Earlier in this course, we discussed linear
polarization of electromagnetic radiation, and I demonstrate this at seventy-five megaHertz
and at ten gigaHertz. Today, I will concentrate exclusively
on the polarization of light, which is at a much higher frequency. The light from the sun or light from light
bulbs is not polarized. So I can ask myself the question,
now, what does it mean when light
is not polarized? Let's think of individual light photons
as plane waves, with a well-defined direction
of polarization. So each one is linearly polarized. A beam is coming straight
out of the blackboard. The first photon arrives, it's linearly polarized
in this direction. The second photon arrives,
linearly polarized in this direction, so the electric field vector
is oscillating like that. Another photon, another photon,
another photon and another photon. And what you see here,
very clearly, that there is no preferred direction
when you average over time and that's what we call--
call unpolarized light. It was Edwin Land who, in 1938,
developed a material that can turn this into linearly polarized light,
for which he became very famous, in addition to this demonstration
that I showed you last time. If I take one of Edwin Land's sheets, which will turn light into polarization
in this direction and I first take one photon,
for instance, this one. That one comes in from the blackboard
towards you and so here it is. Oscillating the E vector like this, E zero is the maximum value
of the electric field strength in that plane electromagnetic wave. And this is the direction of the polarizer
that I have through which this photon goes. I can now make a simple calculation, by projecting this E-vector onto
the preferred direction of polarization and this new E-vector is now down
by the cosine of theta, if this angle is theta, this E-vector is now E--
E zero times the cosine of theta. If you ask me now, whether the light
is reduced in intensity, I would have to say, "Yes, of course," because light intensity depends
on the pointing vector and the pointing vector is always
proportional to E zero squared, because the pointing vector depends on
the cross-product between E and B. And if E is reduced,
B is also reduced. And so we get a cosine square reduction. If, now, I average over all incoming photons-- so I take all of these, which represent
an unpolarized beam-- so I get not only one like so,
but I get one like so, and one like so and one like so, and one like so--
then clearly, I have to calculate now, the mean value of cosine square theta. And the mean value of cosine square theta
is one-half and so if the intensity
of the unpolarized beam, unpolarized light was originally I zero,
once it comes through this polarizer that Edwin Land gave me,
then I get one-half I zero, but that is now hundred percent polarized. And it is hundred percent polarized
in this direction. And the one-half is the result of the average
value of cosine square theta. If this were the case,
it would be an extremely ideal polarizer, we would call this an HN-50 polarizer--
they don't exist, it's only in your head-- and the fifty refers to the fact
that fifty percent get through polarized. In the optic skits that we hand out today
that we will need throughout this course, you don't have HN-50 polarizers,
they don't exist. I don't quite know what yours is,
I didn't measure it, yours may be an HN-25, or maybe an HN-30, which would then mean
that the I zero strength of an unpolarized light of beam would not be half of I zero,
but maybe only point two five, or point three. But in any case, the light that will come through
your linear polarizers will be very closely
two hundred percent polarized. So what I will do now,
I will take unpolarized light and I will have this light coming straight
out of the blackboard perpendicular to you, with strength I zero and here is
one of my polarizers and the light that comes through here
is linearly polarized in this direction. And so we already know that one-half I zero
will come through if it is an ideal polarizer and it is polarized in this direction. I take a second sheet, an identical one,
I put it also in the plane of the blackboard, but I rotate it over an angle theta. So here is now a second sheet,
which has a preferred direction of polarization in-- in this direction and the angle is rotated
over an angle theta. So between this one and this one
is an angle theta. And so you can now immediately tell
what the intensity of the light is that comes through this second polarizer. It must, of course,
be polarized in this direction, because that is the allowed direction
polarization for that second sheet-- and the intensity must now be one-half I zero,
because that's what comes in and then I have to multiply it
by the cosine square of theta. I don't have to average it now
over all angles, because there is only one value of theta
between this sheet and this sheet, so this is now the new intensity
and it's all polarized in this direction. And this law, whereby the light intensity
is reduced by the factor cosine square theta, is known as Malus' Law. Malus' Law. If theta were thirty degrees, the light intensity
here would be one-half I zero times the cosine square of thirty degrees,
which is oh point seven five. If theta were zero degrees, that means that
this sheet is in the same direction as this one, if everything were ideal, one-half I zero
would get through the second sheet. If theta is ninety degrees,
then nothing will get through, because the cosine of ninety degrees
is zero. We call that crossed polarizers. If you cross them like this,
no light will get through. Now, before I demonstrate this,
I have to be honest with you, because the idea of reducing the energy
of individual photons-- by reducing their electric field strength,
as I did, is a cheat. A light photon has a well-defined energy which depends uniquely
on the frequency of the light. Blue light has a higher frequency
than red light, so blue light has a higher energy
than red light. And when you send blue light through a polarizer,
the way I did here, it either comes through
or it doesn't come through. But if it does come through,
it is still blue light, there is no such thing
as a reduction in energy. Whereas this reduction, by cosine theta,
would imply that the energy goes down and that moo- would imply, then,
that there would be a color change, that it would no longer be blue. And that's not the case. If you want to treat this properly,
you have to do it in a quantum mechanical way. The interesting thing is that if you use quantum
mechanics, you find exactly the same law, you find also Malus' Law. So the law is OK, even though the derivation
is not kosher. Now, I want you to get out of your envelope
one of your green plates, which is a linear polarizer. This is the kind of plate that you have,
you have three in there. Only take one out. These two lights shining on me,
unpolarized light. So the light that comes to you now
is unpolarized. I'm now going to hold in front of my face
this polarizer. So the light that comes through is linearly
polarized in this direction. And you are going to play the role
of the second polarizer. Close one eye, put the polarizer in front
of your eye and rotate it. And you will see a huge difference
in light intensity. If you cross-polarize with me,
then you can't see me. That may make you very happy. But keep in mind, if you can't see me,
then I can't see you, either. So rotate it around
and convince yourself that this light that reaches you is now,
indeed, linearly polarized and when you rotate around your
polarimeters-- we call them polarimeters,
we call them polarizers-- you can see me either,
or you cannot see me at all, and there is anything
and everything in between. Very well. There is a second way that we can produce
hundred percent linearly polarized light and we can do that by reflecting
unpolarized light off a dielectric. For instance, water or glass. None of this follows from Snell's Law, Snell's Law was two hundred fifty years
before Maxwell, polarization wasn't even known
in the days of Snell. But Maxwell's equations allow you to properly
deal with refraction and reflection, including the polarization. And I will make no attempt to derive this
for you in detail, that's really part of 803 if you ever take it, but I will present you with some results
so that you can at least appreciate-- the far-reaching consequences
of the reflection in which we can produce
a hundred percent polarized light. Suppose I have unpolarized light coming in here,
medium one, index of refraction n one, medium two,
index of refraction n two. It's coming in at an incident angle
of theta one, unpolarized. Some of it is reflected-- and this angle
is also theta one as we discussed earlier-- and some of it is refracted into this medium
and this angle we'll call theta two. So this light, unpolarized comes in,
reflects and refracts. If you want to use Maxwell's equations,
at the action, where everything is happening right here
at the surface between the two, you will have to decompose
the incoming light, the electric field vector in two directions. And one direction is perpendicular
to the blackboard, so this is the E-vector and the other direction
is in the blackboard. You will have to do the same here
and you have to do the same here. And if you look at this decomposition,
then notice that both components-- this component, as well as this component,
is perpendicular to the direction of propagation. That is always a must with traveling electric--
magnetic waves. You see the same here. This component and this are both perpendicular
to the reflected beam, this component and this are both perpendicular
to the refracted beam. This one, the one perpendicular
to the blackboard, we normally give a symbol perpendicular,
we call this the incidence plane, the plane through the incident light
and the normal to the surface, we call that the incident plane, in this place--
in this case, that is the blackboard. We call this the perpendicular component,
and we call this the parallel component. And this is, of course,
the incident beam. So this one we call the perpendicular component,
this one we call the parallel component and this is now of the refracted beam. This is the parallel component, this is the perpendicular component
of the reflected beam. The incident light is not polarized
in this sense. So if you average, then there is no
preferred direction of the electric field. That means, then, that in this representation,
the strength of this component and the strength of this component
must be exactly equal, because if one were stronger than the other,
then it wouldn't be unpolarized, then there would be, on average,
a preferred direction. So this component has the same strength as
that component for the incoming light. What Maxwell's equations now can do for us--
it's a lot of work, but you may see it in 803-- it can relate the parallel component in reflection
with the parallel component of incidence, the parallel component of refraction
with the parallel component of incidence, it gives you two relations, two--
two equations. It can also relate the perpendicular component
of reflection with this perpendicular component and the perpendicular component in refraction
with this component. So you get four equations. If this light that comes in is unpolarized, the strength of this component is the same
as this one. In general, you will see,
if you apply these four equations, that that's no longer the case here. They're no longer the same intensity and they're no longer
the same intensity here. That means this reflected light and the refracted
light has now become partially polarized. I will only give you the relation,
one of those four equations. I will only address today the parallel component
of the incident beam and the parallel component
of the reflected beam. And I don't imagine that any one of you
will try to remember that equation. I don't either, I have to look it up
every time that I deal with this. So E zero, which always represents, then,
the maximum possible value of the electric field, of the parallel component, of the reflected beam,
that's the one that I'm after, I'm going to make polarized light
by reflecting, is E zero, the parallel component
of the incident beam times-- and this depends now on the
angle of incidence and on the indices of refraction-- is going to be n one times the cosine of theta two
minus n two times the cosine of theta one. Believe it or not, all of this follows from Maxwell--
divided by n one times the cosine of theta two plus n two
times the cosine of theta one. And if you apply Snell's Law,
you can simplify this equation-- in this case it will help us-- and so you get minus E zero
parallel incidence and now you get here the tangent of theta one, minus theta two, divided by the tangent of theta one
plus theta two. So these two equations are identical. Though that may not be obvious to you,
certainly not obvious to me, either, but if you substitute Snell's Law in here,
you can show that these two are the same. Keep in mind if you're ever interested
in the intensity of this light, then you must always remember that the pointing
vector is proportional to E zero squared, so you always have to square these numbers
when you're interested in light intensity. This is just the strength of the E-vector. There is something very special
hidden in this equation, and that is, when theta one
plus theta two is ninety degrees, then the downstairs here
is infinitely large. And so that means that the parallel component
in reflection is zero. So E parallel in refection goes to zero. And if that one goes to zero,
there is only this one left which is not zero and that means the reflected light is now
hundred percent polarized in this direction, because I have killed
this component completely. But it only works if this is met,
this condition. If this condition is met, that theta one plus
theta two is ninety degrees, then it follows from high school math that the sine of theta two is then
the cosine of theta one. That's immediately obvious, right? You remember the triangle, theta one
plus theta two is ninety degrees, the sine of one angle
is the cosine of the other. And if now, I remember Snell's Law,
which says that the sine of theta one divided by the sine of theta two,
if n two divided by n one, I can replace now,
only for this special case, the sine of-- sine theta I can replace
by the cosine of theta one. And so I get here, now,
the tangent of theta one. And so if this is the tangent of theta one,
that is under these conditions, then we have met the condition
that I was looking for, that I end up with hundred percent
linearly polarized light. And so this is the secret to getting hundred
percent polarized light. And this angle is called the Brewster angle. And so if we, for instance,
look at the transition from air to glass, glass has a index of refraction
approximately one point five-- depends on the kind of glass that you have--
if I go from air to glass, which is what I will do in my demonstration, then the tangent of this angle is n two
divided by n one, this is glass, so this is one point five
and one is one, then you will find that the Brewster angle, theta Brewster turns out to be about
fifty six degrees. I can also make linearly polarized light
by going from glass to air, by bouncing it off this way. Then, of course, I have to invert this
and then you will get a Brewster angle which is smaller, which is thirty-four degrees. But since I will do it with--
from air to glass, I want you to concentrate
on the fifty-six degree angle. The way I'm going to do this demonstration,
it's right set up here, we have light, a light beam that strikes
a piece of plane parallel glass. That's all it is, there's nothing special
about this piece of glass. So the light comes in like so, and here,
I have a piece of glass. This is the angle of incidence,
theta one. And so it's going to be reflected in this
direction whereby this angle is also theta one and something will go in here, that is that angle
theta two, which I don't worry about because I want you to see that this
can become hundred percent polarized. As this light comes in,
it is unpolarized, this component and this component
have equal strength, if theta one is fifty-six degrees
or somewhere in that vicinity, this light is now hundred percent polarized. And I'm going to project that onto the screen, and I'm going to convince you that it is,
indeed, polarized. You cannot use your own polarizers
to see that, because the light in this beam is going to be hundred percent polarized. However, once it reflects off the screen,
it no longer is, so you cannot use your polarimeter, so I have to use my own polarimeter
to show you this. So if you can turn the light off there,
off the overhead, thank you very much, I will turn on the-- the light of my light beam,
there it is and I'm going to make it very dark for you
so that we can see that very well. So the light comes in this direction,
hits the glass and the angle of incidence is now
about forty-five degrees. I purposely didn't make it fifty-six yet. I have here a large sheat of polarizer,
one of Edwin Land's polar-- polarizers and I will rotate that in this beam. You will see that it is partially polarized,
not yet hundred percent, but it's already partially polarized. So there is already an imbalance between
the perpendicular and the parallel component. So if I hold it in the beam and I rotate it,
you will clearly see now that it is much fainter than--
than it is now. And now I will go for the fifty-six angle,
fifty-six degree angle, roughly and so now, I rotate my polarizer, and now, notice,
I can kill that light completely. Hundred percent linearly polarized. I may not have the angle perfect,
but that's OK, you get the idea. It is very close to totally dark. Now you see the light,
it's polarized in this direction and now I can kill it. So that's quite a remarkable thing,
that if we reflect light off a dielectric, that we can-- at one angle, and one angle only, which is the Brewster angle, that we can turn it into hundred percent
linearly polarized light. This does not apply to conductors. The behavior of conductors is very different
from dielectrics such as-- such as water and glass. You can use Maxwell's equations,
of course, to study the reflection of electromagnetic waves
off metals, but you get a very different result. And so never expect to get linearly polarized
light which bounces off metals. I have here, for your pleasure, a metal sphere
and I have a glass sphere and if you still have your linear polarizers at hand, uh, you can now, or a little later, just hold them in front of your eyes
and rotate them around-- of course, you're not seeing light
at the Brewster angle, the chances are that some of the light
that's reflected off this glass that you can clearly see that it is
partially polarized. You can see a difference in light intensity
as you rotate it. You're not going to see that off this metal. Now, I come to a third way of polarization. There is a third way that we can make
hundred percent linear polarized light by the scattering of unpolarized light and we have to scatter
it off very fine particles, much smaller than one tenth of a micron. Dust particles would work very well. Now, the theory of light scattering
is extremely complicated, but I will be able to convince you that if I scatter
the light over an angle of ninety degrees, so it comes in like this and it scatters
over an angle of ninety degrees, that it becomes hundred percent
linearly polarized. I will stay on the center board. Suppose I have light coming in like so. And I have one light photon,
I concentrate on one to start with, and it happens to be that that light photon
is linearly polarized in this direction and so the E-vector is oscillating like this. Later, we're going to add all directions
that we want. I just picked one now. And here are my fine dust particles,
and these dust particles have electrons and the electric field passes by
and these electrons, which are charged, are going to oscillate in this direction. They're going to experience an acceleration,
which is the force that they experience, divided by their mass and therefore,
that is the charge that they have, times the electric field,
divided by their mass. And so as this electric field vector,
this electric field component, oscillating with frequencies omega,
is passing by these electrons, they themselves are going to oscillate
with frequency omega and this is the force that
they will experience. Uh, this is the acceleration
they will experience. Notice that the electrons will experience
a way higher acceleration than the protons, because the protons have a mass which is more
than 1800 times larger than the electron. So whatever follows, it's really the electrons
that do the job and not the protons. So, we have charges
that move up and down, and now comes the question
which we have discussed earlier, so this is just simply to refresh your memory,
if you're here at point P, in what direction will you now see
electromagnetic radiation that is produced by charges that are being accelerated? We discussed that earlier
and we even had a movie about that. And perhaps you will remember
that the electric field, at point P, is now oscillating in this direction. A spherical wave goes out,
if I accelerate charges here. And the rules about this direction
of the electric field are very simple. E is always perpendicular to the direction
of propagation, which is the position vector-- I call this the position vector r-- and the second rule is that a, r and E
are in one plane and that happens to be, in this case,
the plane of my blackboard. But of course, that doesn't have to be
the plane of the blackboard, because I can choose my point P in space here and these rules still apply. The incident photon, which in this case,
I picked only one, is completely destroyed. It is absorbed by the dust. And the electrons which are going to radiate,
reradiate a photon at exactly the same frequency, because if this is oscillating
with angular frequency omega, then the acceleration would be
with angular frequency omega and so this E field will have
angular frequency omega. So it really is as if the photon comes in
and takes off in a different direction, that's why we call this scattering. So the frequency remains the same,
but the direction changes. And the probably that that photon will go
in this direction or this direction is zero, because you remember that no electromagnetic
wave is propagated in the direction of the acceleration, there's a high probability that it goes out
in this plane, perpendicular to a and at this angle theta,
the probability is a little lower. We discussed that earlier. Now, I'm going to convince you why light
that scatters over ninety degrees that comes in like this
and then [wssshhht] comes to you, why that is hundred percent
linearly polarized. Here is a beam of light. And this beam of light is unpolarized. That means, if I look down on this beam,
you have individual photons and I described through those--
maybe a little bit artificially, but I will do that, it was successful with Malus' Law-- I describe through them,
individual directions of polarization. So each photon, on its own, has a uniquely
defined direction of polarization. It is a picture that is not kosher, you really need
quantum mechanics to do this right, but on the other hand, the result that you find
is probably correct. You will find the same result if you did it
in a quantum mechanical way. So here, you have these dust particles
and so what is going to happen is, this light comes in and then [wssshht],
one may be scattered in this direction [wssshht], another one in this direction,
another one in forward direction. And you can go in all directions
as you please. I'm now going to look in the plane
perpendicular to the blackboard, because in the plane perpendicular
to the blackboard, every photon that ends up there
is at ninety degrees angles. It comes in like this, that is ninety degrees,
this is ninety degrees, this is also ninety degrees. And here is that plane. I just draw a circle, but there is nothing
special about the circle. And so the photons come now straight to you,
perpendicular to the blackboard. That's the picture that I have now in mind. And let's say you were looking here. So you were sitting there,
so you have to lift this up, so you're really sitting there. So this is where you are. And let's take one photon
that comes in, which happens to be linearly polarized
in this direction. We pick one photon,
but it's unpolarized light because we're going to add
so many photons that, on average, there is no preferred direction. But I pick one to start with. And now I ask myself the question,
if that photon is scattered in your direction, in this direction, how is the E-vector
oscillating here? So this is now the position vector r and this is the direction a in which
the electrons are going to shake, because the photon comes in,
with an E field shaking like this, so the electrons are going
to shake like this. And you will immediately conclude
that the electric vector here must be oscillating like this. Why? Because it has to be perpendicular to r,
which it is and it has to be in the plane
of a and r. There's only one solution
and then this is the correct solution. Now there is a next photon coming in. And the next photon, I will give it color,
just to distinguish the two, happens to be oscillating
in this direction. And I ask myself the question, if that photon
is scattered in your direction, in what direction is the E-field oscillating? And you'll come to exactly the same conclusion,
in this direction. Why? Because it has to be perpendicular to r,
which it is and it has to be in the plane a and r,
that's the only solution. A little later, there is another photon
that comes in. How is that electric field
being observed here? Of course, in this direction. And so, no matter how they come in,
unpolarized light, you will always see that if the photon
is scattered over ninety degrees, you will always see it
polarized in this direction, and therefore, you have created
linearly polarized light. So if you watch here,
that is at ninety degrees angle-- or if you watch here
at ninety degrees angels-- but of course, it's a whole plane-- then you end up with hundred percent
linearly polarized light. If you go through the same exercise, say,
at an angle here, of forty five degrees, and you look here,
it's only partially polarized. Indeed, if you rotate in front of your eye,
polarimeter, you will see clearly
light intensity changes. But not hundred percent polarized. You couldn't turn it into darkness. And if you look from above-- and you may want to go
through that exercise for yourself, you will see that the light remains completely
unpolarized. So it is only the ninety-degree angle
that is very special. And that's what I'm going to demonstrate
to you. But before I demonstrate this,
there is something that I have to tell you, that I cannot hide from you, I wish I could,
but I can't. It's not something that is my goal
during this lecture, it has nothing to do with polarization. But that's the fact, that the probability,
when you scatter light off very small particles, much smaller than one tenth of a micron or so,
dust particles, that the probability of scattering is way higher
for blue light than it is for red light. The shorter the wavelength,
the higher the probability. If you ever take 803, you're going to see
a derivation of that, a quantitative derivation. Blue light has a ten times higher probability
to be scattered than red light. And so whenever I'm going to do my scatter
experiments on very fine particles, you will see that that light is going to be bluish. You can't miss that. Now, if the particles off which I scatter
are larger than a tenth of a micron, say one micron, this effect of color on probability
of scattering is highly reduced and if I scatter off very large particles, then there is no dependence
any more at all. And in this lies the secret why the sky is blue,
I will get back to that later today, the reason why cigarette smoke can be blue,
if the smoke particles are very small and it's the reason why clouds are white. Because the sunlight hits the clouds,
the light scatters, but the water drops in the clouds are several microns in size and even larger, And so there is no prefered wavelength that scatters and so the clouds look white. And so the first demonstration that I want to do
is very much like what you see here. I'm going to send unpolarized light up here,
straight up. We have bright spotlights there
and the light goes straight up. In here, I'm going to put very small dust
particles. And I have decided to do that smoke,
simply cigarette smoke. So I'm going to hold cigarette smoke
in these beams and the light that will come to you,
no matter where you sit, must have scattered closely
over ninety degrees, right? It comes up like this, but if you see it,
almost for everyone in the audience, ninety degree angle scattering. So with your linear polarizers,
you will be able to see that that light is polarized and it's going to be polarized in this direction,
which is the direction that I have here. So that's the first thing I'm going to do
for this demonstration. So I need cigarettes
and I need smoke. As much as I hate this. [laughter] Yuck! OK. That should do. [laughter] OK. So, you need a lot of light
and as light comes, presumably from here--
yes, there it is. Ah, ready for this? OK, so have your polarizers ready. I want you to see two things. Number one, that the light is bluish
and number two, that it is polarized. Take your time for that. If you don't see it as blue, then the reason
for that is that at low-light intensities, your eyes are not very sensitive
for color any more. It looks quite bluish to me, though. Now I want to do something in addition. I mentioned that if the particles
grow in size, that the scattering is no longer
preferred in the blue. And I can demonstrate that. I can kill two birds with one stone. What I can do is I can hold the smoke
in my lungs for a while and when I do that, the-- the water vapor in my lungs--
will precipitate on these dust particles and they will form small water drops. And when I puff that out, you will see a distinct
difference in color between what you see now and the smoke that comes out of my lungs when
the particles are ten microns and even larger. You will see, then,
that the light is whitish. So this is-- this comes extra,
over and above, it comes for free. In order to make you see the difference,
shortly before I puff out the smoke in here, I will again show you this smoke as it is now,
so you can compare the colors and you will see that there is a difference. Even though this doesn't--
this may not look very bluish to you, for reasons that I mentioned, in darkness, you don't have
a very good sensitive for color. So I'm going to hold this smoke now--
as much as I hate it, this is one of the worst demonstrations
that I have to do-- I hold it in my lungs for a while. [coughing in the audience] I see a huge difference,
but I'm very close. The second puff [puh] [pfew] was very white
compared to the first one. So we were able to catch two birds
with one stone here. The sky is blue because of this phenomenon. Here, you are standing
innocently on the Earth. And sunlight is coming in,
onto the Earth's atmosphere. The sun is there. Sunlight comes in
and the light scatters. And the light that reaches you,
that scatters off these extremely fine dust particles and it also scatters off the air molecules themselves. There are thermal fluctuations
that go on all the time, which causes density fluctuations in the air
and they are sufficient to act as scatterers. And so if light from here comes to you,
the chances are that it is blue, because it has a higher probability than red. And this is also likely to be blue. And so when you look at the sky,
the sky looks blue, that's the reason, it has to do with this strong preference
for color to be scattered when it is blue light. If you look in the direction of the sky at an angle of ninety degrees
to the direction of the sun, the sky is also linearly polarized
for the reasons that we now understand, because there is scattering
over ninety degrees. And so when the sun is out there,
there is always a whole plane, a great circle in the sky,
which is ninety degrees away from the sun. So when you come out with your linear polarizers,
as soon as the weather clears, look at the sky, at the blue sky
and look ninety degrees away from the sun and you will see that the sky
is very strongly polarized. If you look at angles different from ninety degrees,
it's partially polarized. But not as strongly polarized
as it is at ninety degrees. So this explains, in a very natural way,
why the sun, when it rises and why the sun, when it sets,
why the sun is red. Because if the sun rises or the sun sets,
the sun is near the horizon. So now the sunlight comes in like this. Imagine how much atmosphere
it has to travel through, how many scattering particles
it will encounter on the way. And so, right here,
there is scattering. That is blue light, that is blue light,
that is blue light, that is blue light, that has a higher probability,
that is blue light. So what do you think is left over for you? There isn't very much left over. What is left over, the blue is gone,
the green is gone, so if there's anything left over,
it is red. And it is that red light that you see. That's why the sun looks red when it sets
and it looks red when it rises, the same is true for planets
and bright stars and the moon. When they're just above the horizon,
they look very reddish. And if there happens to be a cloud here
in the sky, well, the cloud will also see that red light,
so you get a red cloud. And that's exactly what you see at sunset,
all these clouds turn red. And so that is, again, the consequence of the fact
that the probability for light scattering of blue light is seven times larger, roughly,
than the scattering for red light. So it explains both the blue skies
and the reason why the sky-- why the sunrise and the sunsets are--
are red. I can show you two slides,
whereby you do see this phenomenon, that light that scatters to you
becomes bluish. We can see it in astronomy and the first slide
is a picture of the Pleiades, called the Seven Sisters, very hot stars,
they are surrounded by very small, fine dust and the light that reaches you is not only polarized,
which you cannot see, of course, on the slide, but it's also bluish. And so let's take a look at that first. So here you see the Pleiades,
it's called the Seven Sisters, some people think there are
only seven stars in there, but there are hundreds--
and you see here these very bright stars and here you see the dust surrounding these stars
and this is distinctly blue. That's the effect, the fact that short wavelengths
have a higher probability to be scattered than long wavelengths. So the blue has a higher probability
than the red. And the next slide shows you a man
on the moon. And this person is walking on the moon,
but as he walks on the moon, he produces dust, by just walking, very fine dust particles that come from the soil
that he brings up. And what he is doing, he is creating around
himself sort of a blue atmosphere, a blue sky, because the sunlight
comes from the right and so the light that you see
that comes in your direction is being scattered, of course. Because there is no air on the moon, so that can only be the dust
that he has produced, and you see that that dust is blue. It would probably also be
strongly polarized, because if it changes
ninety degrees angle, then, of course, it would also be
strongly polarized. Now I want to do a demonstration,
the last one, which catches more than two birds
with one stone, it's going to kill three. I have here a bucket with thiosulfate. And we have light coming from this side
which we s-- shine through that bucket. And we're going to put a little bit
of sulfuric acid in there and when we do that, sulfur will precipitate,
small particles of sulfur. These small particles of sulfur
will become the scatterers and so this light,
which is unpolarized white light, will begin to scatter. And you're going to see it. If you're sitting at right angles, then you will see that that light
is linearly polarized, you can enjoy that. If you're sitting there, you're not so well off,
because then the light is not at ninety degrees. But you will see it partially polarized. If you're sitting there,
it's not at ninety degrees either, you will see it partially polarized. But you will also see it blue, because the probability that blue light scattered
is higher than red light. So you're going to see,
slowly in front of your eye, a blue sky is going to develop. It's going to be polarized
in the vertical direction for those people
who are sitting at right angles, partially polarized for the
rest of the audience and then we're going to look at the light
that remains after the light had penetrated
the atmosphere. After the blue light is slowly exhausted. All right. I will also take a polarizer with me,
so I can also show you, then, the polarization. Let me first put that sulfuric acid in. I will do that now, so that I know that I--
OK. So very slowly am I creating, now,
my own atmosphere. And I'm going to make it completely dark. And so you see white light, keep an eye on the--
on the bucket, the bucket cannot be seen by all of us so well,
depending upon where you sit in the audience, but I can already begin to see
that it turned slightly bluish. Of course, I have--
I'm very close. I admit I'm very close,
which is very good. It's slightly bluish, more and more sulfur
is going to precipitate as time goes on, we have to be a little patient. Oh, boy, it's bluish. I will show you that it's polarized. I will rotate in front of it a polarimeter,
and you see, there's a distinct polarization of this light,
if it comes out at ninety degrees. More and more sulfur is precipitating
and look at the sun-- if you think of this as the sun. The sun is, um, is getting a little yellowish,
it's not so white any more. And you wonder why. Well, you should be able to answer that, now. Because the light that is scattered in the
atmosphere, I call this the atmosphere, is blue. It has a higher probability than red. And so what is left over in the direction
that you see on the screen there is the remaining light. And the more blue leaves
and the more green leaves, the redder the sun is going to be. And if we're going to be a little bit more patient
and we certainly have the time for that, you're going to see the sun getting pretty,
pretty bloody red. So keep an eye on it, also have your
linear polarizers and try to see that the light that comes to you
from the atmosphere, if you are at ninety degree angles,
I will once more do it with my polarizers, that that's strongly polarized. Oh, boy, look at the sun. We're getting close,
we're getting close. Whew. Imagine you're now on the beach, very romantic
and there is the sun, you're with a friend, you don't have your polari--
well, from now on, you should always have your polarizer with you,
of course. You can really impress your friend,
believe me. For one thing, you can point out that the
sky at ninety-degree angles from the sun is nearly a hundred percent polarized. You can even tell your friend why the sky
is blue. And-- and as you experience this romantic sunset,
you can also explain why the sun is getting red, because all that blue light and the green light,
gets out first and this is, then,
what is left over. And the sun is really beautiful now,
I already feel these butterflies in my stomach and ants in my pants,
this is sunset all right? [laughter] This is very, very nice sunset. Oh, man. What a beautiful sunset. Yes, indeed, indeed! We are approaching sunset! [laughter] OK, see you Wednesday. [applause]
