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PROFESSOR: In this
demonstration,

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we're going to look at
multiple-beam interference.

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We'll use a plane parallel
cavity at the beginning.

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And then, we'll go on to a
cavity using spherical mirrors.

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00:00:34,780 --> 00:00:37,600
The setup is here.

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We have a laser,
helium-neon laser.

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And here's the output
from the laser.

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Then, we reflect the
beam from the laser

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00:00:46,330 --> 00:00:50,200
into an optical isolator.

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00:00:50,200 --> 00:00:55,480
It's made up of a polarizer
and a quarter-wave plate.

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And the output from the
isolator is over here.

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It's then reflected
by this mirror

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00:01:01,810 --> 00:01:06,250
into the plane mirror cavity.

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So now, if we take a
close look at the cavity,

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you can see that it's made
up of two plane mirrors.

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00:01:14,530 --> 00:01:16,180
Here's one of them.

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00:01:16,180 --> 00:01:17,560
And here's the other.

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00:01:17,560 --> 00:01:22,870
The spacing between them is only
about 3.5 millimeters or so.

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00:01:22,870 --> 00:01:25,450
And one of the
mirrors is attached

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00:01:25,450 --> 00:01:28,120
to a piezoelectric
crystal over here,

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00:01:28,120 --> 00:01:30,670
so that we can change
the length of the cavity

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by simply applying a voltage
to the piezoelectric crystal.

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00:01:37,270 --> 00:01:40,240
As you see, the mounts are
pretty hefty to make sure

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00:01:40,240 --> 00:01:41,770
that the cavity is stable.

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00:01:41,770 --> 00:01:46,270
And adjustments can
be made to the cavity

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00:01:46,270 --> 00:01:50,980
by using the knobs over here.

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00:01:50,980 --> 00:01:54,910
The output of the
cavity, as you can see,

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00:01:54,910 --> 00:01:59,830
will be then displayed
on the screen over there.

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00:01:59,830 --> 00:02:07,540
Now, if we bring in the
screen as an insert,

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00:02:07,540 --> 00:02:14,400
we can see that we
have many, many dots.

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00:02:14,400 --> 00:02:19,570
And each dot
represents a reflection

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00:02:19,570 --> 00:02:22,030
by the pair of mirrors.

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00:02:22,030 --> 00:02:26,140
And you can see as I
misalign the mirrors,

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00:02:26,140 --> 00:02:30,130
I can separate out
the individual spots.

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00:02:30,130 --> 00:02:33,260
As I come in close
to alignment--

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00:02:37,780 --> 00:02:40,160
now, let me go to
the other side,

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00:02:40,160 --> 00:02:42,700
show that I can spread
it out the other way.

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00:02:42,700 --> 00:02:46,630
And then, if I change
the vertical alignment,

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00:02:46,630 --> 00:02:49,030
I can move them
all over the place.

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00:02:49,030 --> 00:02:52,720
Now, I'm ready to bring
them all in, so that they

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00:02:52,720 --> 00:02:54,213
can interfere with each other.

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00:02:54,213 --> 00:02:55,630
When they're
separated, of course,

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00:02:55,630 --> 00:02:57,172
they can't interfere
with each other.

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00:02:57,172 --> 00:03:00,130
Now, they are merging together.

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00:03:00,130 --> 00:03:04,750
And then, very soon we'll
see them interfering.

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00:03:04,750 --> 00:03:06,790
You can see already
they're interfering.

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00:03:06,790 --> 00:03:08,510
And now, it's dark.

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00:03:08,510 --> 00:03:11,080
Now, I can press
on the mirror here.

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00:03:11,080 --> 00:03:18,520
You'll see that I can change the
intensity from bright to dark.

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00:03:18,520 --> 00:03:22,780
And in order to see
it a little bit more

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00:03:22,780 --> 00:03:24,580
clearly, on the
control condition,

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00:03:24,580 --> 00:03:29,620
I'm going to turn
on a sweep voltage

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00:03:29,620 --> 00:03:31,780
to the piezoelectric crystal.

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00:03:31,780 --> 00:03:35,140
So maybe I can tweak the
alignment a little bit better.

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00:03:41,160 --> 00:03:45,600
Now, you can see it's going
from dark and bright--

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very nicely when
the beams interfere.

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00:03:47,220 --> 00:03:52,665
Now, let me separate
out the beams.

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00:03:52,665 --> 00:03:55,510
The interference stops.

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00:03:55,510 --> 00:04:00,120
Then as I bring
them back in when

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I have pretty close
to perfect alignment,

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you can see how they
all interfere together.

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00:04:07,500 --> 00:04:12,510
And the intensity goes
from bright to almost dark.

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Now, in the next part
of the demonstration,

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I'm going to put a
detector on the output

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and see what we see
with the detector.

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00:04:27,040 --> 00:04:29,550
I have now added
the detector, so

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00:04:29,550 --> 00:04:32,130
that we can look
at the output of

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the cavity both on the
detector, as well as directly

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on the screen.

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00:04:38,070 --> 00:04:41,310
So here is where I
put the detector.

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The output of the beam is
reflected by the beam splitter

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00:04:45,270 --> 00:04:48,420
here onto the detector.

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00:04:48,420 --> 00:04:50,460
And the output of
the detector then

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00:04:50,460 --> 00:04:54,880
goes onto the
internal oscilloscope.

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00:04:54,880 --> 00:04:58,390
Also, since this
is a beam splitter,

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the direct output of
the cavity can still

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00:05:02,280 --> 00:05:06,900
be monitored on the screen.

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00:05:06,900 --> 00:05:11,720
Now, let's look at the
screen of the oscilloscope.

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00:05:11,720 --> 00:05:16,572
As you can see, we
have two resonances.

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00:05:16,572 --> 00:05:18,030
But let's forget
about one of them.

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00:05:18,030 --> 00:05:20,690
Let's just concentrate on one.

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00:05:25,840 --> 00:05:28,210
What this represents
is the intensity

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00:05:28,210 --> 00:05:31,240
transmitted through the
cavity as a function

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00:05:31,240 --> 00:05:33,850
of pathlength difference.

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00:05:33,850 --> 00:05:35,530
And the pathlength
difference is being

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00:05:35,530 --> 00:05:39,620
scanned by the piezoelectric
crystal I mentioned before.

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00:05:39,620 --> 00:05:44,510
You can see, if I
block the light,

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00:05:44,510 --> 00:05:46,360
then that's where the zero is.

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00:05:46,360 --> 00:05:49,090
And when the light
is unblocked, you

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00:05:49,090 --> 00:05:52,180
can see that I get
a peak intensity due

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00:05:52,180 --> 00:05:54,460
to the interference
of the multiple beams

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and then to very
little intensity

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due to, again,
destructive interference

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00:06:02,050 --> 00:06:03,430
of the multiple beams.

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00:06:03,430 --> 00:06:07,450
Now, let me bring in
the other resonance.

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00:06:10,270 --> 00:06:13,570
And the other resonnance
is due to the fact

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00:06:13,570 --> 00:06:18,700
that every time
the cavity length

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00:06:18,700 --> 00:06:20,860
is changed by a half
wavelength of light,

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00:06:20,860 --> 00:06:24,070
then we see another resonance.

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00:06:24,070 --> 00:06:26,920
The spacing between
the two resonances

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00:06:26,920 --> 00:06:29,200
is given by the
velocity of light C

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00:06:29,200 --> 00:06:34,420
divided by twice the length
of the cavity, or C over 2L.

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00:06:34,420 --> 00:06:36,670
Another interesting thing
that you want to observe

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00:06:36,670 --> 00:06:41,920
is the quality factor, so-called
the finesse of the cavity.

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00:06:41,920 --> 00:06:46,090
And the finesse of
the cavity is defined

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00:06:46,090 --> 00:06:47,920
as the free-spectral
range, which

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00:06:47,920 --> 00:06:50,290
is the separation between
these two resonances,

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00:06:50,290 --> 00:06:55,180
divided by the width
of the resonance.

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00:06:55,180 --> 00:06:59,620
In this case, the
finess is about 30.

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00:06:59,620 --> 00:07:02,770
Or sometimes, I can adjust
it to about 50 or so

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00:07:02,770 --> 00:07:07,480
because my mirrors
have 95% reflectivity.

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00:07:07,480 --> 00:07:12,700
So what I'd like
to do now is show

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00:07:12,700 --> 00:07:15,580
what happens as I
misalign the cavity.

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00:07:15,580 --> 00:07:19,570
As you can see, every time I
just have to touch the cavity,

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00:07:19,570 --> 00:07:23,100
and the resonances move.

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00:07:23,100 --> 00:07:25,150
You can see now as
I'm misaligning just

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00:07:25,150 --> 00:07:27,790
by turning the
knob just slightly,

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00:07:27,790 --> 00:07:31,577
you can see that the finesse
goes way down because

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00:07:31,577 --> 00:07:32,410
of the misalignment.

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00:07:32,410 --> 00:07:39,280
Now as I try to pick it, and
I hope I can do it on camera,

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00:07:39,280 --> 00:07:41,740
and here we are.

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00:07:41,740 --> 00:07:47,650
I can always bring it
back where I was before.

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00:07:47,650 --> 00:07:51,130
Now you can see, if
I just tap on it,

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00:07:51,130 --> 00:07:56,110
I can move the resonances
all over the place.

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00:07:56,110 --> 00:08:03,220
Now, let's look at the spot
on the screen at the same time

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00:08:03,220 --> 00:08:08,120
as we look at the output of the
detector on the oscilloscope.

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00:08:08,120 --> 00:08:09,760
So this spot on
the screen then is

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00:08:09,760 --> 00:08:12,310
going to appear in the insert.

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00:08:12,310 --> 00:08:16,010
And you can see
that if I misalign--

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00:08:16,010 --> 00:08:18,250
let me do the
misalignment again--

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00:08:18,250 --> 00:08:23,320
you can see that you can
also notice it on the screen

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00:08:23,320 --> 00:08:26,498
also-- that the
spot is misaligned.

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00:08:33,820 --> 00:08:37,370
Let me see if I
can get it again.

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00:08:37,370 --> 00:08:38,740
Here we are.

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00:08:38,740 --> 00:08:42,250
Now, I'm going to take the
automatic scanning out.

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00:08:42,250 --> 00:08:46,460
And instead, I'll do
the scanning by hand.

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00:08:46,460 --> 00:08:49,120
So let's look at the spot.

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00:08:49,120 --> 00:08:53,260
Now you can see, I can vary the
intensity from bright and dark

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00:08:53,260 --> 00:08:56,680
by just simply
leaning on the mirror

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00:08:56,680 --> 00:08:59,740
to change the length
by very little bit.

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00:08:59,740 --> 00:09:05,110
Then, if we can now look
at the oscilloscope output,

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00:09:05,110 --> 00:09:13,720
we can see that when
the spot is pretty dark,

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00:09:13,720 --> 00:09:15,040
there's not much output.

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00:09:15,040 --> 00:09:18,640
And then, as I play
with the cavity here,

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00:09:18,640 --> 00:09:24,160
I can make the output
of the detector go big

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00:09:24,160 --> 00:09:26,740
and then to nothing.

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00:09:26,740 --> 00:09:29,770
Now so far, we only looked
at the light transmitted

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00:09:29,770 --> 00:09:34,030
through the cavity as a result
of multiple-beam interference.

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00:09:34,030 --> 00:09:37,960
We did not look at all at
the light reflected back

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00:09:37,960 --> 00:09:42,430
from the cavity as a result
of multiple-beam interference.

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00:09:42,430 --> 00:09:45,760
I need to modify the
setup just a little bit,

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00:09:45,760 --> 00:09:50,290
so that we can observe the light
reflected back from the cavity.

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00:09:50,290 --> 00:09:53,200
And when we do that,
we'll see that we

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00:09:53,200 --> 00:09:54,430
can learn a lot from it.

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00:09:58,470 --> 00:10:00,870
Now, the setup
has been modified,

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00:10:00,870 --> 00:10:03,570
so that we can observe
the light reflected

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00:10:03,570 --> 00:10:06,030
from the interferometer.

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00:10:06,030 --> 00:10:07,320
Here's the modification.

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00:10:07,320 --> 00:10:11,250
All we've done is added a
beam splitter over here,

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00:10:11,250 --> 00:10:16,770
so that the light reflected
from the interferometer

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00:10:16,770 --> 00:10:18,030
will be sampled--

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00:10:18,030 --> 00:10:19,710
here it is.

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00:10:19,710 --> 00:10:22,740
And then, we pass it onto
this mirror over here,

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00:10:22,740 --> 00:10:24,330
reflected onto
this beam splitter

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00:10:24,330 --> 00:10:28,650
here, and then into
detector number 2.

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00:10:28,650 --> 00:10:30,510
Since this is a
beam splitter, we

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00:10:30,510 --> 00:10:36,130
can also observe the reflected
light onto the screen.

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00:10:36,130 --> 00:10:40,340
Here is this left-hand spot.

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00:10:40,340 --> 00:10:46,380
The spot on the right
is our transmitted beam.

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00:10:50,130 --> 00:10:54,180
As you can see, if I
misalign the cavity,

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00:10:54,180 --> 00:10:57,770
you can see that both
of them will misalign.

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00:11:02,370 --> 00:11:03,870
Now, what I'm going
to do, I'm going

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00:11:03,870 --> 00:11:10,350
to take the scanner off and
do the scanning by hand.

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00:11:10,350 --> 00:11:13,320
Now if you watch
both spots, you'll

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see that the one on the right
that we've seen before flashes,

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00:11:18,870 --> 00:11:23,160
which means the intensity goes
very high and then very low.

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00:11:23,160 --> 00:11:27,870
But the spot on the left
doesn't seem to do anything.

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00:11:27,870 --> 00:11:32,100
Question is, is there anything
happening for the spot

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00:11:32,100 --> 00:11:35,490
on the left when the
transmitted beam is

187
00:11:35,490 --> 00:11:41,940
going through high
peaks and low valleys?

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00:11:41,940 --> 00:11:44,850
In order to do
this, we should look

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00:11:44,850 --> 00:11:49,950
at the oscilloscope, which
represents the output

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00:11:49,950 --> 00:11:53,390
of the two detectors.

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00:11:53,390 --> 00:11:55,880
Now, let me put this
scan back on again.

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00:11:55,880 --> 00:12:01,250
And let's look at
the oscilloscope.

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00:12:01,250 --> 00:12:06,870
The lower trace is
the transmitted light

194
00:12:06,870 --> 00:12:09,580
as we've seen before.

195
00:12:09,580 --> 00:12:14,330
The zero is here, and the peak
transmission is over here.

196
00:12:14,330 --> 00:12:19,400
The upper trace is the one
associated with the light

197
00:12:19,400 --> 00:12:21,155
reflected from the cavity.

198
00:12:24,401 --> 00:12:30,140
If I block the reflected
beam into the detector,

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00:12:30,140 --> 00:12:34,250
you can see that the zero is
over here, which is in line

200
00:12:34,250 --> 00:12:35,420
with that little marker.

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00:12:35,420 --> 00:12:36,170
Let's do it again.

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00:12:36,170 --> 00:12:37,760
Here is the zero.

203
00:12:37,760 --> 00:12:42,730
And when we have no
light transmitted,

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00:12:42,730 --> 00:12:46,460
there's a lot of
light reflected.

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00:12:46,460 --> 00:12:49,430
When we have a lot of
light transmitted, which

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00:12:49,430 --> 00:12:52,580
is the peak of the
transmission resonance,

207
00:12:52,580 --> 00:12:55,460
we have suddenly less
light being reflected,

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00:12:55,460 --> 00:12:57,020
but not quite zero.

209
00:12:57,020 --> 00:12:59,420
Remember, zero is over here.

210
00:12:59,420 --> 00:13:04,910
And the reason why we don't
dip all the way to zero

211
00:13:04,910 --> 00:13:10,640
is because the interference
is not complete.

212
00:13:10,640 --> 00:13:13,430
And maybe you want
to think about that.

213
00:13:13,430 --> 00:13:17,600
Now, let's see what happens
when I misalign the cavity.

214
00:13:17,600 --> 00:13:20,510
Let's look on the screen again.

215
00:13:20,510 --> 00:13:23,870
The upper trace, as we
see, is the reflected beam.

216
00:13:23,870 --> 00:13:25,970
And the lower trace is
the transmitted beam.

217
00:13:25,970 --> 00:13:31,460
As I misalign, first you see
that the length of the cavity

218
00:13:31,460 --> 00:13:32,180
changes.

219
00:13:32,180 --> 00:13:35,980
All we need is a lambda
by 2, and we get a change.

220
00:13:35,980 --> 00:13:37,520
But then, as I
misalign some more,

221
00:13:37,520 --> 00:13:41,000
you can see that
the finesse drops,

222
00:13:41,000 --> 00:13:44,180
or the width of the
resonance grows.

223
00:13:44,180 --> 00:13:48,500
And then as I realign,
indeed both of them

224
00:13:48,500 --> 00:13:52,860
are effected essentially
in the same way.

225
00:13:52,860 --> 00:13:56,990
So when we have
peak transmission

226
00:13:56,990 --> 00:14:02,120
in the transmitted light,
the reflected light

227
00:14:02,120 --> 00:14:03,680
goes through a minimum.

228
00:14:03,680 --> 00:14:07,580
Ideally, it would
go through zero.

229
00:14:07,580 --> 00:14:12,170
But we don't have
an ideal setup.

230
00:14:12,170 --> 00:14:16,070
In the next part of
the demonstration,

231
00:14:16,070 --> 00:14:19,160
we're going to show
what happens when

232
00:14:19,160 --> 00:14:24,920
the beam going into the cavity
is not the collimated beam.

233
00:14:24,920 --> 00:14:28,490
In this setup so far, the
beam going into the cavity

234
00:14:28,490 --> 00:14:31,250
was reasonably collimated.

235
00:14:31,250 --> 00:14:34,100
So what we'll do,
we'll put a lens,

236
00:14:34,100 --> 00:14:37,640
and we will then
generate an expanding

237
00:14:37,640 --> 00:14:39,470
beam that enters the cavity.

238
00:14:39,470 --> 00:14:43,430
So let's see what happens
when we have such a beam going

239
00:14:43,430 --> 00:14:45,220
into the cavity.