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PROFESSOR: In a
previous demonstration

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on two-beam interference, we
saw that the fringe pattern

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was a series of vertical lines.

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The reason was that the
two beams were plane waves.

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And the lines were due to the
interference of two plane waves

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with a slight
angle between them.

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In this demonstration,
we're going

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to show that you can get all
kinds of shapes in the fringe

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pattern by simply placing
a lens in the setup.

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And here is the setup.

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As you may recall,
here's the laser.

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Here's the beam from the laser
being reflected by this mirror.

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And, here, we're
going to add a lens.

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The light coming out of the lens
and reflected by this mirror

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here will have
some curvature now.

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And when it enters the
Michelson interferometer here,

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the beam going to this
arm being the longer arm--

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slightly longer arm--

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will have slightly
different curvature

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when it interferes with the
beam coming from this arm,

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because the path length here
is shorter than this one.

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The two beams will interfere
and pass along this direction.

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Then they will get reflected
at this mirror through the lens

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and then onto the screen.

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So, now, if we take a close-up
at the fringe pattern,

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we will see that we
have circular fringes.

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And what's interesting
about the circular fringes

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is that the spacing
between the fringes

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can be changed by
disturbing the setup.

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For example, if I change
the length of this arm here,

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I can change the spacing
between the fringes,

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because I'm getting closer.

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I'm closer to the same
curvature as in the other arm.

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If I go further,
again, we can see

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that I can increase
the number of fringes,

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showing that, again,
the curvature has

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changed relative to this
fixed arm over here.

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00:02:34,800 --> 00:02:39,150
Now, I'm going to show
the effect of misalignment

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on the circular fringes.

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If I adjust this mirror
to here, and then

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let's again look at the
fringes, and then you

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can see that by
misaligning this mirror,

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I can get arcs instead
of the bullseye.

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And, in fact, if I look
closely at the arcs,

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I can tell which way the
beams are misaligned.

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All right.

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Now, what I'll try and do is
to try and make the field go

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all dark or all bright
by making the two

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paths as identical as possible.

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Now, you can see, I
only have about a couple

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of fringes in the
interference pattern.

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They're slightly misaligned.

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So I have them a
little better centered.

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So let me close in
one path, and then

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see if I can get
complete darkness

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or complete brightness.

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Let me adjust the
alignment as I move in.

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Here, you can see I'm
getting close to equal path.

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00:04:19,720 --> 00:04:21,980
And then a little bit more.

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Not quite.

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That's almost--
we're almost there.

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You can see, if I
press on the table,

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you can see the screen
going bright and dark.

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I think I have a
little bit to go.

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00:04:51,850 --> 00:05:02,890
And maybe we can get
complete extinction.

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Let's see.

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This is pretty close to
a complete extinction.

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So in this brief
demonstration then,

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we've shown that you can get
circular fringes, bullseye,

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arcs, and what
have you, by simply

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making the input beam
to the interferometer

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have some curvature.

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00:05:36,060 --> 00:05:40,830
And by adjusting the path length
difference between the two

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arms, you can get a
variety of fringe systems.