


Wave Optics
As you may know, one of the weird things about light is
that some of its properties can be explained only by treating it
as a wave, while others can be explained only by treating it as a
particle. The classical physics that we have applied until now deals
only with the particle properties of light. We will now take a look
at some phenomena that can only be explained with a wave model of
light.
Young’s DoubleSlit Experiment
The wave theory of light came to prominence with Thomas
Young’s doubleslit experiment, performed in 1801. We mention this
because it is often called “Young’s doubleslit experiment,” and
you’d best know what SAT II Physics means if it refers to this experiment.
The doubleslit experiment proves that light has wave properties
because it relies on the principles of constructive interference and destructive
interference, which are unique to waves.
The doubleslit experiment involves light being shone
on a screen with—you guessed it—two very narrow slits in it, separated
by a distance d. A second
screen is set up a distance L from
the first screen, upon which the light passing through the two slits
shines.
Suppose we have coherent light—that is, light
of a single wavelength , which is all traveling
in phase. This light hits the first screen with the two parallel
narrow slits, both of which are narrower than . Since the slits are narrower than the
wavelength, the light spreads out and distributes itself across
the far screen.
At any point P on the back
screen, there is light from two different sources: the two slits.
The line joining P to the point exactly
between the two slits intersects the perpendicular to the front
screen at an angle .
We will assume that the two screens are very far apart—somewhat
more precisely, that L is much bigger
than d. For this reason, this analysis
is often referred to as the “farfield approximation.” This approximation
allows us to assume that angles and , formed by the lines
connecting each of the slits to P,
are both roughly equal to . The light from the right
slit—the bottom slit in our diagram—travels a distance of l = d sin more than the light from the other slit
before it reaches the screen at the point P.
As a result, the two beams of light arrive at P out
of phase by d sin. If d sin = (n + 1/2), where n is
an integer, then the two waves are half a wavelength out of phase
and will destructively interfere. In other words, the two waves
cancel each other out, so no light hits the screen at P.
These points are called the minima of the pattern.
On the other hand, if d sin = n, then the two waves are in phase and constructively interfere,
so the most light hits the screen at these points. Accordingly,
these points are called the maxima of the pattern.
Because the far screen alternates between patches of constructive
and destructive interference, the light shining through the two
slits will look something like this:
Note that the pattern is brightest in the middle, where = 0. This point is called
the central maximum. If you encounter a question regarding doubleslit
refraction on the test, you’ll most likely be asked to calculate
the distance x between the central
maximum and the next band of light on the screen. This distance,
for reasons too involved to address here, is a function of the light’s
wavelength (), the distance between the two slits (d),
and the distance between the two screens (L):
Diffraction
Diffraction is the bending of light around obstacles:
it causes interference patterns such as the one we saw in Young’s
doubleslit experiment. A diffraction grating is a
screen with a bunch of parallel slits, each spaced a distance d apart.
The analysis is exactly the same as in the doubleslit case: there
are still maxima at d sin = n and minima at d sin = (n +
1/2). The only difference is that the pattern
doesn’t fade out as quickly on the sides.
SingleSlit Diffraction
You may also find singleslit diffraction on SAT II Physics.
The setup is the same as with the doubleslit experiment, only with
just one slit. This time, we define d as
the width of the slit and as the angle between
the middle of the slit and a point P.
Actually, there are a lot of different paths that light
can take to P—there is a path from
any point in the slit. So really, the diffraction pattern is caused
by the superposition of an infinite number of waves. However, paths
coming from the two edges of the slit, since they are the farthest
apart, have the biggest difference in phase, so we only have to
consider these points to find the maxima and the minima.
Singleslit diffraction is nowhere near as noticeable
as doubleslit interference. The maximum at n =
0 is very bright, but all of the other maxima are barely
noticeable. For this reason, we didn’t have to worry about the diffraction
caused by both slits individually when considering Young’s experiment.
Polarization
Light is a transverse wave, meaning that it oscillates
in a direction perpendicular to the direction in which it is traveling.
However, a wave is free to oscillate right and left or up and down
or at any angle between the vertical and horizontal.
Some kinds of crystals have a special property of polarizing light,
meaning that they force light to oscillate only in the direction
in which the crystals are aligned. We find this property in the
crystals in Polaroid disks.
The human eye can’t tell the difference between
a polarized beam of light and one that has not been polarized. However,
if polarized light passes through a second Polaroid disk, the light
will be dimmed the more that second disk is out of alignment with
the first. For instance, if the first disk is aligned vertically
and the second disk is aligned horizontally, no light will pass
through. If the second disk is aligned at a 45º angle
to the vertical, half the light will pass through. If the second
disk is also aligned vertically, all the light will pass through.
Wave Optics on SAT II Physics
SAT II Physics will most likely test your knowledge of
wave optics qualitatively. That makes it doubly important that you
understand the physics going on here. It won’t do you a lot of good
if you memorize equations involving d sin but don’t understand when and why interference
patterns occur.
One of the more common ways of testing wave optics is
by testing your familiarity with different terms. We have encountered
a number of terms—diffraction, polarization, reflection, refraction,
interference, dispersion—all of which deal with different manipulations
of light. You may find a question or two that describe a certain
phenomenon and ask which term explains it.
Example

The answer to the question is B. Polarization
affects how a wave of light is polarized, but it does not change
its direction. Dispersion is a form of refraction, where light is
bent as it passes into a different material. In diffraction, the
light waves that pass through a slit then spread out across a screen.
Finally, in reflection, light bounces off an object, thereby changing
its direction by as much as 180º.
