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PROFESSOR: In this
demonstration,

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

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

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

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The setup is here.

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We have a laser,
helium-neon laser.

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And here's the output
from the laser.

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Then, we reflect the
beam from the laser

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into an optical isolator.

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It's made up of a polarizer
and a quarter-wave plate.

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And the output from the
isolator is over here.

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It's then reflected
by this mirror

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into the plane mirror cavity.

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

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

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Here's one of them.

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And here's the other.

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The spacing between them is only
about 3.5 millimeters or so.

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And one of the
mirrors is attached

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to a piezoelectric
crystal over here,

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so that we can change
the length of the cavity

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by simply applying a voltage
to the piezoelectric crystal.

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As you see, the mounts are
pretty hefty to make sure

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that the cavity is stable.

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And adjustments can
be made to the cavity

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by using the knobs over here.

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The output of the
cavity, as you can see,

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will be then displayed
on the screen over there.

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Now, if we bring in the
screen as an insert,

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we can see that we
have many, many dots.

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And each dot
represents a reflection

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by the pair of mirrors.

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And you can see as I
misalign the mirrors,

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I can separate out
the individual spots.

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As I come in close
to alignment--

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now, let me go to
the other side,

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show that I can spread
it out the other way.

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And then, if I change
the vertical alignment,

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I can move them
all over the place.

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Now, I'm ready to bring
them all in, so that they

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can interfere with each other.

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When they're
separated, of course,

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they can't interfere
with each other.

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Now, they are merging together.

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And then, very soon we'll
see them interfering.

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You can see already
they're interfering.

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And now, it's dark.

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Now, I can press
on the mirror here.

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You'll see that I can change the
intensity from bright to dark.

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And in order to see
it a little bit more

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clearly, on the
control condition,

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I'm going to turn
on a sweep voltage

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to the piezoelectric crystal.

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So maybe I can tweak the
alignment a little bit better.

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Now, you can see it's going
from dark and bright--

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very nicely when
the beams interfere.

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Now, let me separate
out the beams.

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The interference stops.

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Then as I bring
them back in when

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I have pretty close
to perfect alignment,

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you can see how they
all interfere together.

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And the intensity goes
from bright to almost dark.

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Now, in the next part
of the demonstration,

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I'm going to put a
detector on the output

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and see what we see
with the detector.

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I have now added
the detector, so

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that we can look
at the output of

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the cavity both on the
detector, as well as directly

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on the screen.

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So here is where I
put the detector.

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The output of the beam is
reflected by the beam splitter

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here onto the detector.

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And the output of
the detector then

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goes onto the
internal oscilloscope.

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Also, since this
is a beam splitter,

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the direct output of
the cavity can still

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be monitored on the screen.

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Now, let's look at the
screen of the oscilloscope.

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As you can see, we
have two resonances.

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But let's forget
about one of them.

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Let's just concentrate on one.

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What this represents
is the intensity

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transmitted through the
cavity as a function

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of pathlength difference.

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And the pathlength
difference is being

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scanned by the piezoelectric
crystal I mentioned before.

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You can see, if I
block the light,

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then that's where the zero is.

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And when the light
is unblocked, you

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can see that I get
a peak intensity due

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to the interference
of the multiple beams

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and then to very
little intensity

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due to, again,
destructive interference

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of the multiple beams.

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Now, let me bring in
the other resonance.

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And the other resonnance
is due to the fact

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that every time
the cavity length

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is changed by a half
wavelength of light,

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then we see another resonance.

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The spacing between
the two resonances

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is given by the
velocity of light C

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divided by twice the length
of the cavity, or C over 2L.

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Another interesting thing
that you want to observe

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is the quality factor, so-called
the finesse of the cavity.

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And the finesse of
the cavity is defined

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as the free-spectral
range, which

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is the separation between
these two resonances,

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divided by the width
of the resonance.

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In this case, the
finess is about 30.

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Or sometimes, I can adjust
it to about 50 or so

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because my mirrors
have 95% reflectivity.

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So what I'd like
to do now is show

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what happens as I
misalign the cavity.

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As you can see, every time I
just have to touch the cavity,

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and the resonances move.

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You can see now as
I'm misaligning just

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by turning the
knob just slightly,

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you can see that the finesse
goes way down because

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of the misalignment.

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Now as I try to pick it, and
I hope I can do it on camera,

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and here we are.

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I can always bring it
back where I was before.

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Now you can see, if
I just tap on it,

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I can move the resonances
all over the place.

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Now, let's look at the spot
on the screen at the same time

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as we look at the output of the
detector on the oscilloscope.

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So this spot on
the screen then is

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going to appear in the insert.

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And you can see
that if I misalign--

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let me do the
misalignment again--

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you can see that you can
also notice it on the screen

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also-- that the
spot is misaligned.

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Let me see if I
can get it again.

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Here we are.

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Now, I'm going to take the
automatic scanning out.

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And instead, I'll do
the scanning by hand.

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So let's look at the spot.

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Now you can see, I can vary the
intensity from bright and dark

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by just simply
leaning on the mirror

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to change the length
by very little bit.

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Then, if we can now look
at the oscilloscope output,

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we can see that when
the spot is pretty dark,

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there's not much output.

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And then, as I play
with the cavity here,

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I can make the output
of the detector go big

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and then to nothing.

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Now so far, we only looked
at the light transmitted

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through the cavity as a result
of multiple-beam interference.

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We did not look at all at
the light reflected back

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from the cavity as a result
of multiple-beam interference.

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I need to modify the
setup just a little bit,

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so that we can observe the light
reflected back from the cavity.

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And when we do that,
we'll see that we

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can learn a lot from it.

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Now, the setup
has been modified,

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so that we can observe
the light reflected

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from the interferometer.

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Here's the modification.

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All we've done is added a
beam splitter over here,

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so that the light reflected
from the interferometer

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will be sampled--

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here it is.

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And then, we pass it onto
this mirror over here,

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reflected onto
this beam splitter

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here, and then into
detector number 2.

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Since this is a
beam splitter, we

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can also observe the reflected
light onto the screen.

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Here is this left-hand spot.

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The spot on the right
is our transmitted beam.

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As you can see, if I
misalign the cavity,

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you can see that both
of them will misalign.

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Now, what I'm going
to do, I'm going

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to take the scanner off and
do the scanning by hand.

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Now if you watch
both spots, you'll

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

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which means the intensity goes
very high and then very low.

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But the spot on the left
doesn't seem to do anything.

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Question is, is there anything
happening for the spot

00:11:32.100 --> 00:11:35.490
on the left when the
transmitted beam is

00:11:35.490 --> 00:11:41.940
going through high
peaks and low valleys?

00:11:41.940 --> 00:11:44.850
In order to do
this, we should look

00:11:44.850 --> 00:11:49.950
at the oscilloscope, which
represents the output

00:11:49.950 --> 00:11:53.390
of the two detectors.

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Now, let me put this
scan back on again.

00:11:55.880 --> 00:12:01.250
And let's look at
the oscilloscope.

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The lower trace is
the transmitted light

00:12:06.870 --> 00:12:09.580
as we've seen before.

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The zero is here, and the peak
transmission is over here.

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The upper trace is the one
associated with the light

00:12:19.400 --> 00:12:21.155
reflected from the cavity.

00:12:24.401 --> 00:12:30.140
If I block the reflected
beam into the detector,

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you can see that the zero is
over here, which is in line

00:12:34.250 --> 00:12:35.420
with that little marker.

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Let's do it again.

00:12:36.170 --> 00:12:37.760
Here is the zero.

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And when we have no
light transmitted,

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there's a lot of
light reflected.

00:12:46.460 --> 00:12:49.430
When we have a lot of
light transmitted, which

00:12:49.430 --> 00:12:52.580
is the peak of the
transmission resonance,

00:12:52.580 --> 00:12:55.460
we have suddenly less
light being reflected,

00:12:55.460 --> 00:12:57.020
but not quite zero.

00:12:57.020 --> 00:12:59.420
Remember, zero is over here.

00:12:59.420 --> 00:13:04.910
And the reason why we don't
dip all the way to zero

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is because the interference
is not complete.

00:13:10.640 --> 00:13:13.430
And maybe you want
to think about that.

00:13:13.430 --> 00:13:17.600
Now, let's see what happens
when I misalign the cavity.

00:13:17.600 --> 00:13:20.510
Let's look on the screen again.

00:13:20.510 --> 00:13:23.870
The upper trace, as we
see, is the reflected beam.

00:13:23.870 --> 00:13:25.970
And the lower trace is
the transmitted beam.

00:13:25.970 --> 00:13:31.460
As I misalign, first you see
that the length of the cavity

00:13:31.460 --> 00:13:32.180
changes.

00:13:32.180 --> 00:13:35.980
All we need is a lambda
by 2, and we get a change.

00:13:35.980 --> 00:13:37.520
But then, as I
misalign some more,

00:13:37.520 --> 00:13:41.000
you can see that
the finesse drops,

00:13:41.000 --> 00:13:44.180
or the width of the
resonance grows.

00:13:44.180 --> 00:13:48.500
And then as I realign,
indeed both of them

00:13:48.500 --> 00:13:52.860
are effected essentially
in the same way.

00:13:52.860 --> 00:13:56.990
So when we have
peak transmission

00:13:56.990 --> 00:14:02.120
in the transmitted light,
the reflected light

00:14:02.120 --> 00:14:03.680
goes through a minimum.

00:14:03.680 --> 00:14:07.580
Ideally, it would
go through zero.

00:14:07.580 --> 00:14:12.170
But we don't have
an ideal setup.

00:14:12.170 --> 00:14:16.070
In the next part of
the demonstration,

00:14:16.070 --> 00:14:19.160
we're going to show
what happens when

00:14:19.160 --> 00:14:24.920
the beam going into the cavity
is not the collimated beam.

00:14:24.920 --> 00:14:28.490
In this setup so far, the
beam going into the cavity

00:14:28.490 --> 00:14:31.250
was reasonably collimated.

00:14:31.250 --> 00:14:34.100
So what we'll do,
we'll put a lens,

00:14:34.100 --> 00:14:37.640
and we will then
generate an expanding

00:14:37.640 --> 00:14:39.470
beam that enters the cavity.

00:14:39.470 --> 00:14:43.430
So let's see what happens
when we have such a beam going

00:14:43.430 --> 00:14:45.220
into the cavity.