a/In this view from overhead, a
straight, sinusoidal water wave
encounters a barrier with two
gaps in it. Strong wave vibration
occurs at angles X and Z, but
there is none at all at angle Y.
(The figure has been retouched
from a real photo of water waves.
In reality, the waves beyond the
barrier would be much weaker
than the ones before it, and they
would therefore be difficult to
see.)
b/This doesn’t happen.
12.5 Wave optics
Electron microscopes can make images of individual atoms, but why
will a visible-light microscope never be able to? Stereo speakers
create the illusion of music that comes from a band arranged in
your living room, but why doesn’t the stereo illusion work with bass
notes? Why are computer chip manufacturers investing billions of
dollars in equipment to etch chips with x-rays instead of visible
light?
The answers to all of these questions have to do with the subject
of wave optics. So far this book has discussed the interaction of
light waves with matter, and its practical applications to optical
devices like mirrors, but we have used the ray model of light almost
exclusively. Hardly ever have we explicitly made use of the fact that
light is an electromagnetic wave. We were able to get away with the
simple ray model because the chunks of matter we were discussing,
such as lenses and mirrors, were thousands of times larger than a
wavelength of light. We now turn to phenomena and devices that
can only be understood using the wave model of light.12.5.1 Diffraction
Figure a shows a typical problem in wave optics, enacted with
water waves. It may seem surprising that we don’t get a simple
pattern like figure b, but the pattern would only be that simple
if the wavelength was hundreds of times shorter than the distance
between the gaps in the barrier and the widths of the gaps.
Wave optics is a broad subject, but this example will help us
to pick out a reasonable set of restrictions to make things more
manageable:
(1) We restrict ourselves to cases in which a wave travels through
a uniform medium, encounters a certain area in which the medium
has different properties, and then emerges on the other side into a
second uniform region.
(2) We assume that the incoming wave is a nice tidy sine-wave
pattern with wavefronts that are lines (or, in three dimensions,
planes).
(3) In figure a we can see that the wave pattern immediately
beyond the barrier is rather complex, but farther on it sorts itself
out into a set of wedges separated by gaps in which the water is
still. We will restrict ourselves to studying the simpler wave patterns
that occur farther away, so that the main question of interest is how
intense the outgoing wave is at a given angle.
The kind of phenomenon described by restriction (1) is called
diffraction. Diffraction can be defined as the behavior of a wave
when it encounters an obstacle or a nonuniformity in its medium.
In general, diffraction causes a wave to bend around obstacles and812 Chapter 12 Optics