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SHAOUL EZEKIEL: In
this demonstration,

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we're going to show the
effect of the light source

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on fringe contrast in a
two-beam interferometer.

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But in particular,
we want to look

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at the effect of the spectrum
of the light source on fringe

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contrast.

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The setup is here.

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We have a special laser
for this demonstration.

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And I'll tell you
more about it later.

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The light from the laser is
reflected by the mirror here.

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Then we have a polarizer here.

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And then light is
reflected by a mirror here.

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This is a beam splitter.

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I'll explain later.

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And then the light here enters
the Michelson interferometer.

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Here is one arm of
the interferometer.

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And here is the other arm
of the interferometer.

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The beams leaving the
interferometer are here.

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And then they are reflected
by this mirror into this lens

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and onto the screen.

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Now, the screen is
a little bit dim.

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So let's look at an enhanced
image in the insert.

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As you can see, you
can see the fringes

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from the interferometer.

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00:01:36,060 --> 00:01:37,572
But just to convince
you that this

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is coming from this
interferometer,

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I'm going to adjust the
alignment in one arm

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to show you that, indeed,
this is associated

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with the interferometer here.

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All right, now let's
look at the light source

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that we're going to study.

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This laser here is
sort of special.

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It operates in two frequencies,
sometimes three frequencies.

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But the interesting thing
about these frequencies

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is that they have different
polarizations, at least

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adjacent frequencies have
orthogonal polarizations.

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00:02:18,870 --> 00:02:23,460
So using a polarizer
over here, I

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can select either one
frequency or two frequencies.

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In order to check
that, indeed, I've

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selected one frequency
or two frequencies,

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I'm going to sample the
laser beam using this beam

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splitter here.

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00:02:43,560 --> 00:02:46,680
Now, I don't know if you can
see the beam on the card.

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It's pretty weak.

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But this beam is being sent
into this optical spectrum

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analyzer, which is a scanning
Fabry-Perot interferometer.

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The output of the
optical spectrum analyzer

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is displayed on the
oscilloscope screen over here.

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As you can see, it
is single frequency.

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The output of the laser
entering the interferometer

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is single frequency.

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Now, as I change
the transmission

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axis of the polarizer here, I
can select the other frequency,

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or, in this case, the
other frequencies,

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as shown over here.

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Sometimes the laser oscillates
two frequencies, sometimes

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in three.

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And at the moment, it's
oscillating in three.

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If I go back, I can
select one frequency.

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And halfway rotation
of the polarizer,

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or 45 degree rotation
of the polarizer,

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I can select more
than one frequency.

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And if I go
completely 90 degrees,

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then I can select
two frequencies.

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Now, let me set my
polarizer so that I only

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have only one frequency.

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So let's go to
the interferometer

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and look at the fringes as
a function of path length

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difference.

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Here we are.

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Here's the interferometer again.

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And here are the fringes.

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And you can see the
contrast is pretty good.

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The zero over here
indicates that this arm

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is equal to this arm.

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Now, I'm going to vary the
length of the arm over here.

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00:04:49,040 --> 00:04:53,880
And you can see that the
fringe contrast is pretty good.

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00:04:53,880 --> 00:04:58,090
Now, here I am, 11 centimeter
path length difference.

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Fringes are pretty good.

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Around 20 centimeters, pretty
good-- remember, the laser

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is single frequency at present.

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00:05:09,645 --> 00:05:13,300
At about 30
centimeter difference,

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fringe is pretty good.

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00:05:15,730 --> 00:05:21,580
And so on, the fringe
contrast doesn't deteriorate.

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00:05:21,580 --> 00:05:30,160
So let me go back to the
equal path condition.

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So let's look at
the scope as I bring

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in more than one
frequency from the laser.

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As we can see on the scope,
we have one frequency.

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Now, as I rotate
the polarizer, I

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can now bring in the
other frequencies.

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So in this position,
essentially, we

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have two dominant
frequencies plus another one.

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00:05:53,850 --> 00:05:57,090
Now, let's go back
to the interferometer

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and look at the fringe
contrast as a function

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of path length
difference with the laser

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at several frequencies.

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So here, at equal
path length, I can see

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the fringes are pretty good.

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And then as I go away
from equal path length,

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the fringe contrast
begins to deteriorate.

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And you can see around here,
when I'm around about eight

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or nine centimeters away, the
fringe contrast is pretty bad.

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See, it's still bad, bad
still, again, still pretty bad.

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Now, it picks up.

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Now fringe contrast
is getting better.

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Now at a position
22 centimeters,

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that means a path length
difference at 22 centimeters,

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I have as good fringe
contrast as before.

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Then if I go further, fringe
contrast again deteriorates.

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Here we see it's pretty
much gone over here.

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Now I'm around 30 centimeters
path length difference.

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Then as I go all the way to
44 centimeter path length

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difference, you can see the
fringe contrast is back again.

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Let's go even further.

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Fringe contrast deteriorates.

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And I think, finally, if
I go to 66 centimeters,

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fringe contrast comes back.

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But I need some
readjustment of the beams.

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You can see, though,
that the fringe

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contrast has been restored.

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And so on, so every
22 centimeters,

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the fringe contrast comes back.

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Let me go back again and
check around, let's say,

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44 centimeters.

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And fringe contrast is bad.

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Around 30 centimeters or so--

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I'm sorry, at 44 centimeters,
fringe contrast's pretty good.

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00:08:04,440 --> 00:08:08,410
Around 30 centimeters,
it's pretty bad.

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Around 22 centimeters,
it's pretty good.

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And around 10 or so
centimeters, it's pretty bad.

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Now, clearly, the
fringe contrast

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seems to be dependent on
the spectrum of the laser.

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Just to make sure,
let's stay at a position

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where the fringe
contrast is pretty bad.

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And let's change the
spectrum of the laser going

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into the interferometer.

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Let me first adjust the position
of the peaks on the scope.

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And now what I'd like
to do is, while we're

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watching the contrast,
I would like now

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to go back to the single
frequency condition.

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As you can see, the
contrast is pretty good.

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And as I go to the multiple,
multi-frequency position,

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the contrast disappears.

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So clearly, when the laser
entering the interferometer

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has only one frequency,
contrast is pretty good.

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When it has several frequencies,
at this path length difference,

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there is no contrast at all.

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Now, let me go to the
equal arm position.

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Let's again look at
the fringe contrast

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as a function of the
spectrum of the laser.

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So if we can look
at the scope and now

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we have single
frequency operation.

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The fringe contrast's
pretty good.

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If you have multiple
frequencies,

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the contrast is
also pretty good.

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So there's no change in the
fringe contrast with frequency.

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00:10:08,580 --> 00:10:15,430
Let me now go to 22 centimeter
path length difference.

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And now, again, we look
at the fringe contrast

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and its dependence on the
spectrum of the light.

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You can see here that when--

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let me readjust the
fringes a little bit.

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That's it.

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You can see when the laser
is at a single frequency,

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fringe contrast's pretty good.

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When it has several
frequencies, fringe contrast

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is also pretty good.

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But when I am at a position
about 10 centimeters

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or so away, now, if we can
look at the fringes, let me--

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you can see the fringes are--
fringe contrast is pretty bad.

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And then again, when I
go to single frequency,

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00:11:04,620 --> 00:11:07,610
you can see that the fringe
contrast is pretty good.

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00:11:07,610 --> 00:11:13,560
And then multiple frequency,
fringe contrast is pretty bad.

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00:11:13,560 --> 00:11:17,400
So what we have seen
is the influence

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of the spectrum of the laser
light on the fringe contrast

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in a two-beam interferometer.

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We saw that when the
laser is operating

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at a single frequency,
the fringe contrast

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00:11:30,810 --> 00:11:34,290
is unaffected by path
length difference.

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When the laser was oscillating
at several frequencies,

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we saw that there were positions
where the fringe contrast went

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to almost zero.

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00:11:45,960 --> 00:11:49,820
But the fringe contrast
reappeared every 22

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centimeters.

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00:11:52,100 --> 00:11:56,498
I'd like you to remember
that the laser cavity here--

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00:11:56,498 --> 00:11:57,790
let's look at the laser cavity.

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00:11:57,790 --> 00:12:04,030
The laser cavity is
22 centimeters long.

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00:12:04,030 --> 00:12:06,810
So maybe there is a connection
between the length of the laser

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00:12:06,810 --> 00:12:12,210
cavity and the
positions of good fringe

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00:12:12,210 --> 00:12:15,670
contrast in the interferometer.

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00:12:15,670 --> 00:12:19,140
What I'd like you to think
about is why does fringe

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00:12:19,140 --> 00:12:24,030
contrast deteriorate when
the laser is oscillating

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00:12:24,030 --> 00:12:26,840
at several frequencies?