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PROFESSOR: In this
demonstration,

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we're going to explore a very
curious phenomena in two beam

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interference, which is,
where does the light go

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when we have destructive
interference or a dark field?

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And we'll use our normal
Michelson Interferometer

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to study this phenomena.

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Here it is.

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We have the laser here.

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It is the beam from the laser
being reflected by mirror here,

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and then we go
through this lens,

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then from the lens
onto this Mirror

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and then from this mirror,
then we enter the Michelson

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Interferometer.

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Here is one arm
of interferometer,

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and here is the other arm.

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And then the beams
leaving the interferometer

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will go onto this mirror,
through this lens,

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and then onto the screen.

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Now as you can
see on the screen,

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we have circular fringes.

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And the inset, we have
enhanced the effect,

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so that you can see the
fringes a bit better.

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Now what I'm going to do is
move this mirror here slowly,

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until I equalize the arms
of the interferometer.

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So I can make the diameter of
the central fringe very large.

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As you can see here, the
diameter of the central fringe

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is getting bigger.

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And then as I get closer
and closer to equal path.

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And as you can see now, the
size of the central fringe

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is getting even bigger, until
I reach somewhere over here,

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which is almost approximately
where the paths are equal.

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And then you can see that,
if I press now over here,

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I can change the path length
difference or the misalignment

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to give me a uniform dark field.

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As you can see, again, I'm
going to press, again, here.

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And you'll see that the field
goes completely dark and then

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bright, depending on the
path length difference.

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Now just to show
you that, indeed,

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when the field is dark
that we really have

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light in the interferometer.

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So what I will do, I
will block one arm,

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and then, again,
let's take a close up.

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Then you can see that
when I block one arm that,

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indeed, there is light coming
off the interferometer block

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one arm, and then
I block this arm.

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And you can see, again, that
there is light coming out.

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But is when I have
the beams interfering,

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then I can get the field to
go completely dark as in here.

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So it's not that there
is no light there.

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It's just because
they are interfering,

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and the interference is
destructive interference.

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So the question is,
where does the light

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go when we have total
darkness coming out

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of the interferometer.

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In order to study this, let's
examine the interferometer

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a little bit more closely.

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Let me remind you, again,
what's going on in here.

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The light enters
the interferometer

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and gets reflected by this
beam splitter onto this mirror.

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And then this mirror
reflects light back

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into the beam splitter.

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A portion of which leaves
the interferometer,

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and then the other
part, the other 50%,

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goes back in this direction
actually into the source.

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The other arm, again,
reflects the light back

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into the beam
splitter, and then we

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have the reflection
off the bean splitter

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then interferes with the beam
coming from the other arm.

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And that's what we've
been seeing on the screen,

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but let's keep track of the beam
that passes through the beam

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splitter, again,
back into the source

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to interfere with the
beam coming from this arm.

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Now in order to
do this, I'm going

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to use this beam splitter here.

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And then I will
place it over here,

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so that I can reflect
the light out here.

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So I can look at and
monitor the beam going back

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into the source.

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And then when we come back, we
have it all nicely adjusted.

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So we can see both spots, the
interference of the beam going

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in this direction, as well as
the normal interference pattern

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that we've seen on the screen.

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Now that I have the
beam splitter in place

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to monitor the light
returning to the source,

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let me show you how we're going
to look at it on the screen.

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The light then coming
out of the interferometer

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back into the source will be
reflected by the beam splitter

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here.

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Then I've added a mirror here to
reflect the beam into the lens.

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And then from this lens, we
get the spot on the left.

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So the spot on the
left on the screen

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then is associated
with the light

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that's returning to the source.

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The spot on the right is the
spot that we looked at before.

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That's the one that's
coming through this lens,

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and then, as you can see,
we've added some white lines

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to make the lens a
little bit more visible.

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And then this is the
beam that is coming out

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of the interferometer
that we looked at before.

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So again, the spot on
the left is the beam

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returning to the source.

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The spot on the
right is the beam

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that's leaving
the interferometer

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that we've seen before.

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And now, let's take a close look
at the intensities in these two

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spots as I press on the
table to change the path lens

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difference in the two arms
of the interferometer.

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And as you can see as
I press on the table

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that when the spot on the right
goes dark, the spot on the left

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is bright.

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And then when the spot
on the left is dark,

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the spot on the right is bright.

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So you can see that
they alternate, and I'll

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do it, again, when the
spot on the left is dark.

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This one on the right is bright,
and then the one on the right

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is dark.

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The other one is
bright, so you can

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see the intensities alternate.

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This implies that when we
have constructive interference

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in one beam, we have destructive
interference in the other beam

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and vise versa.

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Now in order to see
the effect even better,

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I'm going to take this
mirror, and change,

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and move it backwards.

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So I can change the
length of one of the arms,

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so we can get back to the rings.

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Now as we see on the
screen and close up,

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we see the effect even
more dramatically.

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The spot on the right
is our normal beam

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that leaves the
entire parameter,

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and the spot on
the left is the one

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that is associated with the
beam going back into the source.

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And I think you can see
it here very clearly

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that when the central
fringe is dark in one spot,

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you can see that on the
other spot, it's opposite.

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So when it's dark in one,
it's bright in the other.

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When it's bright in one,
it's dark in the other,

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and this is a very even more
dramatic way of showing it.

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So we've seen that
when no light comes out

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of the interferometer,
all the light goes back

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into the source,
which means that when

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we have destructive
interference in one beam,

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we have constructive
interference in the other beam.

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The puzzle is that in order to
get destructive interference,

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it means that the path length
difference between the two arms

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must be either a
half wavelengths

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of light or odd multiples of
half wavelengths of light.

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Now, if indeed the
path length difference

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is half wavelengths
of light, then why

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isn't there destructive
interference in the beam

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going back into the source?

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Because the paths are identical.

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So the puzzle I want to
leave you with to think about

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is, how's that we get
constructive interference

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in one beam and destructive
interference in the other beam

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when the two paths are indeed
the same in both cases?