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PROFESSOR: In a previous demonstration
on two-beam interference, we saw that the fringe pattern
was a series of vertical lines.
The reason was that the two beams were plane waves.
And the lines were due to the interference of two plane waves
with a slight angle between them.
In this demonstration, we're going
to show that you can get all kinds of shapes in the fringe
pattern by simply placing a lens in the setup.
And here is the setup.
As you may recall, here's the laser.
Here's the beam from the laser being reflected by this mirror.
And, here, we're going to add a lens.
The light coming out of the lens and reflected by this mirror
here will have some curvature now.
And when it enters the Michelson interferometer here,
the beam going to this arm being the longer arm--
slightly longer arm--
will have slightly different curvature
when it interferes with the beam coming from this arm,
because the path length here is shorter than this one.
The two beams will interfere and pass along this direction.
Then they will get reflected at this mirror through the lens
and then onto the screen.
So, now, if we take a close-up at the fringe pattern,
we will see that we have circular fringes.
And what's interesting about the circular fringes
is that the spacing between the fringes
can be changed by disturbing the setup.
For example, if I change the length of this arm here,
I can change the spacing between the fringes,
because I'm getting closer.
I'm closer to the same curvature as in the other arm.
If I go further, again, we can see
that I can increase the number of fringes,
showing that, again, the curvature has
changed relative to this fixed arm over here.
Now, I'm going to show the effect of misalignment
on the circular fringes.
If I adjust this mirror to here, and then
let's again look at the fringes, and then you
can see that by misaligning this mirror,
I can get arcs instead of the bullseye.
And, in fact, if I look closely at the arcs,
I can tell which way the beams are misaligned.
All right.
Now, what I'll try and do is to try and make the field go
all dark or all bright by making the two
paths as identical as possible.
Now, you can see, I only have about a couple
of fringes in the interference pattern.
They're slightly misaligned.
So I have them a little better centered.
So let me close in one path, and then
see if I can get complete darkness
or complete brightness.
Let me adjust the alignment as I move in.
Here, you can see I'm getting close to equal path.
And then a little bit more.
Not quite.
That's almost-- we're almost there.
You can see, if I press on the table,
you can see the screen going bright and dark.
I think I have a little bit to go.
And maybe we can get complete extinction.
Let's see.
This is pretty close to a complete extinction.
So in this brief demonstration then,
we've shown that you can get circular fringes, bullseye,
arcs, and what have you, by simply
making the input beam to the interferometer
have some curvature.
And by adjusting the path length difference between the two
arms, you can get a variety of fringe systems.