,210
So the basic
principle that I would

1704
01:25:09,210 --> 01:25:12,810
like you to carry with you
when you leave this class today

1705
01:25:12,810 --> 01:25:16,140
is that the basic
law that covers

1706
01:25:16,140 --> 01:25:20,780
light propagation in
the ray description

1707
01:25:20,780 --> 01:25:22,950
is that this quantity,
the optical path,

1708
01:25:22,950 --> 01:25:23,850
must be preserved--

1709
01:25:23,850 --> 01:25:25,963
I'm sorry, it must be minimized.

1710
01:25:25,963 --> 01:25:27,380
Of course, it has
to be preserved.

1711
01:25:27,380 --> 01:25:29,475
It also has to be minimized.

1712
01:25:29,475 --> 01:25:31,350
So if you have different
paths-- for example,

1713
01:25:31,350 --> 01:25:35,480
if you compare the path gamma
and the path gamma prime--

1714
01:25:35,480 --> 01:25:40,510
the light will take the path
where this quantity is minimal,

1715
01:25:40,510 --> 01:25:41,415
OK?

1716
01:25:41,415 --> 01:25:43,040
Now, that sounds very
abstract, I know,

1717
01:25:43,040 --> 01:25:45,650
but I will make it more
specific with examples.

1718
01:25:45,650 --> 01:25:47,990
For those of you who are
mechanical engineers-- or, more

1719
01:25:47,990 --> 01:25:50,030
likely, applied
mechanicians-- this

1720
01:25:50,030 --> 01:25:51,710
is reminiscent of
another principle

1721
01:25:51,710 --> 01:25:55,010
that you may have learned in
your Lagrangian mechanics.

1722
01:25:55,010 --> 01:25:58,790
You can make the same,
the exact same arguments

1723
01:25:58,790 --> 01:26:02,510
about particles moving
in a gravitational field.

1724
01:26:02,510 --> 01:26:04,670
Particles moving in--
that's the reason

1725
01:26:04,670 --> 01:26:07,660
why stars rotate
around the sun, why

1726
01:26:07,660 --> 01:26:09,110
they have elliptical
trajectories,

1727
01:26:09,110 --> 01:26:11,140
and so on, and so forth--
is because they also

1728
01:26:11,140 --> 01:26:16,200
obey a minimum path principle.

1729
01:26:16,200 --> 01:26:21,320
And well, let's see
it in action here.

1730
01:26:21,320 --> 01:26:23,590
So we apply this
principle-- we'll

1731
01:26:23,590 --> 01:26:25,600
apply it in several
occasions during the class,

1732
01:26:25,600 --> 01:26:29,290
but today, I would like
to apply to discover

1733
01:26:29,290 --> 01:26:31,570
what happens to
light when it arrives

1734
01:26:31,570 --> 01:26:34,490
at an interface
between two dialectics.

1735
01:26:34,490 --> 01:26:38,058
So on the left, you have
one dielectric-- say air--

1736
01:26:38,058 --> 01:26:39,850
and on the right-hand
side of an interface,

1737
01:26:39,850 --> 01:26:42,705
you have another
dielectric-- say glass.

1738
01:26:42,705 --> 01:26:44,080
So what will happen
to the light?

1739
01:26:44,080 --> 01:26:46,180
Well, two things will happen.

1740
01:26:46,180 --> 01:26:48,250
Some fraction of the
light energy-- that is,

1741
01:26:48,250 --> 01:26:52,060
some fraction of
individual photons--

1742
01:26:52,060 --> 01:26:54,080
will be reflected.

1743
01:26:54,080 --> 01:26:59,440
And some other fraction of the
light will enter the interface,

1744
01:26:59,440 --> 01:27:02,080
but it might enter
at an angle that

1745
01:27:02,080 --> 01:27:04,240
is different than
the angle of arrival.

1746
01:27:07,710 --> 01:27:12,120
That portion of light that
goes in, we call it refracted.

1747
01:27:12,120 --> 01:27:14,370
So this is the refracted
portion of the light.

1748
01:27:14,370 --> 01:27:16,710
It's a little bit confusing,
because the two terms

1749
01:27:16,710 --> 01:27:19,020
are the same except
for two letters.

1750
01:27:19,020 --> 01:27:21,690
So I hope you can sort of
recapture the difference.

1751
01:27:21,690 --> 01:27:26,010
One is reflected, and
the other is refracted.

1752
01:27:26,010 --> 01:27:28,750
So the question is, what is
the direction that these rays

1753
01:27:28,750 --> 01:27:31,040
propagate at the interface?

1754
01:27:31,040 --> 01:27:34,810
So we will invoke the minimal
path principle for that.

1755
01:27:34,810 --> 01:27:36,750
So consider, first, reflection.

1756
01:27:36,750 --> 01:27:38,220
And what I'm about
to say applies

1757
01:27:38,220 --> 01:27:42,600
to the electric interface just
as well as a mirror, a metal

1758
01:27:42,600 --> 01:27:45,080
or metallic mirror.

1759
01:27:45,080 --> 01:27:46,910
So the minimum
path principle says

1760
01:27:46,910 --> 01:27:49,850
that the light must be
reflected symmetrically.

1761
01:27:49,850 --> 01:27:54,200
So the reflected ray
makes the same angle

1762
01:27:54,200 --> 01:27:57,078
with the normal as the
incident ray, because that's

1763
01:27:57,078 --> 01:27:58,120
the minimum path, really.

1764
01:27:58,120 --> 01:28:04,140
If you force the light to
go to a different path--

1765
01:28:04,140 --> 01:28:06,308
for example, this way--

1766
01:28:06,308 --> 01:28:08,850
then you can see very easily,
it is a very simple calculation

1767
01:28:08,850 --> 01:28:16,192
to show that P, O, tilde p-prime
is longer than P, O, P, OK?

1768
01:28:16,192 --> 01:28:18,150
I will let you think
about that on your selves.

1769
01:28:18,150 --> 01:28:21,390
You can very easily convince
yourselves that this is true.

1770
01:28:21,390 --> 01:28:25,170
And therefore, the light must
follow the symmetric path.

1771
01:28:25,170 --> 01:28:26,850
So this is rule number one.

1772
01:28:26,850 --> 01:28:29,660
Let me skip the next slide.

1773
01:28:29,660 --> 01:28:32,980
I'll skip a little bit, and then
I'll come back to this later.

1774
01:28:32,980 --> 01:28:35,010
But I want to first
say something else.

1775
01:28:44,690 --> 01:28:47,120
OK.

1776
01:28:47,120 --> 01:28:49,150
When we think about the law of--

1777
01:28:49,150 --> 01:28:52,070
let's say we think about
the refracted light.

1778
01:28:52,070 --> 01:28:54,220
The [INAUDIBLE] is the medium.

1779
01:28:54,220 --> 01:28:56,680
OK, so the first thing
we need to do in order

1780
01:28:56,680 --> 01:28:59,938
to complete this calculation
is to define two points

1781
01:28:59,938 --> 01:29:00,480
from the ray.

1782
01:29:00,480 --> 01:29:03,550
So let's say you have
point p on the incident ray

1783
01:29:03,550 --> 01:29:06,460
and then point p-prime
on the refracted ray.

1784
01:29:09,250 --> 01:29:12,560
So let's compute this
quantity of the optical path.

1785
01:29:12,560 --> 01:29:15,910
So the optical part
equals the index

1786
01:29:15,910 --> 01:29:18,460
of refraction on
the leg on the left,

1787
01:29:18,460 --> 01:29:21,790
times the length
of the day from p

1788
01:29:21,790 --> 01:29:25,525
to the interface, and then
the index of refraction

1789
01:29:25,525 --> 01:29:28,270
in n prime on the
right-hand side,

1790
01:29:28,270 --> 01:29:32,430
times the length of the ray
from the interface to p prime.

1791
01:29:32,430 --> 01:29:35,280
So this, I will repeat
what I have on the slide.

1792
01:29:35,280 --> 01:29:37,072
I will repeat it
on the blackboard.

1793
01:29:41,010 --> 01:29:45,250
So you have n times
the hypotenuse.

1794
01:29:45,250 --> 01:29:47,805
So my notation here is
x for this distance,

1795
01:29:47,805 --> 01:29:49,980
z for this distance.

1796
01:29:49,980 --> 01:29:58,350
So that's the
hypotenuse plus n prime,

1797
01:29:58,350 --> 01:30:01,600
times the other hypotenuse.

1798
01:30:01,600 --> 01:30:05,340
So this other hypotenuse, if
I call h the vertical distance

1799
01:30:05,340 --> 01:30:08,160
between the two
points, simple geometry

1800
01:30:08,160 --> 01:30:10,300
solves that this
other hypotenuse

1801
01:30:10,300 --> 01:30:11,660
is something like that.

1802
01:30:19,610 --> 01:30:27,570
OK, so the question here--

1803
01:30:27,570 --> 01:30:28,860
how do I pose the question?

1804
01:30:28,860 --> 01:30:29,960
What is the unknown here?

1805
01:30:38,700 --> 01:30:42,930
What have I left unspecified?

1806
01:30:42,930 --> 01:30:45,170
Let me start with what I
have already specified.

1807
01:30:45,170 --> 01:30:47,810
I specified theta, the
angle of incidence.

1808
01:30:47,810 --> 01:30:51,060
I specified the two
points, p and p prime.

1809
01:30:51,060 --> 01:30:55,225
And I specified the
vertical distance h.

1810
01:30:55,225 --> 01:30:56,850
And also, I should
say that the z prime

1811
01:30:56,850 --> 01:31:01,750
is also specified, because z and
z prime are specified because,

1812
01:31:01,750 --> 01:31:04,560
OK, I have specified the
coordinates of p and p prime.

1813
01:31:04,560 --> 01:31:05,130
What is left?

1814
01:31:08,080 --> 01:31:14,178
theta prime, or another quantity
that is also left unspecified?

1815
01:31:18,760 --> 01:31:21,150
x and x prime, right?

1816
01:31:21,150 --> 01:31:23,120
Because the ray
might go like this.

1817
01:31:27,730 --> 01:31:30,910
All we know is that
the line starts at p

1818
01:31:30,910 --> 01:31:32,740
and ends at p prime.

1819
01:31:32,740 --> 01:31:33,880
It can go like this.

1820
01:31:33,880 --> 01:31:35,200
It can go like this.

1821
01:31:35,200 --> 01:31:36,420
It can go like this.

1822
01:31:36,420 --> 01:31:37,990
It can go like this, right?

1823
01:31:37,990 --> 01:31:39,830
Which is the case?

1824
01:31:39,830 --> 01:31:41,860
OK, so therefore,
each one of those

1825
01:31:41,860 --> 01:31:43,900
has a different value of x.

1826
01:31:43,900 --> 01:31:46,850
So how do we find x?

1827
01:31:46,850 --> 01:31:52,520
Well, Fermat says that light
must minimize this quantity.

1828
01:31:52,520 --> 01:31:55,120
The quantity that I
wrote on the blackboard

1829
01:31:55,120 --> 01:31:59,540
and on the slide, Fermat says
that it has to be minimized.

1830
01:31:59,540 --> 01:32:03,320
And OPL, by the way, stands
for Optical Path Length.

1831
01:32:03,320 --> 01:32:05,070
So to minimize it,
I have to compute

1832
01:32:05,070 --> 01:32:10,400
the derivative of this quantity
with respect to my unknown.

1833
01:32:10,400 --> 01:32:13,813
I manage to have only one
unknown of this quantity.

1834
01:32:13,813 --> 01:32:15,980
To find this unknown, I'd
better take the derivative

1835
01:32:15,980 --> 01:32:17,190
and set it to 0.

1836
01:32:17,190 --> 01:32:22,510
So if I take the derivative,
I will get n times--

1837
01:32:22,510 --> 01:32:23,590
what is the derivative?

1838
01:32:23,590 --> 01:32:24,090
Someone?

1839
01:32:29,378 --> 01:32:31,170
I guess I've had more
coffee than everyone,

1840
01:32:31,170 --> 01:32:32,825
so I can still do
the derivative.

1841
01:32:32,825 --> 01:32:35,960
So it is nx divided
by the square root,

1842
01:32:35,960 --> 01:32:42,600
minus n prime h minus x, divided
by the other square root, OK?

1843
01:32:45,590 --> 01:32:47,420
OK, give me, now, a
simple observation that

1844
01:32:47,420 --> 01:32:48,670
solves the problem right away.

1845
01:32:57,850 --> 01:32:58,880
That's right.

1846
01:32:58,880 --> 01:33:07,240
This quantity, x
over the hypotenuse,

1847
01:33:07,240 --> 01:33:08,480
is the sign of this angle.

1848
01:33:08,480 --> 01:33:12,110
This angle is the same
as this angle, right?

1849
01:33:12,110 --> 01:33:15,018
Therefore, this
quantity is its sine.

1850
01:33:15,018 --> 01:33:16,310
And the same for the other one.

1851
01:33:16,310 --> 01:33:23,000
The other quantity over here
is the sine of theta prime.

1852
01:33:23,000 --> 01:33:27,770
So if you substitute these
quantities into the derivation,

1853
01:33:27,770 --> 01:33:32,490
then you find this
relationship over here.

1854
01:33:32,490 --> 01:33:38,770
n times sine theta must equal
n prime times sine theta prime.

1855
01:33:38,770 --> 01:33:42,600
And this is the law of
refraction, also known

1856
01:33:42,600 --> 01:33:43,380
as Snell's Law.

1857
01:33:50,320 --> 01:33:53,560
So officially, I think,
we're out of time.

1858
01:33:53,560 --> 01:33:56,940
But I can take a
couple of very few--

1859
01:33:56,940 --> 01:33:59,720
I should say very
quick questions,

1860
01:33:59,720 --> 01:34:02,148
about that or about
anything else.

1861
01:34:02,148 --> 01:34:04,320
Yes?

1862
01:34:04,320 --> 01:34:09,880
AUDIENCE: So how is it that
you can assume p and p prime,

1863
01:34:09,880 --> 01:34:11,990
without knowing
these other things?

1864
01:34:11,990 --> 01:34:13,365
GEORGE BARBASTATHIS:
OK, so I was

1865
01:34:13,365 --> 01:34:15,443
hoping that you would ask that.

1866
01:34:15,443 --> 01:34:16,610
That's a very good question.

1867
01:34:16,610 --> 01:34:19,080
So the way this
problem is solved

1868
01:34:19,080 --> 01:34:26,310
is as follows I take for granted
that there is a light ray that

1869
01:34:26,310 --> 01:34:28,610
goes between p and p prime.

1870
01:34:28,610 --> 01:34:30,110
The reason I can
take it for granted

1871
01:34:30,110 --> 01:34:32,340
is another very basic
principle that says

1872
01:34:32,340 --> 01:34:35,040
that if I have a light source--

1873
01:34:35,040 --> 01:34:40,430
say it's p-- then
light propagates

1874
01:34:40,430 --> 01:34:43,460
in spherical bundles.

1875
01:34:43,460 --> 01:34:52,130
So I will actually have many,
many rays coming from p.

1876
01:34:52,130 --> 01:34:57,090
And if I have another point,
any point out here, p prime,

1877
01:34:57,090 --> 01:35:03,730
I will also have many,
many rays arriving here

1878
01:35:03,730 --> 01:35:05,720
from the left-hand side.

1879
01:35:05,720 --> 01:35:09,420
One of these rays
has come from p.

1880
01:35:09,420 --> 01:35:14,280
So the question is, how
can you connect these rays?

1881
01:35:14,280 --> 01:35:18,450
Well, the principle that
allows you to connect them

1882
01:35:18,450 --> 01:35:21,180
is the minimum path principle.

1883
01:35:21,180 --> 01:35:22,860
The problem can
become impossible.

1884
01:35:22,860 --> 01:35:25,680
I will show you examples
later where, in fact, you

1885
01:35:25,680 --> 01:35:29,723
might have a case where
no rays reach p prime.

1886
01:35:29,723 --> 01:35:30,640
You can see that here.

1887
01:35:30,640 --> 01:35:32,970
If I play with the numbers
and make one of these--

1888
01:35:32,970 --> 01:35:35,940
if I play with the numbers
so that one of the sines

1889
01:35:35,940 --> 01:35:39,320
becomes bigger than 1, then
the problem becomes impossible,

1890
01:35:39,320 --> 01:35:39,820
right?

1891
01:35:39,820 --> 01:35:42,210
So what it means is that
light never makes it there.

1892
01:35:45,760 --> 01:35:48,940
So this way of thinking
is very typical

1893
01:35:48,940 --> 01:35:53,680
when we deal with minimization
principles like Fermat

1894
01:35:53,680 --> 01:35:56,800
and Lagrangian
principles in mechanics.

1895
01:35:56,800 --> 01:35:59,830
We assume that our
particle, or our system,

1896
01:35:59,830 --> 01:36:03,270
or whatever has followed
a trajectory that

1897
01:36:03,270 --> 01:36:06,880
connects an initial point in
the space with the final point

1898
01:36:06,880 --> 01:36:08,100
in the space.

1899
01:36:08,100 --> 01:36:10,480
And then we try to find a
trajectory that minimizes

1900
01:36:10,480 --> 01:36:13,450
the part between the two points,
whether it is optical path

1901
01:36:13,450 --> 01:36:17,800
length, or Lagrangian
in mechanics,

1902
01:36:17,800 --> 01:36:20,380
or a lot of other
different contexts

1903
01:36:20,380 --> 01:36:22,660
where the same thinking applied.

1904
01:36:29,760 --> 01:36:31,057
Any other questions?

1905
01:36:34,800 --> 01:36:36,250
OK, so I will see you--

1906
01:36:36,250 --> 01:36:39,100
I will see you all in
Singapore next week,

1907
01:36:39,100 --> 01:36:43,500
and I will see you all
on video next week.