Note that the pattern is brightest in the middle, where = 0. This point is called the
central maximum. If you encounter a question regarding double-slit 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 double-slit 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 double-slit 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.
Single-Slit Diffraction
You may also find single-slit diffraction on SAT II Physics. The setup is the same as with
the double-slit 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.
Single-slit diffraction is nowhere near as noticeable as double-slit 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.