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PROFESSOR: In this
demonstration,
we're going to explore a very
curious phenomena in two beam
interference, which is,
where does the light go
when we have destructive
interference or a dark field?
And we'll use our normal
Michelson Interferometer
to study this phenomena.
Here it is.
We have the laser here.
It is the beam from the laser
being reflected by mirror here,
and then we go
through this lens,
then from the lens
onto this Mirror
and then from this mirror,
then we enter the Michelson
Interferometer.
Here is one arm
of interferometer,
and here is the other arm.
And then the beams
leaving the interferometer
will go onto this mirror,
through this lens,
and then onto the screen.
Now as you can
see on the screen,
we have circular fringes.
And the inset, we have
enhanced the effect,
so that you can see the
fringes a bit better.
Now what I'm going to do is
move this mirror here slowly,
until I equalize the arms
of the interferometer.
So I can make the diameter of
the central fringe very large.
As you can see here, the
diameter of the central fringe
is getting bigger.
And then as I get closer
and closer to equal path.
And as you can see now, the
size of the central fringe
is getting even bigger, until
I reach somewhere over here,
which is almost approximately
where the paths are equal.
And then you can see that,
if I press now over here,
I can change the path length
difference or the misalignment
to give me a uniform dark field.
As you can see, again, I'm
going to press, again, here.
And you'll see that the field
goes completely dark and then
bright, depending on the
path length difference.
Now just to show
you that, indeed,
when the field is dark
that we really have
light in the interferometer.
So what I will do, I
will block one arm,
and then, again,
let's take a close up.
Then you can see that
when I block one arm that,
indeed, there is light coming
off the interferometer block
one arm, and then
I block this arm.
And you can see, again, that
there is light coming out.
But is when I have
the beams interfering,
then I can get the field to
go completely dark as in here.
So it's not that there
is no light there.
It's just because
they are interfering,
and the interference is
destructive interference.
So the question is,
where does the light
go when we have total
darkness coming out
of the interferometer.
In order to study this, let's
examine the interferometer
a little bit more closely.
Let me remind you, again,
what's going on in here.
The light enters
the interferometer
and gets reflected by this
beam splitter onto this mirror.
And then this mirror
reflects light back
into the beam splitter.
A portion of which leaves
the interferometer,
and then the other
part, the other 50%,
goes back in this direction
actually into the source.
The other arm, again,
reflects the light back
into the beam
splitter, and then we
have the reflection
off the bean splitter
then interferes with the beam
coming from the other arm.
And that's what we've
been seeing on the screen,
but let's keep track of the beam
that passes through the beam
splitter, again,
back into the source
to interfere with the
beam coming from this arm.
Now in order to
do this, I'm going
to use this beam splitter here.
And then I will
place it over here,
so that I can reflect
the light out here.
So I can look at and
monitor the beam going back
into the source.
And then when we come back, we
have it all nicely adjusted.
So we can see both spots, the
interference of the beam going
in this direction, as well as
the normal interference pattern
that we've seen on the screen.
Now that I have the
beam splitter in place
to monitor the light
returning to the source,
let me show you how we're going
to look at it on the screen.
The light then coming
out of the interferometer
back into the source will be
reflected by the beam splitter
here.
Then I've added a mirror here to
reflect the beam into the lens.
And then from this lens, we
get the spot on the left.
So the spot on the
left on the screen
then is associated
with the light
that's returning to the source.
The spot on the right is the
spot that we looked at before.
That's the one that's
coming through this lens,
and then, as you can see,
we've added some white lines
to make the lens a
little bit more visible.
And then this is the
beam that is coming out
of the interferometer
that we looked at before.
So again, the spot on
the left is the beam
returning to the source.
The spot on the
right is the beam
that's leaving
the interferometer
that we've seen before.
And now, let's take a close look
at the intensities in these two
spots as I press on the
table to change the path lens
difference in the two arms
of the interferometer.
And as you can see as
I press on the table
that when the spot on the right
goes dark, the spot on the left
is bright.
And then when the spot
on the left is dark,
the spot on the right is bright.
So you can see that
they alternate, and I'll
do it, again, when the
spot on the left is dark.
This one on the right is bright,
and then the one on the right
is dark.
The other one is
bright, so you can
see the intensities alternate.
This implies that when we
have constructive interference
in one beam, we have destructive
interference in the other beam
and vise versa.
Now in order to see
the effect even better,
I'm going to take this
mirror, and change,
and move it backwards.
So I can change the
length of one of the arms,
so we can get back to the rings.
Now as we see on the
screen and close up,
we see the effect even
more dramatically.
The spot on the right
is our normal beam
that leaves the
entire parameter,
and the spot on
the left is the one
that is associated with the
beam going back into the source.
And I think you can see
it here very clearly
that when the central
fringe is dark in one spot,
you can see that on the
other spot, it's opposite.
So when it's dark in one,
it's bright in the other.
When it's bright in one,
it's dark in the other,
and this is a very even more
dramatic way of showing it.
So we've seen that
when no light comes out
of the interferometer,
all the light goes back
into the source,
which means that when
we have destructive
interference in one beam,
we have constructive
interference in the other beam.
The puzzle is that in order to
get destructive interference,
it means that the path length
difference between the two arms
must be either a
half wavelengths
of light or odd multiples of
half wavelengths of light.
Now, if indeed the
path length difference
is half wavelengths
of light, then why
isn't there destructive
interference in the beam
going back into the source?
Because the paths are identical.
So the puzzle I want to
leave you with to think about
is, how's that we get
constructive interference
in one beam and destructive
interference in the other beam
when the two paths are indeed
the same in both cases?
