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SHAOUL EZEKIEL: Now
we're ready to look

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at the state of polarization
of the transmitted

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and reflected beams on
a glass-air interface

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as a function of the input
polarization of the light

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and also as a function of
the input angle of incidence.

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The setup is here is the laser.

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The laser beam we
reflected by this mirror

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into this quarter-wave plate.

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So we have here, we have
circularly polarized light.

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Then we pass it through
the polarizer here.

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So in this region, we have
plane polarized light.

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And the polarization is
set by the transmission

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axis of this polarizer.

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Here's our prism.

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Here is the transmitted
beam over here.

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And here is the
reflected beam over here.

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Now, just to make sure that,
indeed, in this region here

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we have plane polarized
light incident at the prism,

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we will take this polarizer and
test that, indeed, the light is

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plane polarized in this region.

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In a way, we're checking
on this polarizer.

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So let me put a screen over
here so we can see the light.

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So now, if indeed the
light is plane polarized,

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then I should be
able to extinguish it

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by simply rotating
the transmission

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axis of the polarizer here.

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And here, indeed,
you can see that I

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can extinguish the light.

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So indeed, the light
is plane polarized.

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I now will change
the transmission axis

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of this polarizer, let's
say, to some angle here

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and then again check that,
indeed, I can extinguish

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the light again at this angle.

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Let me go back over here.

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And yes, indeed, I
can extinguish it

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And you can see that there is 90
degrees between this polarizer

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and this polarizer.

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So now we're happy that
the light is, indeed,

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plane polarized in
this region regardless

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of where I set the transmission
axis of the polarizer.

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Let me put it back to vertical.

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We'll take this polarizer
out, take the screen.

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Now we're ready to study
the state of polarization

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of the transmitted beam
and the reflected beam.

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First, we start with
the transmitted beam.

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So I'm going to
place the polarizer

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in the way of the
transmitted beam like this.

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And with the state of
polarization coming in

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along the vertical
plane, as shown here,

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I'm now going to demonstrate
that the light transmitted

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is indeed plane polarized.

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And, as you can see,
I can extinguish it

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with this polarizer here, which
means the state of polarization

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is linear and also perpendicular
to this horizontal axis.

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Now I will change the state of
polarization of the input beam,

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let's say to some
angle like this.

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And now let me see if I
can extinguish it again.

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Yes indeed, I can
extinguish it again.

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And you also notice
that the angle here is

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orthogonal to the angle here.

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So we've shown that the
state of polarization

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of the transmitted
beam is indeed

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plane polarized regardless
of the orientation

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of the transmission axis
of the polarizer here.

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Now we're going to look at
the state of polarization

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of the reflected beam.

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So now I'll put
the polarizer here

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in the way of the reflected beam
then adjust the reflected beam

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to go through the polarizer.

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And let's see again with the
polarization at this angle,

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with the input
polarization at this angle.

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Let me now rotate the
analyzing polarizer here

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to see whether, indeed, I can--

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00:05:03,080 --> 00:05:06,380
first let me transmit the
maximum amount of light.

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Let me see now if I
can extinguish it.

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00:05:09,890 --> 00:05:18,920
And indeed, I can, which shows
that for this orientation

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of the transmission axis of
the input polarizer, indeed

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I have plane polarized light.

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Let me check it for
vertical polarization.

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And indeed, I can
extinguish it here too.

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And I'll do one more of the
horizontal polarization,

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about so.

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And let me see if
I extinguish that.

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And indeed, I can
extinguish the light.

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So again, we've shown that
the state of polarization

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of the reflected beam is plane
polarized, again regardless

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of the orientation
of the transmission

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axis of this polarizer.

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Now we're ready to look at
the state of polarization

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of the reflected beam after the
critical angle or the totally

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internally reflected beam.

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But first, I'd like
to convince you

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that we are looking at the
totally internally reflected

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beam.

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So let's look at
the setup again.

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This is the transmitted beam.

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And this is the reflected beam
for any angle of incidence

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below the critical angle.

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So as I increase the
angle of incidence

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until I reach the
critical angle,

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you can see that the transmitted
beam is extinguished.

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And all we have left
is the reflected beam.

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So from here on, this is
the totally internally

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reflected beam.

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So I'm going to now adjust
the angle of incidence

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to about 50 degrees
or so this direction.

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And now I'll place the
polarizer in the way

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to analyze the state of
polarization of the totally

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internally reflected beam.

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Now, the input polarization is--

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p polarization, or polarization
in the horizontal plane,

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is set by this polarizer.

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Let's see what the
state of polarization

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is of the totally
internally reflected beam.

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And you can see that, indeed, I
can extinguish the light, which

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means that for p
polarization input,

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the polarization of the
reflected beam or the totally

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internally reflected
beam is plane polarized,

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and indeed, also p polarization.

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Now let's go to s polarization.

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It means polarization
in the vertical plane.

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So we are here about vertical.

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Let me now adjust
the analyzer here

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to see whether I can
extinguish the beam again.

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Let me do a little
more tweaking.

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Just a little bit
more, and indeed, you

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can see that I can
extinguish the beam again.

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This again says that
for polarization

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in the vertical plane or s
polarization, the polarization

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of the totally internally
reflected beam is also s

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polarization, also linear
polarized and s polarization.

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Now let me go away from
s or p polarization

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by changing the angle
of the transmission

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axis of the polarizer,
which means what I'm doing

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is changing the orientation
of the plane of polarization

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of the input b.

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Now let's see if we can
extinguish the beam.

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As you can see, the
intensity varies

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as I rotate the polarizer.

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But I cannot extinguish
it like I did before.

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This implies that there is a
phase shift between the s and p

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polarizations in the totally
internally reflected beam.

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In fact, let me change
the input orientation

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to about 45 degrees.

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And indeed, again, I
cannot extinguish the beam.

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And this, again, implies that
the state of polarization

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of the totally
internally reflected beam

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for this kind of orientation of
the polarization of the input

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beam, that indeed,
the totally internally

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reflected beam is
elliptically polarized.

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And this elliptical
polarization can be made use of.

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For example, for a 50
degree angle of incidence,

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one can get a phase
difference between s

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and p polarization
of about 50 degrees.

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This phase shift, then,
is very interesting

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and has been exploited
for the construction

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of quarter-wave plates
and half-wave plates

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simply by taking advantage
of this phase shift

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on reflection on a
glass-air interface.

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For example, a
quarter-wave plate

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requires two such reflections
to make up 90 degrees.

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And a half-wave plate requires
four such reflections.