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I'm going to ask you a few
questions which have to do with

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a rainbow.
All of us have looked at

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rainbows.
But the question always comes

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up, have you really ever seen
it?

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I can ask you the same question
about art.

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All of us have looked at art,
which is very different from

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seeing art.
And so, here I have 15

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questions.
And let's look at them.

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And ask yourself,
how many of them can I answer?

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We've all looked at rainbows.
So, the first question is,

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what is the color sequence?
Is the red on the outside or on

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the inside?
And, what is the radius of the

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bow?
And what I mean by that is the

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following.
Say if here's the horizon and

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you see a rainbow.
Then there is somewhere a point

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that you can call the center of
the circle.

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And then you can always measure
the angle and terms of degrees,

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not in inches but in terms of
degrees.

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What is that [radius?]
typically?

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And then, we can ask the same
question about the length of the

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bow, the width of the bow.
There are colors here.

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How wide is that in terms of
angle, roughly?

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I don't expect you to be
precise, but roughly.

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Have you ever noticed that
there is an enormous difference

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and the light intensity outside
the bow and inside the bow?

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And if so, where is it bright
and where is it dark?

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Have you ever noticed that?
It will be staring you in the

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face when you look at the
rainbow.

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What time of day do you expect
the rainbow?

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Do you expect to see the north,
east, south,

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or west?
Are there more than one bow?

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And, yes, I already answered
that for you.

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There really is a secondary
goal.

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And then, the question is,
what is the color sequence of

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that second bow?
And where do you have to look

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for it?
What is its radius,

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and what is its width?
And then comes the question

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that all of you can answer
because of my problem set number

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ten.
There was a 10.4,

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which addressed the issue,
are the bows polarized?

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And then, what is the direction
of polarization?

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And is the polarization week or
is the polarization strong?

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All right, Professor Tegmark,
how many questions can you

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answer?
That's not bad.

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That is not bad.
Who can answer all 15?

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14?
13?

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12?
11?

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10?
Don't be ashamed.

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Nine?
Eight?

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Now comes an area where you may
have to become ashamed.

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Seven?
Six?

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Who can answer six?
That's not bad.

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Five?
Four?

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Who can only answer four?
Three?

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Two?
One?

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Who can answer zero?
I'm proud of you.

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All of you can at least answer
one.

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All right, I'm going to make
you see a rainbow the way you

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have never seen it before
because most of you have never

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seen a rainbow.
This is the picture that you

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also had on your problem set
number ten.

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Light from the sun in this case
comes straight from the left.

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We are going to give the sun an
angle in the sky very shortly.

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We used to call this angle
theta one.

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I called it I now for today,
angle of incidence.

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And I call this R.
When the light gets into the

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water drop, I call that the
angle of refraction.

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I call that R.
And so, with [Snell's?] law,

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we would then have that N1
times the sine of I,

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which is the angle of incidence
with which the light strikes the

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water drop, N1 times sine I
equals N2 times the sine of R.

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And for all practical purposes
N1 is one.

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That is in air.
And N2 is then an average value

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for water, N2.
Average value is about 1.336

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averaged over the colors.
I asked you in problem 10.4 to

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concentrate on the following
trajectory.

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Light strikes the water.
Some of it is reflected at A.

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I'm not interested in that.
I want to know what goes into

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the water.
At B, some of it comes out.

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I'm not interested in that.
I want to know how much is

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reflected.
And then, at C,

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some of it is reflected into
the water drop.

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Some of it is reflected into
the water drop.

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I'm not interested in that.
I want to know what's coming

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out.
And what you see now is what

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comes out and makes an angle phi
with this horizontal line.

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And, this angle,
phi, is going to play an

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important role in the rainbow.
The first thing I asked you in

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problem 10.4 oh form of the
first things to calculate,

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phi, in terms of I and R,
well, here is I,

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and the same angle I shows up
here.

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Here is an R.
Here is an R.

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Here is an R.
Here is an R.

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It's only a little bit of high
school algebra to show that phi

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is 4R minus 2I.
And, you've all done that

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because you've already turned in
your homework.

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So, what is interesting now:
if you take I is zero degrees,

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which is the light that strikes
the rainbow head on,

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so to speak,
then I is zero,

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right, because I is the angle
between the incident radiation

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and the normal to the surface.
So, that is zero.

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Then, R is also zero,
the angle of refraction,

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and consequently phi is zero.
In fact, what the latest doing

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penetrates the raindrop and it
comes straight back.

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So this angle,
phi, is then zero.

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But now comes something that is
very nonintuitive.

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If you increase I,
then we will all accept that R

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goes up.
And we will also all accept

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that phi goes up.
What is not so intuitive is

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that there comes a certain angle
of I for which phi has a maximum

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value which is roughly near 60
degrees for I.

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And when you hit the water drop
higher, that value for phi,

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which is the maximum value,
will go down.

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So there is no longer an angle,
phi, larger than a certain

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maximum, which I call phi
maximum.

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And, you can see that very
easily.

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It is a simple exercise that is
no more difficult than applying

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Snell's law.
You see Snell's law there at

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the top, and I remind you that
phi is 4R minus 2I.

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So, you pick an angle of I.
You calculate R with Snell's

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law, and you calculate phi.
And you see,

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indeed, that in the beginning
as I goes up,

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R goes up and phi goes up.
But, when you reach I of about

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60°, you see that phi reaches a
maximum, which is somewhere near

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41.6 degrees.
And, look when I is 70° and

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80° that phi is distinctly
lower.

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And this now is going to be the
key point in our rainbow.

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The first question that I can
ask you in 8.03 may be a little

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harder to ask high school
students.

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Can you calculate,
really, at what angle I you

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will get at maximum value for
phi?

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In other words,
this is sort of trial and

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error.
Can you actually algebraically

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derive that?
And that was also part of the

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homework assignment.
If what you now do is you say,

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[defy?] the I equals zero.
And then you have a long way to

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go.
It's actually surprising.

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It takes a long way
algebraically to finally

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conclude that indeed you can
calculate that angle of I for

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which phi is a maximum.
The cosine square of that angle

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is N squared minus one divided
by three.

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In other words,
this only gives you the angle

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of I for which phi is a maximum.
And so, you substitute in here

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the value for N.
In this case,

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you take 1.336.
And then you know what I is.

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Well, once you know what I is,
you can calculate what R is

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with Snell's law.
And then you know what phi

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maximum is because you know that
phi is, I wrote it on the

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blackboard here,
4R minus 2I.

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So, let us write now on the
blackboard here what happens for

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the different colors.
So we have here,

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N red is 1.331.
Notice that I'm now going to be

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rather specific about colors
because that's,

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of course, behind the rainbow.
And violet, which is sort of

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the shortest wavelength that we
can see for violet light,

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N is 1.343 for clean water.
Seawater: it is a little

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different.
So, it notice there is a 1%

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difference.
That means the speed of light

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for violet, blue light is about
1% lower in water than the speed

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of light of red light.
And so, with this equation,

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now, with these different
numbers for N,

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we can now calculate what I is
for which phi is a maximum

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value.
And, you will find,

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now, 58, 59.53.
You can now calculate the value

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for R, for which phi reaches
that maximum.

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You do that from using Snell's
law.

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You get 40.36 degrees.
And so, now you have your goal,

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which is your phi max value,
which is 42.37.

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And if you want to,
you can round all these off,

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of course.
And if we do the same for

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violet light,
then you get 58.83.

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And then for R,
we get 39.58.

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And for phi max,
you get 40.65.

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So, what does this mean,
now?

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This means that if sunlight
strikes a water drop,

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just one water drop,
that's all it takes,

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that a cone of light will be
reflected into the direction of

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the sun because all angles for I
are present.

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The sunlight comes from the
left, so all angles for I are

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present.
And so, let me put here one

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raindrop.
And let's still assume for now

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that the sunlight comes straight
from the left.

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It means, then,
that the largest value for phi

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is going to be a cone of light
because the whole problem is,

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of course, [axial?] symmetric.
You're dealing here with

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spheres.
So, red is really the winner.

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Red has the largest value for
phi maximum that exists.

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And [through?] that,
we have made a special triangle

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which has here,
for me, this angle of 42°.

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This was made a long time ago.
And so, I can now draw here an

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angle of 42°,
and 42° in this direction

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because the whole thing is axial
symmetric.

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And, that means a cone of light
whereby this angle rounded off

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is then 42.4°.
That is that maximum value for

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phi.
There's no value for phi that

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is larger.
And then, I need my violet

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light.
Where did I leave it?

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Oh, we have one here.
And then, the other colors have

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a smaller value for phi maximum.
This is not to scale.

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But this is,
then, the violet light.

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And so, inside here,
you have that cone for the

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violet light for which this
angle is smaller.

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It's about 40.65°.
At angles smaller than the

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maximum value for violet light,
all colors are being reflected

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back.
There is no restriction.

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There is only a restriction on
a maximum value for phi,

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but not on the minimum value.
That means that all other

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colors can come back inside this
cone.

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And therefore,
since all colors come back

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roughly with the same intensity,
it will be white light because

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all colors overlap.
Your brains will tell you that

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it is white light.
But, if you only concentrate on

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this journey,
refraction at A,

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reflection at B,
and refraction at A,

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there is no light that can come
out outside this cone.

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Keep that in mind.
So, suppose I had a screen

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here, and I had a small opening
through the screen so that the

219
00:14:25,683 --> 00:14:31,360
sunlight can fall through.
And I project on that screen,

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I intersect this cone with that
screen.

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What you'd see,
then, is the following.

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You would see a circle on the
outside, which is red.

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And then, you would see all the
other colors that follow.

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And then, the last color is the
violet, blue violet.

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The inside would be white
light.

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And outside,
there would be no light.

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Now, there's a key question
that some of you must be burning

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to ask.
And that is,

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how come the violet light in a
rainbow is so clear?

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The red is clear.
It's obvious why the red is

232
00:15:17,912 --> 00:15:22,267
clear, because the red is not
polluted by any other colors.

233
00:15:22,267 --> 00:15:25,795
Only the red can come out at an
angle of 42.4°.

234
00:15:25,795 --> 00:15:30,000
But the violet comes out at a
smaller angle.

235
00:15:30,000 --> 00:15:34,323
At that same smaller angle of
40.65°, to read can also come

236
00:15:34,323 --> 00:15:36,594
out.
And the green can also come

237
00:15:36,594 --> 00:15:38,939
out.
And the yellow can also come

238
00:15:38,939 --> 00:15:41,211
out.
So, why then is it that the

239
00:15:41,211 --> 00:15:45,387
violet is still so prominent?
That comes now down to light

240
00:15:45,387 --> 00:15:48,921
intensities.
If you calculate for the

241
00:15:48,921 --> 00:15:51,885
various colors,
and here you plot phi,

242
00:15:51,885 --> 00:15:55,488
the light intensity,
and remember intensity is

243
00:15:55,488 --> 00:15:59,252
always watts per square meter in
terms of units,

244
00:15:59,252 --> 00:16:03,256
then you will see that the red
light is the winner.

245
00:16:03,256 --> 00:16:07,260
This is this angle,
this 42.4° has a maximum here.

246
00:16:07,260 --> 00:16:10,303
It's enhanced.
It's not obvious at all.

247
00:16:10,303 --> 00:16:14,147
But, there is an enhancement at
that phi maximum.

248
00:16:14,147 --> 00:16:18,632
And then, the green light,
which is a little bit inverse,

249
00:16:18,632 --> 00:16:22,396
because phi maximum for green
is a little lower,

250
00:16:22,396 --> 00:16:28,147
would also have a maximum.
And then, ultimately the violet

251
00:16:28,147 --> 00:16:31,888
light, which is the last one,
will also have a maximum.

252
00:16:31,888 --> 00:16:35,490
And so, it is because of the
enhancements at that phi

253
00:16:35,490 --> 00:16:39,509
maximum, which is by no means
obvious, which doesn't follow

254
00:16:39,509 --> 00:16:42,695
from Snell's law,
but it follows from Fresnel's

255
00:16:42,695 --> 00:16:45,951
equations, that is the reason
why the blue here,

256
00:16:45,951 --> 00:16:49,000
the violet here,
still dominates.

257
00:16:49,000 --> 00:16:54,129
And here, although colors
overlap.

258
00:16:54,129 --> 00:17:01,590
And so, that's why you see the
white light there.

259
00:17:01,590 --> 00:17:09,518
So, now comes the question,
why do we see a rainbow?

260
00:17:09,518 --> 00:17:19,000
Well, I'm going to put you now
somewhere at a location.

261
00:17:19,000 --> 00:17:22,577
This is the ground.
And here you are.

262
00:17:22,577 --> 00:17:27,149
And the sun is in this
direction, the sunlight.

263
00:17:27,149 --> 00:17:31,621
And you know that because you
see your shadow.

264
00:17:31,621 --> 00:17:35,198
This is your head.
This is your body.

265
00:17:35,198 --> 00:17:40,565
And these are your legs.
You're looking straight at the

266
00:17:40,565 --> 00:17:45,335
shadow at your head here 180°
away from the sun.

267
00:17:45,335 --> 00:17:51,000
The sun is there and you see
your head there.

268
00:17:51,000 --> 00:17:54,551
And let us assume now because
that is a condition for a

269
00:17:54,551 --> 00:17:58,102
rainbow that it is raining or
that there is water here,

270
00:17:58,102 --> 00:18:01,126
and that somehow,
the sunlight is not obscured.

271
00:18:01,126 --> 00:18:03,823
In other words,
if it's also raining here,

272
00:18:03,823 --> 00:18:06,848
that's tough luck.
Then the sunlight cannot get

273
00:18:06,848 --> 00:18:08,886
through.
And so, you won't see a

274
00:18:08,886 --> 00:18:11,385
rainbow.
So, it is important that it is

275
00:18:11,385 --> 00:18:15,265
clear in the direction to the
sun, and that the sunlight can

276
00:18:15,265 --> 00:18:20,000
strike the raindrops without any
interference of clouds.

277
00:18:20,000 --> 00:18:24,296
So, it just so happens that
it's raining.

278
00:18:24,296 --> 00:18:28,592
And you look at the direction
of the sky.

279
00:18:28,592 --> 00:18:35,037
You are looking up in the sky.
And you pick any raindrop that

280
00:18:35,037 --> 00:18:40,299
you want on this line.
There are zillions of them.

281
00:18:40,299 --> 00:18:46,099
Let's just pick this one.
So, the sunlight strikes that

282
00:18:46,099 --> 00:18:52,968
raindrop like so.
And what does this one drop do?

283
00:18:52,968 --> 00:19:00,392
Like all the other zillions of
drops, they reflect into the

284
00:19:00,392 --> 00:19:06,279
direction of the sun a cone
which is like this.

285
00:19:06,279 --> 00:19:10,248
Each one does that
individually.

286
00:19:10,248 --> 00:19:12,935
So, there we go:
42°.

287
00:19:12,935 --> 00:19:19,079
Here is that cone.
And I will not draw the violet

288
00:19:19,079 --> 00:19:23,844
one.
And you look at that raindrop,

289
00:19:23,844 --> 00:19:29,060
and at all the others in this
direction will you see any

290
00:19:29,060 --> 00:19:31,241
light.
The answer is no.

291
00:19:31,241 --> 00:19:37,215
If you accept this picture that
no light can be further out than

292
00:19:37,215 --> 00:19:40,534
the maximum value of the cone
angle.

293
00:19:40,534 --> 00:19:45,275
So, you don't see any light
reflected from the sun.

294
00:19:45,275 --> 00:19:50,396
So, you see the dark sky,
because when it is raining in

295
00:19:50,396 --> 00:19:56,599
general, the sky is dark.
Now, you look in this

296
00:19:56,599 --> 00:20:01,552
direction.
You pick any raindrops in this

297
00:20:01,552 --> 00:20:06,133
direction.
There are zillions of them.

298
00:20:06,133 --> 00:20:11,457
Let's pick this one.
So, here comes the sun.

299
00:20:11,457 --> 00:20:17,152
And this one raindrop,
like zillions of others,

300
00:20:17,152 --> 00:20:23,219
is going to reflect into the
direction of the sun,

301
00:20:23,219 --> 00:20:30,771
a cone of light [whereby?] this
angle, 42°, and this angle is

302
00:20:30,771 --> 00:20:34,714
42°.
There it is.

303
00:20:34,714 --> 00:20:39,285
What will you see?
You see light.

304
00:20:39,285 --> 00:20:41,714
What color?
White.

305
00:20:41,714 --> 00:20:50,285
You are looking straight into
the inner cone because look how

306
00:20:50,285 --> 00:20:56,713
small the angle is.
You're looking right into this

307
00:20:56,713 --> 00:21:01,055
area somewhere here.
And so, you see white light.

308
00:21:01,055 --> 00:21:05,577
So, you look high in the sky.
You see the dark sky,

309
00:21:05,577 --> 00:21:08,291
the background.
You look lower,

310
00:21:08,291 --> 00:21:12,271
and then you say,
[ow?], white light from the

311
00:21:12,271 --> 00:21:15,256
sun.
And you will see in pictures,

312
00:21:15,256 --> 00:21:18,964
it's enormous.
But now, you look in a very

313
00:21:18,964 --> 00:21:23,396
special direction.
You are going to look into this

314
00:21:23,396 --> 00:21:30,000
direction, the direction which
is 42° away from this line

315
00:21:30,000 --> 00:21:33,437
So this angle,
now, is the famous 42.

316
00:21:33,437 --> 00:21:37,256
If you want to make it 42.4,
that's fine,

317
00:21:37,256 --> 00:21:39,929
degrees.
Away from this line,

318
00:21:39,929 --> 00:21:44,512
away from your shadow,
42.4°, and here is water,

319
00:21:44,512 --> 00:21:49,000
zillions of water drops along
the line.

320
00:21:49,000 --> 00:21:54,098
And here is the sun.
And the sunlight comes in like

321
00:21:54,098 --> 00:21:57,565
this.
What is this water drop going

322
00:21:57,565 --> 00:22:01,338
to do?
It's going to refract back into

323
00:22:01,338 --> 00:22:07,151
the direction of the sun a cone.
This happens to be in the

324
00:22:07,151 --> 00:22:11,434
direction of the 42°.
And then, of course,

325
00:22:11,434 --> 00:22:14,799
this is the direction of the
42°.

326
00:22:14,799 --> 00:22:20,000
So, here is that cone.
What do you see?

327
00:22:20,000 --> 00:22:23,146
What will you see?
You will see red light.

328
00:22:23,146 --> 00:22:25,754
You will see the light,
this light.

329
00:22:25,754 --> 00:22:30,282
So, you look high in the sky.
No light is reflected from the

330
00:22:30,282 --> 00:22:33,044
water.
You look at the 42.4° and you

331
00:22:33,044 --> 00:22:36,420
see only red.
And then you look way lower and

332
00:22:36,420 --> 00:22:40,180
you see white light.
And we now understand why you

333
00:22:40,180 --> 00:22:44,400
are going to see the other
colors, because we understand

334
00:22:44,400 --> 00:22:48,928
the enhancement due to Fresnel
equations of the green and of

335
00:22:48,928 --> 00:22:53,744
the violet.
And so, if here is the [SOUND

336
00:22:53,744 --> 00:22:57,435
OFF/THEN ON],
this is away from you now,

337
00:22:57,435 --> 00:23:02,924
since the whole thing is axial
symmetric, you can turn this

338
00:23:02,924 --> 00:23:07,845
around that line because a
sphere is axial symmetric,

339
00:23:07,845 --> 00:23:11,157
right?
All the rain drops have axial

340
00:23:11,157 --> 00:23:14,564
symmetry.
So, what you can do in this

341
00:23:14,564 --> 00:23:18,255
direction, 42°,
you can also do in this

342
00:23:18,255 --> 00:23:23,293
direction, 42°.
The sphere doesn't know the

343
00:23:23,293 --> 00:23:27,454
difference between up and down
and left and right.

344
00:23:27,454 --> 00:23:32,380
And so, what you're going to
see now is you're going to see

345
00:23:32,380 --> 00:23:35,947
an outside bow,
which has a radius of about

346
00:23:35,947 --> 00:23:39,430
42.5 degrees.
Here would be your shadow on

347
00:23:39,430 --> 00:23:42,742
the ground.
And so, this angle would be,

348
00:23:42,742 --> 00:23:46,394
very roughly,
then, the 42° if I round that

349
00:23:46,394 --> 00:23:49,027
off.
And then, you would see the

350
00:23:49,027 --> 00:23:54,247
other colors follow.
And then ultimately you would

351
00:23:54,247 --> 00:23:57,734
see the violet.
And, you know which angle that

352
00:23:57,734 --> 00:24:00,369
would be.
That would be at the 46.5

353
00:24:00,369 --> 00:24:03,082
there.
I draw the bow specifically a

354
00:24:03,082 --> 00:24:07,732
little lower than your horizon
because there is nothing wrong

355
00:24:07,732 --> 00:24:10,832
with the rain falling,
of course, nearby.

356
00:24:10,832 --> 00:24:15,017
If the rain is very close,
you can actually extend this

357
00:24:15,017 --> 00:24:17,730
even further.
So you often see that,

358
00:24:17,730 --> 00:24:23,000
but the rainbow extends below
the horizon, of course.

359
00:24:23,000 --> 00:24:26,951
And so, this angle,
then, indicates the elevation

360
00:24:26,951 --> 00:24:30,984
of the sun, how high the sun is
above the horizon.

361
00:24:30,984 --> 00:24:34,606
And if the sun is very low
above the horizon,

362
00:24:34,606 --> 00:24:39,051
this point will be here.
And you will see a much larger

363
00:24:39,051 --> 00:24:41,932
bow.
In fact, the bow at sunrise and

364
00:24:41,932 --> 00:24:46,460
sunset, this angle is 90°.
But, if the sun rises in the

365
00:24:46,460 --> 00:24:51,231
sky, then this point goes down.
And with that,

366
00:24:51,231 --> 00:24:54,045
the bow goes down,
and therefore,

367
00:24:54,045 --> 00:24:57,914
during midday,
you almost never see rainbows.

368
00:24:57,914 --> 00:25:02,047
That's the reason,
because the whole bow is then

369
00:25:02,047 --> 00:25:06,532
below the horizon unless you
spray water around you.

370
00:25:06,532 --> 00:25:11,017
Nature produces two bows.
One is called the primary,

371
00:25:11,017 --> 00:25:14,623
which is that one.
And other is called the

372
00:25:14,623 --> 00:25:17,964
secondary.
And the secondary bow is the

373
00:25:17,964 --> 00:25:22,977
result of light that makes one
extra reflection inside the

374
00:25:22,977 --> 00:25:27,174
water.
And so, I have not shown here

375
00:25:27,174 --> 00:25:31,599
every time when the light comes
in that some of it gets back

376
00:25:31,599 --> 00:25:34,825
into the air.
I've only shown the trajectory

377
00:25:34,825 --> 00:25:38,575
of the key light that I need to
make the secondary.

378
00:25:38,575 --> 00:25:42,250
Here, the light strikes high up
on the water drop.

379
00:25:42,250 --> 00:25:46,599
Here it strikes low on water.
In fact, this angle is around

380
00:25:46,599 --> 00:25:48,924
72°.
It refracts into the rain,

381
00:25:48,924 --> 00:25:52,224
reflection number one,
reflection number two,

382
00:25:52,224 --> 00:25:57,010
and here it comes out.
And this is then that angle,

383
00:25:57,010 --> 00:25:59,380
phi.
Compare that with this angle,

384
00:25:59,380 --> 00:26:02,180
phi, right?
The radiation comes out like

385
00:26:02,180 --> 00:26:06,202
this, and I define this as the
angle with the horizontal.

386
00:26:06,202 --> 00:26:10,510
So, that's really this angle.
Sorry that it's a little bit on

387
00:26:10,510 --> 00:26:14,172
the edge of the blackboard.
If you do your homework,

388
00:26:14,172 --> 00:26:17,404
the same way that I have done
for the primary,

389
00:26:17,404 --> 00:26:22,000
you will see that now there is
not a maximum value.

390
00:26:22,000 --> 00:26:26,631
But there is now a minimum
value for phi.

391
00:26:26,631 --> 00:26:33,347
So now, we have phi minimum.
And the values for phi minimum

392
00:26:33,347 --> 00:26:39,599
for the red light is 50.37°.
And for the violet light,

393
00:26:39,599 --> 00:26:43,884
it is 53.47°.
So, this means that the

394
00:26:43,884 --> 00:26:50,715
secondary bow is higher in the
sky than the primary because,

395
00:26:50,715 --> 00:26:57,235
look, the radii are larger.
But it also means that the

396
00:26:57,235 --> 00:27:01,363
colors are reversed.
The red is inside the violet

397
00:27:01,363 --> 00:27:03,856
bow.
So, if I make an attempt,

398
00:27:03,856 --> 00:27:08,843
this would be the outside of
the bow, and this would be the

399
00:27:08,843 --> 00:27:12,369
inside of the bow.
And then, very roughly,

400
00:27:12,369 --> 00:27:16,152
the radius, if I round that off
a little bit,

401
00:27:16,152 --> 00:27:22,000
the radius is about 50 because
this radius is about 52°.

402
00:27:22,000 --> 00:27:24,517
Now, the secondary bow is much
fainter.

403
00:27:24,517 --> 00:27:27,962
And that's why many of you
would have been staring at

404
00:27:27,962 --> 00:27:31,474
rainbows were so impressed by
the primary, which is so

405
00:27:31,474 --> 00:27:35,051
dominant that you don't pay
attention to the secondary.

406
00:27:35,051 --> 00:27:38,629
It's much feinter (sic).
The reason why it's feinter is

407
00:27:38,629 --> 00:27:42,737
that you people know because you
worked with Fresnel equations.

408
00:27:42,737 --> 00:27:46,049
You have an extra reflection
inside the water drop.

409
00:27:46,049 --> 00:27:49,428
That means, of course,
the light intensity goes down

410
00:27:49,428 --> 00:27:52,277
dramatically.
The secondary is substantially

411
00:27:52,277 --> 00:27:56,076
feinter.
So now, I'd like to look at

412
00:27:56,076 --> 00:27:59,461
some slides to see what we have
derived here,

413
00:27:59,461 --> 00:28:02,692
whether we can see that also in
our slides.

414
00:28:02,692 --> 00:28:06,615
So, we'll turn this off,
make sure that I have light

415
00:28:06,615 --> 00:28:09,461
enough.
Yes, it's OK to start with the

416
00:28:09,461 --> 00:28:12,461
first slide.
Yeah, if you turn the light

417
00:28:12,461 --> 00:28:15,230
off, thank you very much.
So, Marcos?

418
00:28:15,230 --> 00:28:19,000
Oh, I have to do that myself,
right?

419
00:28:19,000 --> 00:28:22,171
I've been promoted to advancer
of the slides.

420
00:28:22,171 --> 00:28:25,702
So here you see a situation
that, oh, I wanted to,

421
00:28:25,702 --> 00:28:29,162
yeah, OK, that's fine.
This, the maestro himself,

422
00:28:29,162 --> 00:28:33,270
his name was Isaac Newton.
He understood the rainbow quite

423
00:28:33,270 --> 00:28:35,000
well.
In his book optics,

424
00:28:35,000 --> 00:28:38,531
you see this picture.
And you see here the viewer,

425
00:28:38,531 --> 00:28:40,477
which is you.
This is, then,

426
00:28:40,477 --> 00:28:42,783
that direction away from the
sun.

427
00:28:42,783 --> 00:28:45,594
So this is where your shadow
would fall.

428
00:28:45,594 --> 00:28:51,000
And here you see the inner
[ball?], which is the primary.

429
00:28:51,000 --> 00:28:55,839
[SOUND OFF/THEN ON] the lights
from the sun has one reflection

430
00:28:55,839 --> 00:28:57,901
in the back.
And then here,

431
00:28:57,901 --> 00:29:02,423
you see the secondary bow by
the light hits the water drop

432
00:29:02,423 --> 00:29:05,041
below, and then comes in this
way.

433
00:29:05,041 --> 00:29:08,849
So, the secondary bow is
outside the primary bow.

434
00:29:08,849 --> 00:29:13,768
And then, here is a sketch that
I made that indicates that even

435
00:29:13,768 --> 00:29:18,448
if the sun is very high in the
sky, if you want an ego trip,

436
00:29:18,448 --> 00:29:22,732
and if you spray your lawn,
then you can have a rainbow

437
00:29:22,732 --> 00:29:26,620
encircling your legs,
which gives you a feeling of

438
00:29:26,620 --> 00:29:31,672
great power.
Believe me, I've done it many

439
00:29:31,672 --> 00:29:34,714
times.
This is a painting from the

440
00:29:34,714 --> 00:29:39,967
eighth century from Turkey.
And I've always been intrigued

441
00:29:39,967 --> 00:29:44,391
by this painting.
It undoubtedly has a connection

442
00:29:44,391 --> 00:29:49,000
with the Bible because you see a
hand here.

443
00:29:49,000 --> 00:29:53,648
And I think in the Bible it
says I do set my bow in the

444
00:29:53,648 --> 00:29:55,627
clouds.
Now, you wonder,

445
00:29:55,627 --> 00:29:58,468
the color sequence is not
correct.

446
00:29:58,468 --> 00:30:02,427
But then again,
there is only blue and there is

447
00:30:02,427 --> 00:30:05,354
only red.
So, I think in this case,

448
00:30:05,354 --> 00:30:09,744
we have a few options.
One option is that the artist

449
00:30:09,744 --> 00:30:13,273
really didn't look carefully at
a rainbow.

450
00:30:13,273 --> 00:30:17,405
That's a possibility.
It's another possibility is

451
00:30:17,405 --> 00:30:23,000
that physics was different in
the eighth century.

452
00:30:23,000 --> 00:30:26,050
I think we can dismiss that
possibility.

453
00:30:26,050 --> 00:30:29,804
And then the third one,
which I think is the most

454
00:30:29,804 --> 00:30:34,340
likely, that it was a conscious
decision on the part of the

455
00:30:34,340 --> 00:30:37,156
artist.
He purposely or she purposely

456
00:30:37,156 --> 00:30:40,754
reversed the colors.
It was his or her opinion,

457
00:30:40,754 --> 00:30:44,664
impression of a rainbow.
And that's what art is all

458
00:30:44,664 --> 00:30:46,932
about.
And then, two colors is

459
00:30:46,932 --> 00:30:51,000
perfectly fine to get the idea
across.

460
00:30:51,000 --> 00:30:56,295
Anything in this country is for
sale, so, also rainbows.

461
00:30:56,295 --> 00:31:01,397
And they are dirt cheap.
For [SOUND OFF/THEN ON] bucks

462
00:31:01,397 --> 00:31:04,863
you can get a rainbow.
But as always,

463
00:31:04,863 --> 00:31:08,714
you get what you pay for.
This is a fake.

464
00:31:08,714 --> 00:31:11,698
Who wants a fake?
Because, look,

465
00:31:11,698 --> 00:31:14,875
the colors are the wrong
sequence.

466
00:31:14,875 --> 00:31:19,208
So let's not even look at this.
Rainbow maker,

467
00:31:19,208 --> 00:31:24,586
yeah, sure, ha.
When I started lecturing 8.03,

468
00:31:24,586 --> 00:31:27,862
that's a long time ago.
It was in 1973.

469
00:31:27,862 --> 00:31:32,775
And, I wanted so badly to
pictures of rainbows that I have

470
00:31:32,775 --> 00:31:37,603
made myself using a water hose
and spraying water around.

471
00:31:37,603 --> 00:31:41,913
And I managed to do that.
In fact, my daughter did.

472
00:31:41,913 --> 00:31:45,103
And so, water is coming from
the left.

473
00:31:45,103 --> 00:31:48,896
And what you see here is
clearly the primary,

474
00:31:48,896 --> 00:31:55,596
the red on the outside.
You see the blue violet on the

475
00:31:55,596 --> 00:31:59,911
inside.
You see all this white light?

476
00:31:59,911 --> 00:32:05,785
You understand now,
why there is this white light.

477
00:32:05,785 --> 00:32:12,378
But, look outside the bow.
You don't see the white light

478
00:32:12,378 --> 00:32:17,173
reflected.
So, that's why you see the sky

479
00:32:17,173 --> 00:32:20,170
so dark.
My poor daughter,

480
00:32:20,170 --> 00:32:27,242
Emma, she suffered so much with
a father who is a physicist.

481
00:32:27,242 --> 00:32:33,494
[LAUGHTER]
It was January because my

482
00:32:33,494 --> 00:32:41,182
lecture started in February.
And, it really was freezing

483
00:32:41,182 --> 00:32:44,537
cold.
And she was crying.

484
00:32:44,537 --> 00:32:52,365
But look, you have to sacrifice
sometimes for the sake of

485
00:32:52,365 --> 00:32:56,000
science.
Poor Emma.

486
00:32:56,000 --> 00:32:59,414
I also wanted to make an
attempt to get a picture of a

487
00:32:59,414 --> 00:33:01,992
secondary.
That is very difficult because

488
00:33:01,992 --> 00:33:05,085
the secondary is so feint.
So, I did that over my

489
00:33:05,085 --> 00:33:07,469
driveway.
I lived in Winchester at the

490
00:33:07,469 --> 00:33:09,530
time.
And so, you clearly see the

491
00:33:09,530 --> 00:33:12,043
primary.
I don't have to point out where

492
00:33:12,043 --> 00:33:14,685
the primary is.
And this is the secondary.

493
00:33:14,685 --> 00:33:17,842
It is further out.
And you see that the colors are

494
00:33:17,842 --> 00:33:21,000
reversed.
And it is much feinter.

495
00:33:21,000 --> 00:33:26,000



496
00:33:26,000 --> 00:33:28,518
A friend of mine,
Michael Sorgey [SP?],

497
00:33:28,518 --> 00:33:30,440
sent me this slide,
very nice.

498
00:33:30,440 --> 00:33:33,025
It was a waterfall somewhere in
Austria.

499
00:33:33,025 --> 00:33:37,135
You see very dramatic the white
lights from inside the bow that

500
00:33:37,135 --> 00:33:39,455
reflected light from inside the
bow.

501
00:33:39,455 --> 00:33:42,438
And then, it terminates right
here at the red,

502
00:33:42,438 --> 00:33:45,155
and of course there is water
here as well.

503
00:33:45,155 --> 00:33:49,000
But, it doesn't come back in
your direction.

504
00:33:49,000 --> 00:33:52,495
And that's why you see the dark
forest behind it.

505
00:33:52,495 --> 00:33:56,500
And now comes here a picture
that was given to me by Doc

506
00:33:56,500 --> 00:33:58,902
Johnson.
This picture was taken in

507
00:33:58,902 --> 00:34:02,689
Sapporo where there is the
famous VLA, the Very Large

508
00:34:02,689 --> 00:34:06,475
Array, radio telescope.
And now you see truly all the

509
00:34:06,475 --> 00:34:10,407
features that you want to see.
Your primary bow follows

510
00:34:10,407 --> 00:34:14,048
sequence as predicted.
And notice how much brighter

511
00:34:14,048 --> 00:34:19,000
this guy is inside the bow than
it is outside the bow.

512
00:34:19,000 --> 00:34:25,125
And then you see the secondary.
You see that the colors are

513
00:34:25,125 --> 00:34:27,976
reversed.
Now, keep in mind,

514
00:34:27,976 --> 00:34:31,778
the secondary only has a phi
minimum.

515
00:34:31,778 --> 00:34:38,115
So, that means light can go out
at a larger angle because phi

516
00:34:38,115 --> 00:34:43,818
minimum means only [NOISE
OBSCURES] brighter again than

517
00:34:43,818 --> 00:34:51,000
here because white light can
make it from two reflections.

518
00:34:51,000 --> 00:34:55,463
So, you see here quite
dramatically why it is so white

519
00:34:55,463 --> 00:35:00,010
here, why it is so dark here,
but why some of the light

520
00:35:00,010 --> 00:35:04,810
returns because of the fact that
the secondary has the phi

521
00:35:04,810 --> 00:35:08,010
minimum.
All this is the result of what

522
00:35:08,010 --> 00:35:12,136
we call geometric optics:
Snell's law and Fresnel,

523
00:35:12,136 --> 00:35:15,757
nothing else.
However, this is all very nice

524
00:35:15,757 --> 00:35:20,810
and dandy as long as the water
drops have a diameter of a few

525
00:35:20,810 --> 00:35:24,944
millimeters.
When the water drops become

526
00:35:24,944 --> 00:35:29,337
smaller, and this effect begins
to be noticeable around 1 or 2

527
00:35:29,337 --> 00:35:32,290
mm, then refraction starts to
play a role.

528
00:35:32,290 --> 00:35:36,756
And reflection has the ability
for constructive and destructive

529
00:35:36,756 --> 00:35:39,349
interference as we have seen in
8.03.

530
00:35:39,349 --> 00:35:43,526
And without going through the
mouth, which I cannot do this

531
00:35:43,526 --> 00:35:47,415
time, there is some other
lectures that I do go through

532
00:35:47,415 --> 00:35:51,123
the math.
I'm just telling you the result

533
00:35:51,123 --> 00:35:54,958
that you can see now sometimes
dark bands inside the bow.

534
00:35:54,958 --> 00:35:59,068
It's always on the inside of
the primary, and then of course,

535
00:35:59,068 --> 00:36:01,328
other areas are a little
brighter.

536
00:36:01,328 --> 00:36:04,616
The dark bands are then
destructive interference.

537
00:36:04,616 --> 00:36:08,657
And when you look carefully at
this one, these are called by

538
00:36:08,657 --> 00:36:12,904
the way super [numero rebows?].
And, when you look at this one,

539
00:36:12,904 --> 00:36:16,945
you can actually see such a
dark band here with a little bit

540
00:36:16,945 --> 00:36:20,884
of imagination.
Destruction becomes very

541
00:36:20,884 --> 00:36:25,596
important if the size of the
water drops gets down to 100 °,

542
00:36:25,596 --> 00:36:28,031
1/10 of a millimeter,
and 50 °.

543
00:36:28,031 --> 00:36:32,429
And when it is even smaller
than 50 °, diffraction ruins

544
00:36:32,429 --> 00:36:35,413
all the colors.
All the colors begin to

545
00:36:35,413 --> 00:36:39,026
overlap, and the bow also
becomes much lighter.

546
00:36:39,026 --> 00:36:43,267
And then when the colors go
away, you see white lights.

547
00:36:43,267 --> 00:36:45,701
And so, you see a white
rainbow.

548
00:36:45,701 --> 00:36:50,995
It's also called a fog bow.
I have never seen a white

549
00:36:50,995 --> 00:36:53,788
rainbow.
But I was so fortunate that

550
00:36:53,788 --> 00:36:57,778
when I lectured in 1973 for the
first time in 8.03,

551
00:36:57,778 --> 00:37:02,486
that there was a student in my
audience to that summer after

552
00:37:02,486 --> 00:37:06,556
the lecture went on an
expedition to the North Pole.

553
00:37:06,556 --> 00:37:11,104
And he was at [Fletcher?]
Island, and he sent me a picture

554
00:37:11,104 --> 00:37:15,653
of a white rainbow which you
will see very shortly that he

555
00:37:15,653 --> 00:37:21,000
took 340 miles from the North
Pole at Fletcher Island.

556
00:37:21,000 --> 00:37:24,408
He took it at 2 a.m.
in the morning at midnight in

557
00:37:24,408 --> 00:37:27,052
July when the sun is above the
horizon.

558
00:37:27,052 --> 00:37:30,530
And there is a striking example
of a white rainbow.

559
00:37:30,530 --> 00:37:34,704
And whenever you see a white
rainbow, it must still be water.

560
00:37:34,704 --> 00:37:37,695
It's not ice.
Ice doesn't give you rainbows.

561
00:37:37,695 --> 00:37:41,660
You need spherical symmetry.
You need spherical objects to

562
00:37:41,660 --> 00:37:44,443
get rainbows.
You always see super numero

563
00:37:44,443 --> 00:37:48,756
rebows because of the fact that
it is diffraction that is doing

564
00:37:48,756 --> 00:37:51,052
it.
And so, you see here this dark

565
00:37:51,052 --> 00:37:55,155
band here.
And then it starts white again.

566
00:37:55,155 --> 00:37:59,117
So, this is not so uncommon
that in white rainbows you see

567
00:37:59,117 --> 00:38:02,245
super numero rebows.
I've never seen this one.

568
00:38:02,245 --> 00:38:06,278
And, there is another thing,
another kind of rainbow that I

569
00:38:06,278 --> 00:38:09,058
have never seen that I would
like to see.

570
00:38:09,058 --> 00:38:12,604
And that is a rainbow that you
can see very shortly,

571
00:38:12,604 --> 00:38:15,941
very close to sunset,
very shortly before sunset,

572
00:38:15,941 --> 00:38:20,768
or very strongly after sunrise.
We all know because we have

573
00:38:20,768 --> 00:38:23,061
covered [rainy?] scattering in
8.03.

574
00:38:23,061 --> 00:38:26,729
Why, then, the sun only lets
red lights penetrate to you?

575
00:38:26,729 --> 00:38:29,873
The whole sky becomes red.
The clouds become red.

576
00:38:29,873 --> 00:38:33,475
There is only red light.
There's no white light anymore.

577
00:38:33,475 --> 00:38:36,947
There's no blue light.
There's no green light anymore.

578
00:38:36,947 --> 00:38:40,681
So, what is nature going to do
when it produces a rainbow?

579
00:38:40,681 --> 00:38:43,956
Everything turns red,
and that is what you see them

580
00:38:43,956 --> 00:38:45,724
here.
This is a red rainbow.

581
00:38:45,724 --> 00:38:49,000
And I wish I would ever see
that.

582
00:38:49,000 --> 00:38:53,510
Notice that all that white
light from inside the boat is

583
00:38:53,510 --> 00:38:56,708
red now.
But also notice that the bow is

584
00:38:56,708 --> 00:39:00,152
still there.
That clearly is an enhancement

585
00:39:00,152 --> 00:39:03,104
of red light at that angle of
42.4°.

586
00:39:03,104 --> 00:39:05,482
That's because of Mr.
Fresnel.

587
00:39:05,482 --> 00:39:09,255
That enhancement is still there
at phi maximum.

588
00:39:09,255 --> 00:39:12,125
That is not undone by the red
light.

589
00:39:12,125 --> 00:39:16,963
And so, it's not surprising,
then, that the bow itself still

590
00:39:16,963 --> 00:39:21,473
stands out very clearly,
and then that the inside of the

591
00:39:21,473 --> 00:39:27,099
bow becomes now also red.
You have now reached the point

592
00:39:27,099 --> 00:39:30,667
that you should be able to
answer all the questions.

593
00:39:30,667 --> 00:39:34,655
And to prepare you for that,
I think this is a good moment

594
00:39:34,655 --> 00:39:38,294
to have our four minute break,
our traditional break.

595
00:39:38,294 --> 00:39:40,883
So, we will reconvene in four
minutes.

596
00:39:40,883 --> 00:39:44,661
And then I expect all of you to
be able to answer these

597
00:39:44,661 --> 00:39:47,530
questions.
So, we will start again in four

598
00:39:47,530 --> 00:39:51,158
minutes.
[SOUND OFF/THEN ON] All right,

599
00:39:51,158 --> 00:39:53,748
so here is your chance.
Most of them,

600
00:39:53,748 --> 00:39:56,194
of course, are trivial for you
now.

601
00:39:56,194 --> 00:40:00,151
Clearly red is on the outside.
The radius is about 42°.

602
00:40:00,151 --> 00:40:02,741
You work through that
quantitatively,

603
00:40:02,741 --> 00:40:06,553
and the length of the bow,
yeah, that depends on where

604
00:40:06,553 --> 00:40:09,503
it's raining.
I mean, if it's only raining

605
00:40:09,503 --> 00:40:13,532
there, you would only see a
small portion of the rainbow,

606
00:40:13,532 --> 00:40:16,266
of course.
And what is important is the

607
00:40:16,266 --> 00:40:21,503
elevation of the sun.
The higher the elevation of the

608
00:40:21,503 --> 00:40:25,782
sun, the less rainbow you see.
We just discussed that.

609
00:40:25,782 --> 00:40:30,062
And then, the width of the bow,
ah, that's a good one.

610
00:40:30,062 --> 00:40:34,180
The width of the bow,
you would think that the width

611
00:40:34,180 --> 00:40:38,540
of the bow is the difference
between the two angles phi

612
00:40:38,540 --> 00:40:41,608
maximum.
And, that means that the width

613
00:40:41,608 --> 00:40:45,807
of the bow would then be 1.8°.
But, that's not true.

614
00:40:45,807 --> 00:40:50,652
If there are any astronomers in
my audience, you can probably

615
00:40:50,652 --> 00:40:55,496
tell me why you have to add to
the 1.8°, why you have to add

616
00:40:55,496 --> 00:41:01,017
half a degree.
The actual width is closer to

617
00:41:01,017 --> 00:41:04,658
2.3°.
The actual width is closer to

618
00:41:04,658 --> 00:41:06,531
2.3°.
Why is that?

619
00:41:06,531 --> 00:41:11,317
I see one hand.
I want to see a few more hands.

620
00:41:11,317 --> 00:41:16,000
Any astronomers?
[LAUGHTER] Why is it?

621
00:41:16,000 --> 00:41:21,000



622
00:41:21,000 --> 00:41:23,280
You tried, and the others
didn't.

623
00:41:23,280 --> 00:41:26,487
I said, is there an astronomer
in my audience?

624
00:41:26,487 --> 00:41:30,478
So, I'll give you a hint.
The sun is have a degree in the

625
00:41:30,478 --> 00:41:32,758
sky.
That means each point of the

626
00:41:32,758 --> 00:41:36,393
sun makes a rainbow.
And since in this direction you

627
00:41:36,393 --> 00:41:39,885
have half a degree,
and in this direction you have

628
00:41:39,885 --> 00:41:43,091
half a degree,
imagine that when you see these

629
00:41:43,091 --> 00:41:46,940
rainbows there that you
obviously get to spread in this

630
00:41:46,940 --> 00:41:52,000
direction of half a degree,
and also in this direction.

631
00:41:52,000 --> 00:41:54,677
And so, you have to add half a
degree.

632
00:41:54,677 --> 00:41:57,281
And that's actually quite
noticeable.

633
00:41:57,281 --> 00:42:00,248
The finite size of the sun,
have a degree,

634
00:42:00,248 --> 00:42:04,299
is the diameter of our sun.
And so, also the width of the

635
00:42:04,299 --> 00:42:07,844
secondary is not just the
difference between these

636
00:42:07,844 --> 00:42:10,811
numbers, which would give you
about 3.1°.

637
00:42:10,811 --> 00:42:14,501
But it's closer to 3.6°.
And so, we know there is a

638
00:42:14,501 --> 00:42:16,671
secondary.
The time of the day,

639
00:42:16,671 --> 00:42:21,990
yeah, well, when does it rain?
And when is the sun low in the

640
00:42:21,990 --> 00:42:24,247
sky?
Mid-day, you are not likely to

641
00:42:24,247 --> 00:42:27,631
see rainbows because the sun is
too high in the sky.

642
00:42:27,631 --> 00:42:30,020
It depends, of course,
on the season,

643
00:42:30,020 --> 00:42:33,869
whether it's summer or winter.
I've been told that it rains

644
00:42:33,869 --> 00:42:36,988
more often in the afternoon than
in the morning.

645
00:42:36,988 --> 00:42:39,842
If that's true,
then the afternoon is a more

646
00:42:39,842 --> 00:42:43,757
likely time than the morning.
And that is when the bow would

647
00:42:43,757 --> 00:42:46,876
obviously appear,
then, in the east when the sun

648
00:42:46,876 --> 00:42:49,772
is in the west.
And certainly,

649
00:42:49,772 --> 00:42:52,694
in Boston, the sun during
midday would never be in the

650
00:42:52,694 --> 00:42:54,680
north.
You have to go for that to the

651
00:42:54,680 --> 00:42:57,492
Southern Hemisphere.
So, you are not likely to see a

652
00:42:57,492 --> 00:43:00,250
rainbow in the south.
But you might see rainbows in

653
00:43:00,250 --> 00:43:03,613
the north and the winter when
the sun is lower in the horizon.

654
00:43:03,613 --> 00:43:05,985
So, that covers the idea of
time of the day,

655
00:43:05,985 --> 00:43:08,687
and in what direction.
So, the secondary is there.

656
00:43:08,687 --> 00:43:12,051
The color sequence is reversed.
We just discussed the width of

657
00:43:12,051 --> 00:43:14,698
the bow, and the radius of the
bow is about 52°.

658
00:43:14,698 --> 00:43:19,000
And now comes the question that
all of you have worked out.

659
00:43:19,000 --> 00:43:22,088
Problem set number ten is the
bow polarized,

660
00:43:22,088 --> 00:43:25,679
and the answer is yes.
And, is it weakly polarized?

661
00:43:25,679 --> 00:43:27,834
No.
It is enormously polarized.

662
00:43:27,834 --> 00:43:31,353
And you all came up,
I hope, with the right answer

663
00:43:31,353 --> 00:43:35,375
problem, 10.4 H I think it was.
91%, the linear degree of

664
00:43:35,375 --> 00:43:38,895
linear polarization is 91%,
and I will, of course,

665
00:43:38,895 --> 00:43:42,414
demonstrate that today.
As far as the direction of

666
00:43:42,414 --> 00:43:46,220
polarization is concerned,
well, think about Fresnel's

667
00:43:46,220 --> 00:43:50,243
equations, and think about the
Brewster angle because the

668
00:43:50,243 --> 00:43:54,049
Brewster angle is really
responsible for the fact that

669
00:43:54,049 --> 00:43:58,000
the rainbow is so highly
polarized.

670
00:43:58,000 --> 00:44:04,271
Remember, the tangent of the
Brewster angle in this case

671
00:44:04,271 --> 00:44:11,570
would be one divided by 1.336 if
I take this as the average index

672
00:44:11,570 --> 00:44:16,245
of refraction for light.
That leads, then,

673
00:44:16,245 --> 00:44:22,289
to a Brewster angle of about
theta Brewster of roughly

674
00:44:22,289 --> 00:44:25,866
36.8°.
But, remember that R,

675
00:44:25,866 --> 00:44:30,400
this angle of reflection,
when you make the rainbow,

676
00:44:30,400 --> 00:44:34,222
that R is 40°.
That's where the colors come

677
00:44:34,222 --> 00:44:36,800
from.
Well, that is only a few

678
00:44:36,800 --> 00:44:40,000
degrees away from the Brewster
angle.

679
00:44:40,000 --> 00:44:44,977
So, as this light comes in un
polarized, here it is still

680
00:44:44,977 --> 00:44:49,155
perhaps not completely
unpolarized, but not very

681
00:44:49,155 --> 00:44:53,830
strongly polarized.
But it is here that the action

682
00:44:53,830 --> 00:44:55,845
starts.
This angle is within a few

683
00:44:55,845 --> 00:44:59,446
degrees of the Brewster angle.
So this light that comes back

684
00:44:59,446 --> 00:45:02,619
is polarized perpendicular to
the plane of incidence.

685
00:45:02,619 --> 00:45:05,366
And so, whatever comes out here
is, of course,

686
00:45:05,366 --> 00:45:08,051
also perpendicular to the plane
of incidence.

687
00:45:08,051 --> 00:45:10,492
So the E vector is oscillating
like this.

688
00:45:10,492 --> 00:45:13,483
Remember, the plane of
incidents is defined as the

689
00:45:13,483 --> 00:45:18,000
direction of the light and then
normal through the surface.

690
00:45:18,000 --> 00:45:21,117
So that, in this case,
the blackboard.

691
00:45:21,117 --> 00:45:23,982
And so, the radiation is
polarized.

692
00:45:23,982 --> 00:45:28,110
You have calculated it for 91%
linearly polarized.

693
00:45:28,110 --> 00:45:32,323
And, because of the actual
symmetry of the problem,

694
00:45:32,323 --> 00:45:36,873
that means it is polarized like
this in this direction.

695
00:45:36,873 --> 00:45:39,654
And here it's polarized like
this.

696
00:45:39,654 --> 00:45:43,529
And here it's polarized like
that, nearly 100%.

697
00:45:43,529 --> 00:45:47,574
When I see a rainbow,
I always check whether it's

698
00:45:47,574 --> 00:45:52,208
really polarized because I
always worry about it someday

699
00:45:52,208 --> 00:45:58,010
maybe it will be polarized.
And so when I go to the beach,

700
00:45:58,010 --> 00:45:59,954
which I often do:
Plum Island,

701
00:45:59,954 --> 00:46:03,305
one hour north of here;
wonderful reservation land.

702
00:46:03,305 --> 00:46:06,723
And in the afternoon,
the sun is there and the ocean

703
00:46:06,723 --> 00:46:09,739
water is there.
Then the waves come in and the

704
00:46:09,739 --> 00:46:12,756
water splashes up.
And then, 42° away from my

705
00:46:12,756 --> 00:46:15,638
shadow, when the water splashes
up, rainbow.

706
00:46:15,638 --> 00:46:17,447
Rainbow here,
rainbow there.

707
00:46:17,447 --> 00:46:21,000
The water splashes up high,
beautiful.

708
00:46:21,000 --> 00:46:23,470
Rainbow just for me.
Beautiful.

709
00:46:23,470 --> 00:46:28,494
And I remember a few years ago
I took a friend to Plum Island.

710
00:46:28,494 --> 00:46:31,129
His name is Bill Predorski
[SP?].

711
00:46:31,129 --> 00:46:35,329
He's also a physicist.
And we were looking at it and

712
00:46:35,329 --> 00:46:38,376
splashing the water.
And I said, Bill,

713
00:46:38,376 --> 00:46:42,082
look at the rainbow.
Bill looks, what rainbow?

714
00:46:42,082 --> 00:46:44,141
It's not raining,
he says.

715
00:46:44,141 --> 00:46:49,000
I said, look at the water.
Look at the waves.

716
00:46:49,000 --> 00:46:52,255
Bill looks: nothing.
I said, well,

717
00:46:52,255 --> 00:46:55,904
let's just wait for a really
good one.

718
00:46:55,904 --> 00:46:59,554
And boy, it was a real wave
coming in.

719
00:46:59,554 --> 00:47:03,993
And the water splashed up,
a gorgeous rainbow.

720
00:47:03,993 --> 00:47:09,023
Bill did not see a thing.
So I got a little annoyed.

721
00:47:09,023 --> 00:47:13,363
And then, I looked at Bill.
I looked at Bill.

722
00:47:13,363 --> 00:47:18,000
And he looked like this.
[LAUGHTER]

723
00:47:18,000 --> 00:47:20,630
And then, I knew.
And he knew too,

724
00:47:20,630 --> 00:47:25,413
because polarized sunglasses
are designed in such a way which

725
00:47:25,413 --> 00:47:29,876
was covered in 8.03 that the
direction of polarization is

726
00:47:29,876 --> 00:47:32,666
like this.
But the bow is like that.

727
00:47:32,666 --> 00:47:36,173
And so, you killed the bow.
So, I said, Bill,

728
00:47:36,173 --> 00:47:39,442
would you please take your
sunglasses off?

729
00:47:39,442 --> 00:47:41,753
And he did.
And I was waiting,

730
00:47:41,753 --> 00:47:46,615
and boy, there came a wave so
fantastic and Bill looked and he

731
00:47:46,615 --> 00:47:51,000
says, nice rainbow water,
very low key.

732
00:47:51,000 --> 00:47:54,179
He comes from the south,
you know?

733
00:47:54,179 --> 00:47:56,491
Nice rainbow water.
Yeah.

734
00:47:56,491 --> 00:48:01,887
That was a nice experience.
So, now I want to demonstrate

735
00:48:01,887 --> 00:48:06,415
to you a rainbow.
I asked all of you to bring an

736
00:48:06,415 --> 00:48:09,498
umbrella.
But most of you didn't.

737
00:48:09,498 --> 00:48:14,508
Who brought an umbrella?
See, the problem is that the

738
00:48:14,508 --> 00:48:20,000
majority did not.
And we were afraid of that.

739
00:48:20,000 --> 00:48:22,935
So therefore,
we had to change the

740
00:48:22,935 --> 00:48:28,539
demonstration from real rain to
something that's a little bit of

741
00:48:28,539 --> 00:48:32,453
rain, in fact,
it is so little rain that it's

742
00:48:32,453 --> 00:48:36,190
only one raindrop.
It's not very much rain,

743
00:48:36,190 --> 00:48:37,702
is it?
Here it is.

744
00:48:37,702 --> 00:48:41,349
One raindrop,
can I make you see a rainbow

745
00:48:41,349 --> 00:48:45,441
with one raindrop?
No, because you see here why

746
00:48:45,441 --> 00:48:51,876
you need millions of them.
Can I make you see this with

747
00:48:51,876 --> 00:48:54,342
one raindrop?
Yes, I can.

748
00:48:54,342 --> 00:48:58,760
Here's my light gun.
I'm going to blind you.

749
00:48:58,760 --> 00:49:03,486
And then, out of this one drop
comes this cone,

750
00:49:03,486 --> 00:49:07,390
red on the outside,
blue on the inside,

751
00:49:07,390 --> 00:49:11,705
and then white.
And, that's what I can show

752
00:49:11,705 --> 00:49:14,993
you.
And I can show you that this

753
00:49:14,993 --> 00:49:21,008
light is highly polarized.
I asked you to bring your

754
00:49:21,008 --> 00:49:25,587
polarizes, but not for this
demonstration because when the

755
00:49:25,587 --> 00:49:30,006
light reflects off the screen,
the polarization is lost.

756
00:49:30,006 --> 00:49:34,344
It's only on the way to the
screen that it's polarized.

757
00:49:34,344 --> 00:49:37,317
One water drop,
don't expect too much.

758
00:49:37,317 --> 00:49:41,655
It's only one water drop.
So, the rainbow will be feint

759
00:49:41,655 --> 00:49:45,431
if we call it a rainbow for now.
And, of course,

760
00:49:45,431 --> 00:49:50,251
you don't want to be blinded.
So, we are also going to absorb

761
00:49:50,251 --> 00:49:55,152
the sunlight so that you would
actually be able to see the bow

762
00:49:55,152 --> 00:49:59,233
there.
The light is so feint that your

763
00:49:59,233 --> 00:50:02,186
eyes have to adjust first to the
darkness.

764
00:50:02,186 --> 00:50:06,580
So, if we turn the lights off,
I'll give you 30 seconds to get

765
00:50:06,580 --> 00:50:09,533
used to the darkness.
And in the meantime,

766
00:50:09,533 --> 00:50:14,000
it is so properly timed that
the screen is coming down.

767
00:50:14,000 --> 00:50:26,000



768
00:50:26,000 --> 00:50:28,000
So let your eyes adjust.


769
00:50:28,000 --> 00:50:44,000


770
00:50:44,000 --> 00:50:46,788
And there it is.
If that's not red on the

771
00:50:46,788 --> 00:50:49,717
outside, what is?
If that's not blue on the

772
00:50:49,717 --> 00:50:52,715
inside, what is?
And you see the white light

773
00:50:52,715 --> 00:50:54,737
here?
This is the primary bow.

774
00:50:54,737 --> 00:50:58,571
This is not the secondary.
This is some weird reflection

775
00:50:58,571 --> 00:51:02,057
because of the glass.
And this is highly polarized.

776
00:51:02,057 --> 00:51:05,892
I have a polarimeter [SP?]
here, and I will hold that in

777
00:51:05,892 --> 00:51:08,611
the beam.
This is the way that the light

778
00:51:08,611 --> 00:51:10,842
can go through.
Can you see that?

779
00:51:10,842 --> 00:51:13,770
It goes through.
And now, I rotate it 90°,

780
00:51:13,770 --> 00:51:19,000
and I can kill that light.
It is nearly 100% polarized.

781
00:51:19,000 --> 00:51:21,371
If I do it here,
the angle is different.

782
00:51:21,371 --> 00:51:23,255
Polarization angle is like
this.

783
00:51:23,255 --> 00:51:26,417
So, this is the way that I can
let the light through.

784
00:51:26,417 --> 00:51:29,032
Of course, there's always
absorption, right,

785
00:51:29,032 --> 00:51:31,646
with a polarized?
Always 50% is lost anyhow,

786
00:51:31,646 --> 00:51:33,409
and then there's,
in addition,

787
00:51:33,409 --> 00:51:36,145
some absorption.
But it's clear that the light

788
00:51:36,145 --> 00:51:38,881
goes through there.
And now, I rotate it 90°,

789
00:51:38,881 --> 00:51:41,070
and then you kill it.
But, of course,

790
00:51:41,070 --> 00:51:43,927
the white light,
which is very close to the bow,

791
00:51:43,927 --> 00:51:46,724
is also the result of
reflection at that point,

792
00:51:46,724 --> 00:51:49,886
B, in the back of the water
drop so that white light,

793
00:51:49,886 --> 00:51:52,440
certainly the white lake here
and there is,

794
00:51:52,440 --> 00:51:57,000
of course, also very close to
the Brewster angle.

795
00:51:57,000 --> 00:51:59,312
So, that is also highly
polarized.

796
00:51:59,312 --> 00:52:03,375
And so, you can see that the
white light goes through here.

797
00:52:03,375 --> 00:52:06,949
And, if I rotate it 90°,
that white light also goes

798
00:52:06,949 --> 00:52:08,350
away.
And, of course,

799
00:52:08,350 --> 00:52:11,713
when you go further in,
then the degree of linear

800
00:52:11,713 --> 00:52:14,375
polarization becomes less.
So, this is,

801
00:52:14,375 --> 00:52:19,000
then, what you can do.
Yeah, we can have lights again.

802
00:52:19,000 --> 00:52:24,535
This is what you can do,
then, with one water drop.

803
00:52:24,535 --> 00:52:30,735
It has all the ingredients,
all the physics that you need

804
00:52:30,735 --> 00:52:34,832
to explain and understand the
rainbow.

805
00:52:34,832 --> 00:52:39,039
But it's really not the rainbow
itself.

806
00:52:39,039 --> 00:52:45,571
There are other phenomenon in
the sky which are very common.

807
00:52:45,571 --> 00:52:51,895
And, they are also remarkable.
And many of you may never have

808
00:52:51,895 --> 00:52:54,233
seen them.
And yet, they are so common

809
00:52:54,233 --> 00:52:57,644
that I see them every week.
And so I want you to become

810
00:52:57,644 --> 00:53:01,372
alert to them without going into
the details of the physics.

811
00:53:01,372 --> 00:53:04,910
Ice crystals high up in the
atmosphere can cause stunning

812
00:53:04,910 --> 00:53:07,248
halos.
The most famous one is the 22°

813
00:53:07,248 --> 00:53:11,228
halo that you can see around the
sun, and you can see around the

814
00:53:11,228 --> 00:53:13,250
moon.
You can see it's summer and

815
00:53:13,250 --> 00:53:16,978
winter because high up in the
atmosphere, temperature is way

816
00:53:16,978 --> 00:53:20,352
below freezing.
Red is on the inside.

817
00:53:20,352 --> 00:53:22,542
Colors are never truly
spectacular.

818
00:53:22,542 --> 00:53:26,599
The 22° halo is so common that
it's fair to say I see it almost

819
00:53:26,599 --> 00:53:29,304
every week.
And the reason why you probably

820
00:53:29,304 --> 00:53:32,652
don't, who wants to look in the
direction of the sun?

821
00:53:32,652 --> 00:53:35,615
That's a terrible thing to do.
Well, what I do,

822
00:53:35,615 --> 00:53:38,706
I first hold up my fist,
and I block out the sun.

823
00:53:38,706 --> 00:53:41,540
And then I look.
And that's why I see them so

824
00:53:41,540 --> 00:53:42,699
often.
The moon is,

825
00:53:42,699 --> 00:53:46,305
of course, easier because you
don't have to block out the

826
00:53:46,305 --> 00:53:49,461
lights from the moon.
So, if you look at the moon,

827
00:53:49,461 --> 00:53:53,196
very often several times a
month you see this gorgeous 22°

828
00:53:53,196 --> 00:53:57,709
halo.
And then, there are many other

829
00:53:57,709 --> 00:54:03,400
phenomenon of which I will show
you also a picture which are all

830
00:54:03,400 --> 00:54:07,374
the results of ice crystals.
They have names.

831
00:54:07,374 --> 00:54:10,716
They are called sun dogs,
a 46° halo.

832
00:54:10,716 --> 00:54:15,322
24 individual names are
identified in books in these

833
00:54:15,322 --> 00:54:20,832
various arcs tangent that you
see [SOUND OFF/THEN ON] from the

834
00:54:20,832 --> 00:54:25,431
ice crystals.
So, if I can have the next

835
00:54:25,431 --> 00:54:31,043
slide on this and make it dark,
then I think we are coming up

836
00:54:31,043 --> 00:54:34,971
to the 22° halo.
You see the red is on the

837
00:54:34,971 --> 00:54:37,964
inside.
It's not as colorful as a

838
00:54:37,964 --> 00:54:43,669
rainbow, but it's very distinct.
There is no question when you

839
00:54:43,669 --> 00:54:47,035
see it.
You know you are looking at a

840
00:54:47,035 --> 00:54:49,920
22° halo.
And this is,

841
00:54:49,920 --> 00:54:52,682
then, a phenomenon that is very
rare.

842
00:54:52,682 --> 00:54:57,056
I've never seen it so complete.
And this is the 22° halo.

843
00:54:57,056 --> 00:55:01,122
And then there is here one that
you don't see so well,

844
00:55:01,122 --> 00:55:05,265
which is the 46° halo.
And these things are called sun

845
00:55:05,265 --> 00:55:07,644
dogs.
And this arc has a special

846
00:55:07,644 --> 00:55:09,869
name.
The sun dogs I see often

847
00:55:09,869 --> 00:55:14,089
actually here in Boston.
They're not so uncommon at all.

848
00:55:14,089 --> 00:55:19,000
This picture was taken in the
South Pole station.

849
00:55:19,000 --> 00:55:24,187
So, this business is ice
crystals, is quite common.

850
00:55:24,187 --> 00:55:27,403
I lost my light,
but I found it.

851
00:55:27,403 --> 00:55:33,317
There is another phenomenon
which probably all of you have

852
00:55:33,317 --> 00:55:39,853
seen, which is called The Glory.
And The Glory is not the result

853
00:55:39,853 --> 00:55:46,181
of a refraction and reflection.
But The Glory is the result of

854
00:55:46,181 --> 00:55:50,435
diffraction.
You only see Glories when you

855
00:55:50,435 --> 00:55:55,745
have extremely fine water drops.
For instance,

856
00:55:55,745 --> 00:55:58,957
as you have them in clouds,
sometimes, and most commonly,

857
00:55:58,957 --> 00:56:02,341
you can see it when you fly
over clouds, and you have a seat

858
00:56:02,341 --> 00:56:05,094
away from the sun.
In fact, that's the reason why

859
00:56:05,094 --> 00:56:07,905
I always, when I make
reservations I always want a

860
00:56:07,905 --> 00:56:10,945
seat away from the sun.
Then you look in the direction

861
00:56:10,945 --> 00:56:13,182
where the shadow of your plane
would be.

862
00:56:13,182 --> 00:56:16,336
And if you fly very low,
you can actually see the shadow

863
00:56:16,336 --> 00:56:19,924
of your plane.
And then you see around the

864
00:56:19,924 --> 00:56:23,845
shadow of your plane these
beautifully colorful circles.

865
00:56:23,845 --> 00:56:27,552
They are complete circles.
Their diameter is a strong

866
00:56:27,552 --> 00:56:30,332
function of the size of the
water drops.

867
00:56:30,332 --> 00:56:34,253
Like with all diffractions,
the smaller the water drops,

868
00:56:34,253 --> 00:56:37,960
the larger the angle.
And the larger the water drops,

869
00:56:37,960 --> 00:56:41,596
the smaller the angle.
So, when you fly over various

870
00:56:41,596 --> 00:56:45,160
clouds, you may see that the
Glory changes in size.

871
00:56:45,160 --> 00:56:48,724
I've seen that many times.
And so, let me show you,

872
00:56:48,724 --> 00:56:54,000
then, a picture that I took
several years ago of a glory.

873
00:56:54,000 --> 00:56:57,270
Many of you have seen this.
In fact, I get countless

874
00:56:57,270 --> 00:57:00,669
pictures by e-mail from students
who took my lectures,

875
00:57:00,669 --> 00:57:04,453
and people who didn't take my
lectures who sent me this kind

876
00:57:04,453 --> 00:57:06,570
of stuff and say,
Professor Lewin,

877
00:57:06,570 --> 00:57:10,289
we've seen a complete rainbow.
Well, this has nothing to do

878
00:57:10,289 --> 00:57:13,047
with the rainbow.
Of course, you can see the

879
00:57:13,047 --> 00:57:15,805
angle is also way smaller.
But that depends,

880
00:57:15,805 --> 00:57:18,178
again, on the size of the water
drops.

881
00:57:18,178 --> 00:57:23,332
The angle can be very large.
And you can also know from this

882
00:57:23,332 --> 00:57:27,395
picture where my seat was.
You're always at the center,

883
00:57:27,395 --> 00:57:31,759
of course, where your camera is
at the center of the Glory.

884
00:57:31,759 --> 00:57:35,822
So I was sitting just behind
the wing, which is another

885
00:57:35,822 --> 00:57:40,186
reason why I not only want to
see on the side away from the

886
00:57:40,186 --> 00:57:44,325
sun, but I also want to have a
clear view of the ground,

887
00:57:44,325 --> 00:57:47,936
which is a little bit more
complicated sometimes.

888
00:57:47,936 --> 00:57:52,000
I always dreamed of sainthood.
[LAUGHTER]

889
00:57:52,000 --> 00:57:55,199
Chances are small,
but never zero.

890
00:57:55,199 --> 00:58:01,018
And so, I decided if I could
somehow create a Glory around my

891
00:58:01,018 --> 00:58:06,060
own head, can't do any harm.
Many years ago I visited

892
00:58:06,060 --> 00:58:11,490
Georgia, [the caucuses?].
It was still part of the Soviet

893
00:58:11,490 --> 00:58:14,981
Union.
And my host took me to the 6 m

894
00:58:14,981 --> 00:58:19,054
telescope they are,
which was, at the time,

895
00:58:19,054 --> 00:58:24,000
the largest optical telescope
on Earth.

896
00:58:24,000 --> 00:58:27,897
And I was welcomed very
gracefully, very nice food.

897
00:58:27,897 --> 00:58:32,419
And then, I talked to the local
astronomers, and they said,

898
00:58:32,419 --> 00:58:35,381
you know that this telescope is
a joke.

899
00:58:35,381 --> 00:58:38,032
It just cannot produce any
science.

900
00:58:38,032 --> 00:58:41,306
And I said, well,
what do you mean by that?

901
00:58:41,306 --> 00:58:44,346
They said, well,
it was put at the wrong

902
00:58:44,346 --> 00:58:46,997
location.
Every evening just before

903
00:58:46,997 --> 00:58:51,129
sunset, the fog comes up from
the valley and you can't

904
00:58:51,129 --> 00:58:54,975
observe.
You are in the clouds all

905
00:58:54,975 --> 00:58:57,662
night.
So, it's the most ridiculous

906
00:58:57,662 --> 00:59:02,167
thing here to have a telescope.
And then I said to myself,

907
00:59:02,167 --> 00:59:05,723
this is my chance,
because if the fog comes up

908
00:59:05,723 --> 00:59:09,121
from the valley,
if then I can photograph my

909
00:59:09,121 --> 00:59:13,310
shadow on the wall of fog,
because they said it really

910
00:59:13,310 --> 00:59:17,340
comes up like a wall,
then I will get a glory around

911
00:59:17,340 --> 00:59:21,237
my head.
And I thought they were joking.

912
00:59:21,237 --> 00:59:24,125
I said, well,
nice story, but you must be

913
00:59:24,125 --> 00:59:25,641
joking.
And they said,

914
00:59:25,641 --> 00:59:28,745
well, just come out at 5:30.
We'll show you.

915
00:59:28,745 --> 00:59:31,560
So, I came out at 5:30,
and fair enough,

916
00:59:31,560 --> 00:59:35,386
like a wall it came up.
And in a matter of one minute,

917
00:59:35,386 --> 00:59:39,212
we were in the clouds.
And we stayed in the clouds the

918
00:59:39,212 --> 00:59:42,171
whole night.
[LAUGHTER] The next day I had

919
00:59:42,171 --> 00:59:44,481
my camera.
And the sun was there.

920
00:59:44,481 --> 00:59:46,936
And the fog came perfectly on
time.

921
00:59:46,936 --> 00:59:50,906
The timing was very critical,
because the fog comes very

922
00:59:50,906 --> 00:59:56,763
quickly.
Let me first show you that the

923
00:59:56,763 --> 1:00:01,905
fog indeed comes like a wall.
There it is.

924
1:00:01,905 --> 1:00:06,296
That's the 6 m telescope in
Georgia.

925
1:00:06,296 --> 1:00:13,320
And then, this wall comes.
And in a matter of one minute,

926
1:00:13,320 --> 1:00:17,083
it's over you.
But I was quick.

927
1:00:17,083 --> 1:00:21,097
[LAUGHTER] St.
Walter, after all.

928
1:00:21,097 --> 1:00:29,000
Isn't that a nice example of a
Glory around my head?

929
1:00:29,000 --> 1:00:35,659
OK, then I have the next slide.
Oh, I think I have to do that.

930
1:00:35,659 --> 1:00:40,681
And then, I would like a little
bit more light.

931
1:00:40,681 --> 1:00:46,794
Can you put the light on TV?
I suppose that you recognize

932
1:00:46,794 --> 1:00:50,943
the slide.
It is the mystery picture of

933
1:00:50,943 --> 1:00:56,972
8.03 on the webpage.
It was the astronomy picture of

934
1:00:56,972 --> 1:01:01,383
the day on September 13.
I received about 3,000

935
1:01:01,383 --> 1:01:07,232
responses from viewers all over
the world, and I answered each

936
1:01:07,232 --> 1:01:10,493
one of them.
It took me two months.

937
1:01:10,493 --> 1:01:15,575
I did about 50 per day.
About 50 people have the right

938
1:01:15,575 --> 1:01:22,000
idea about what causes this
phenomenon, only two from MIT.

939
1:01:22,000 --> 1:01:26,486
But of those 50,
there were really only about

940
1:01:26,486 --> 1:01:31,789
five who had a complete
understanding of the physics.

941
1:01:31,789 --> 1:01:36,786
About 400 of the 3000 believed
that it is a Glory,

942
1:01:36,786 --> 1:01:42,700
while clearly you know now
enough that this is not a glory.

943
1:01:42,700 --> 1:01:46,677
Many explanations were very
interesting.

944
1:01:46,677 --> 1:01:50,756
Some believed it was an atomic
explosion.

945
1:01:50,756 --> 1:01:54,253
[LAUGHTER]
More than one.

946
1:01:54,253 --> 1:01:59,265
Others suggested that I was
photographing the total solar

947
1:01:59,265 --> 1:02:02,398
eclipse.
Imagine, the day was given.

948
1:02:02,398 --> 1:02:06,425
It was June 20.
It never occurred to them that

949
1:02:06,425 --> 1:02:10,274
there was no total solar eclipse
on June 20.

950
1:02:10,274 --> 1:02:14,839
But that's a detail.
Some people who knew that I was

951
1:02:14,839 --> 1:02:19,046
an astronomer said,
ah, you were photographing a

952
1:02:19,046 --> 1:02:24,797
supernova explosion.
There were three people

953
1:02:24,797 --> 1:02:32,459
independently who said the rings
were caused by the vibration of

954
1:02:32,459 --> 1:02:37,324
a jackhammer.
That would make a very nice

955
1:02:37,324 --> 1:02:43,162
problem for the final.
How do you get this from a

956
1:02:43,162 --> 1:02:48,270
jackhammer?
And then there was one who says

957
1:02:48,270 --> 1:02:55,202
it's the sun shining through
people like those you find in

958
1:02:55,202 --> 1:03:01,818
sex parlors.
[LAUGHTER] And then he said

959
1:03:01,818 --> 1:03:05,636
between parentheses,
I know.

960
1:03:05,636 --> 1:03:13,272
[LAUGHTER] The very best
solution came from a five year

961
1:03:13,272 --> 1:03:19,353
old girl who wrote me a letter,
handwriting,

962
1:03:19,353 --> 1:03:26,000
and I really want to quote her
verbatim.

963
1:03:26,000 --> 1:03:29,194
She says, Professor Lewin,
it's very simple.

964
1:03:29,194 --> 1:03:33,428
You painted the picture with
crayons on the ground and you

965
1:03:33,428 --> 1:03:36,177
photographed it.
[LAUGHTER] Isn't that

966
1:03:36,177 --> 1:03:39,222
wonderful?
I mean, this five year old kid:

967
1:03:39,222 --> 1:03:41,822
I mean, that's the easiest
solution.

968
1:03:41,822 --> 1:03:45,685
You just drew it on the ground
and take a photograph.

969
1:03:45,685 --> 1:03:49,845
So I sent her a very nice
letter back and I said that she

970
1:03:49,845 --> 1:03:54,155
was very close.
[LAUGHTER] All right,

971
1:03:54,155 --> 1:03:59,288
let's look at this picture.
Read us on the outside.

972
1:03:59,288 --> 1:04:04,933
The pilot is on the inside,
and a white light comes from

973
1:04:04,933 --> 1:04:09,347
inside the bow.
This can only be produced by

974
1:04:09,347 --> 1:04:14,480
spherical transparent beats.
There is no other way.

975
1:04:14,480 --> 1:04:18,278
The radius, very small,
is about 20°.

976
1:04:18,278 --> 1:04:23,000
It cannot possibly be due to
water.

977
1:04:23,000 --> 1:04:26,108
For one thing,
there is no water.

978
1:04:26,108 --> 1:04:31,742
Also, the width of the bow,
the width, which you can easily

979
1:04:31,742 --> 1:04:36,599
measure with a ruler,
the width of the bow is about

980
1:04:36,599 --> 1:04:40,777
16% of the radius,
whereas with water [bow?]

981
1:04:40,777 --> 1:04:45,245
that's only about 5%.
On June 20, I visited the

982
1:04:45,245 --> 1:04:50,685
DeCordova Museum in Lincoln,
sculpture garden and with my

983
1:04:50,685 --> 1:04:57,000
son and my significant other,
who is in the audience.

984
1:04:57,000 --> 1:05:01,008
It was about 1 p.m.,
and we walked by an area where

985
1:05:01,008 --> 1:05:05,898
new construction was going on
because DeCordova was building a

986
1:05:05,898 --> 1:05:08,945
new visiting center.
And my son, Chuck,

987
1:05:08,945 --> 1:05:11,430
all of a sudden said,
dad, look.

988
1:05:11,430 --> 1:05:16,000
And we all looked at it.
And this is what we saw.

989
1:05:16,000 --> 1:05:21,000



990
1:05:21,000 --> 1:05:25,267
I had never seen anything like
that before in my life.

991
1:05:25,267 --> 1:05:30,179
But I knew immediately within
seconds that it can only be made

992
1:05:30,179 --> 1:05:35,171
by spherical transparent beats.
That's the only way it could be

993
1:05:35,171 --> 1:05:37,828
made.
So, I immediately thought of

994
1:05:37,828 --> 1:05:40,727
maybe glass, maybe plastic,
whatever.

995
1:05:40,727 --> 1:05:44,270
But it had to be spherical
transparent beats.

996
1:05:44,270 --> 1:05:47,812
So, I wondered,
why would there be so many of

997
1:05:47,812 --> 1:05:52,000
these beats in this construction
site?

998
1:05:52,000 --> 1:05:56,743
It was not until days later
when I actually discussed it

999
1:05:56,743 --> 1:06:01,832
with Marcos, who is also in the
audience, these glass beats,

1000
1:06:01,832 --> 1:06:06,489
about a quarter millimeter
diameter, are being used for

1001
1:06:06,489 --> 1:06:09,335
sandblasting.
And indeed, a lot of

1002
1:06:09,335 --> 1:06:14,165
sandblasting had been going on.
You can see in that area.

1003
1:06:14,165 --> 1:06:18,650
And so, they had spilled a lot
on the ground luckily.

1004
1:06:18,650 --> 1:06:22,358
In problem 10.4,
I made an effort to give it

1005
1:06:22,358 --> 1:06:27,188
away to you so that you could
score your extra credit for

1006
1:06:27,188 --> 1:06:31,860
8.03.
I really tried to give it away,

1007
1:06:31,860 --> 1:06:35,089
but only one person got the
message.

1008
1:06:35,089 --> 1:06:39,241
I wrote in problem 10.4 and the
last question,

1009
1:06:39,241 --> 1:06:43,208
and I quote myself verbatim,
in a world far,

1010
1:06:43,208 --> 1:06:47,729
far away, rain comes down as
small drops of glass.

1011
1:06:47,729 --> 1:06:51,604
And then, after you have done
all the work,

1012
1:06:51,604 --> 1:06:55,571
all I asked you,
what is now the radius of a

1013
1:06:55,571 --> 1:07:00,000
glass bow, and what was the
answer?

1014
1:07:00,000 --> 1:07:02,592
22.8°.
But none of you made the

1015
1:07:02,592 --> 1:07:07,443
connection with this picture
except for one person who did.

1016
1:07:07,443 --> 1:07:12,127
So, let's look at the physics.
It doesn't take very much.

1017
1:07:12,127 --> 1:07:16,727
If I can have all the lights,
so if we take the index of

1018
1:07:16,727 --> 1:07:19,905
refraction for glass 1.5,
and I use my,

1019
1:07:19,905 --> 1:07:25,167
where is my cosine squared?
I use this equation.

1020
1:07:25,167 --> 1:07:30,912
Then I can calculate what the
maximum angle is of phi.

1021
1:07:30,912 --> 1:07:36,006
And I'm not going to do it for
different colors.

1022
1:07:36,006 --> 1:07:39,692
I'll just take a mean value of
1.5.

1023
1:07:39,692 --> 1:07:44,461
So, I simply substitute 1.5 in
this equation.

1024
1:07:44,461 --> 1:07:49,664
And that gives me,
then, an I, for which the phi,

1025
1:07:49,664 --> 1:07:56,142
the maximum angle is reached.
That is 49.8°.

1026
1:07:56,142 --> 1:08:04,571
That, then, translates with
Snell's law to a phi maximum of,

1027
1:08:04,571 --> 1:08:13,000
angle of refraction of 30.6°.
So, that's simply a matter of

1028
1:08:13,000 --> 1:08:18,857
Snell's law.
And then, phi is 4R minus 2I.

1029
1:08:18,857 --> 1:08:26,000
And so, we now get phi max is
about 22.8°.

1030
1:08:26,000 --> 1:08:30,296
You can calculate for my
picture with a ruler the linear

1031
1:08:30,296 --> 1:08:33,812
size of the bow.
Of course, we always think in

1032
1:08:33,812 --> 1:08:37,796
terms of angular size,
but you can actually dactylic

1033
1:08:37,796 --> 1:08:42,328
linear size if you can give me
TV because you know my head.

1034
1:08:42,328 --> 1:08:45,921
It's about 20 cm.
And so, you can calculate now

1035
1:08:45,921 --> 1:08:51,000
what the radius of that bow is
in terms of linear size.

1036
1:08:51,000 --> 1:08:54,152
And that comes out to be about
65 cm.

1037
1:08:54,152 --> 1:08:59,230
Now, the angle is about 20°.
So I will bend over a little.

1038
1:08:59,230 --> 1:09:03,082
So, my head was about 5 feet
from the ground.

1039
1:09:03,082 --> 1:09:08,248
And then I took the picture,
and that exactly gives you then

1040
1:09:08,248 --> 1:09:12,976
the angle of about 20°.
Now, I made on the spot a very

1041
1:09:12,976 --> 1:09:18,230
quick calculation in my head
about the Brewster angle because

1042
1:09:18,230 --> 1:09:23,308
I remember, since I've taken
8.03, that the tangents of the

1043
1:09:23,308 --> 1:09:29,000
Brewster angle is one over the
index of refraction.

1044
1:09:29,000 --> 1:09:34,557
So, that is one over 1.5.
Now, I didn't have a calculator

1045
1:09:34,557 --> 1:09:40,610
on me, but I came roughly that
the Brewster angle was probably

1046
1:09:40,610 --> 1:09:44,679
around 34°.
And so, I concluded that that

1047
1:09:44,679 --> 1:09:50,633
was probably very close to the R
value, in other words to the

1048
1:09:50,633 --> 1:09:55,000
value here, which makes the
rainbow.

1049
1:09:55,000 --> 1:09:59,736
So, the theta Brewster for the
transition from glass into air

1050
1:09:59,736 --> 1:10:03,210
is about 33.7°.
And it is within 3° of this

1051
1:10:03,210 --> 1:10:05,973
value.
And even though I couldn't be

1052
1:10:05,973 --> 1:10:10,710
so precise there on the spot,
I concluded that they had to be

1053
1:10:10,710 --> 1:10:13,710
highly polarized.
I always carry on me,

1054
1:10:13,710 --> 1:10:17,815
as you will from now on,
always a linear polarizer on

1055
1:10:17,815 --> 1:10:21,735
me.
So I took my linear polarizer

1056
1:10:21,735 --> 1:10:25,132
and I impressed my significant
other.

1057
1:10:25,132 --> 1:10:29,283
You can ask her.
And I said, look through the

1058
1:10:29,283 --> 1:10:33,622
linear polarizer.
And indeed, when we looked at

1059
1:10:33,622 --> 1:10:38,245
the bow: highly polarized.
I took some beats home,

1060
1:10:38,245 --> 1:10:42,679
scooped them up.
There were lots of them because

1061
1:10:42,679 --> 1:10:49,000
I immediately realized I was
going to use this for 8.03.

1062
1:10:49,000 --> 1:10:53,918
And we ordered a few kilograms
which is dirt cheap.

1063
1:10:53,918 --> 1:10:59,524
It only cost a few dollars.
And Marcos glued them on black

1064
1:10:59,524 --> 1:11:01,000
paper here.


1065
1:11:01,000 --> 1:11:06,000


1066
1:11:06,000 --> 1:11:12,221
Here is the black paper.
Here are the glass beats on the

1067
1:11:12,221 --> 1:11:16,407
black paper.
The sun is in the back of

1068
1:11:16,407 --> 1:11:19,574
6-120.
And, we hired someone,

1069
1:11:19,574 --> 1:11:26,135
an expert, to turn on the Sun.
And we hired someone to turn

1070
1:11:26,135 --> 1:11:31,000
off the lights in the lecture
hall.

1071
1:11:31,000 --> 1:11:36,312
And here, I am standing in
front of the glass beats.

1072
1:11:36,312 --> 1:11:40,375
On June 20, the sun was high in
the sky.

1073
1:11:40,375 --> 1:11:45,479
And the glass beats were there.
Today, December 7,

1074
1:11:45,479 --> 1:11:51,000
the Sun is there.
And the glass beats are here.

1075
1:11:51,000 --> 1:11:54,035
And you won't believe what I'm
seeing.

1076
1:11:54,035 --> 1:11:57,646
I'm seeing that.
I see a beautiful glass bow.

1077
1:11:57,646 --> 1:12:02,487
I see white from the inside.
I have my linear polarizer with

1078
1:12:02,487 --> 1:12:04,784
me.
And boy, is it polarized!

1079
1:12:04,784 --> 1:12:07,000
[SOUND OFF/THEN ON]


1080
1:12:07,000 --> 1:12:50,000


1081
1:12:50,000 --> 1:12:52,307
And I want all of you to see
this.

1082
1:12:52,307 --> 1:12:55,874
I don't think this has ever
been demonstrated in any

1083
1:12:55,874 --> 1:12:57,552
lecture.
When you see it,

1084
1:12:57,552 --> 1:13:01,748
you will just never forget it.
Not only will you never forget

1085
1:13:01,748 --> 1:13:05,174
this, but whenever in your life
you see a rainbow,

1086
1:13:05,174 --> 1:13:08,531
you'll think of me.
I want you to be very careful

1087
1:13:08,531 --> 1:13:12,517
as you come down the stairs.
Bring your linear polarizers,

1088
1:13:12,517 --> 1:13:15,804
and take your time.
We have at least ten minutes

1089
1:13:15,804 --> 1:13:20,000
left in this lecture.
I planned it that way.

1090
1:13:20,000 --> 1:13:23,222
Be very careful,
don't run into this stuff.

1091
1:13:23,222 --> 1:13:27,443
I hope to see all of you on
Thursday when I will give my

1092
1:13:27,443 --> 1:13:31,433
last farewell lecture,
and then you're on your own if

1093
1:13:31,433 --> 1:13:34,502
you think you can handle it.
So, walk by.

1094
1:13:34,502 --> 1:13:37,571
The closer you are,
the nicer the bow is.

1095
1:13:37,571 --> 1:13:41,561
And, if you close one eye,
you even see a better bow.

1096
1:13:41,561 --> 1:13:43,940
And, this is a question for
you.

1097
1:13:43,940 --> 1:13:48,698
Why would it help if you close
one eye, which I did not have to

1098
1:13:48,698 --> 1:13:53,412
do on June 20?
So, take your time.

1099
1:13:53,412 --> 1:13:59,000
Don't rush, and use your linear
polarizers.

1100
1:13:59,000 --> 1:14:12,000



1101
1:14:12,000 --> 1:14:17,000
Don't rush.


1102
1:14:17,000 --> 1:14:25,000


1103
1:14:25,000 --> 1:14:28,301
We have nine more minutes,
and at nine minutes,

1104
1:14:28,301 --> 1:14:32,465
you can slowly get out of here.
And, all of you should have

1105
1:14:32,465 --> 1:14:36,341
plenty of time to stand there
for at least ten seconds.

1106
1:14:36,341 --> 1:14:38,351
Go very close.
Close one eye.

1107
1:14:38,351 --> 1:14:41,868
When you are close,
you see it even more dramatic.

1108
1:14:41,868 --> 1:14:45,745
Of course, the angle will
always be 23° no matter what

1109
1:14:45,745 --> 1:14:48,759
your distance is.
But if you're very close,

1110
1:14:48,759 --> 1:14:54,000
then the linear size of the bow
will change, not the angle.

1111
1:14:54,000 --> 1:14:58,651
And then, convince yourself
about the degree of

1112
1:14:58,651 --> 1:15:02,595
polarization.
Do you have a polarimeter,

1113
1:15:02,595 --> 1:15:04,213
Jeffrey?
So do I.

1114
1:15:04,213 --> 1:15:07,247
Yeah, yeah.
You're a physicist,

1115
1:15:07,247 --> 1:15:12,000
of course.
I didn't mean to insult you.

1116
1:15:12,000 --> 1:16:48,000



1117
1:16:48,000 --> 1:16:51,401
The angular size is independent
of your distance,

1118
1:16:51,401 --> 1:16:55,653
but the linear size of the bow,
of course, becomes smaller if

1119
1:16:55,653 --> 1:16:57,000
you are closer.


1120
1:16:57,000 --> 1:17:08,000


1121
1:17:08,000
Well, you can always borrow one.