Physics 102 Lab 8: Measuring wavelengths with a diffraction grating
Dr. Timothy C. Black
Spring, 2005
Theoretical Discussion
The diffraction of classical waves refers to the phenomenon wherein the waves encounter an obstacle that
fragments the wave into components that interfere with one another. Interference simply means that the
wavefronts add together to make a new wave which can be significantly different than the original wave. For
example, a pair of sine waves having the same amplitude, but being 180◦out of phase will sum to zero, since
everywhere one is positive, the other is negative by an equal amount.
Although the diffraction of light waves ostensibly appears the same as the diffraction of classical waves such
as water or sound waves, it is an intrinsically quantum mechanical process. Indeed, while the diffraction
pattern of a wave of water requires the simultaneous presence of a macroscopic number of water molecules,
(of the order of 1024), an optical diffraction pattern can be built up over time by permitting photons to
transit the diffracting obstacle one at a time!. This is really pretty amazing if you think about it.
It is important to understand the physical processes that are occuring that give rise to the diffraction
phenomenon. For the sake of concreteness, we will consider the diffraction of light through a diffraction
grating, which is the device that we will be using in today’s lab. A diffraction grating consists of a transparent
material into which a very large number of uniformly spaced wires have been embedded. One section of such
a grating is shown in figure 1. As the light impinges on the grating, the light waves that fall between the
wires propagate straight on through. The light that impinges on the wires, however, is absorbed or reflected
backward. At certain points in the forward direction the light passing through the spaces (or slits) in between
the wires will be in phase, and will constructively interfere. The condition for constructive interference can
be understood by studying figure 1: Whenever the difference in pathlength between the light passing through
different slits is an integral number of wavelengths of the incident light, the light from each of these slits will
be in phase, and the it will form an image at the specified location. Mathematically, the relation is simple:
dsin θ=mλ
where dis the distance between adjacent slits (which is the same is the distance between adjacent wires)[1],
θis the angle the re-created image makes with the normal to the grating surface, λis the wavelength of the
light, and m= 0,1,2, . . . is an integer.
FIG. 1: Geometry determining the conditions for diffraction from a multi-wire grating
Diffraction gratings can be used to split light into its constituent wavelengths (colors). In general, it gives
better wavelength separation than does a prism, although the output light intensity is usually much smaller.
