Chapter 52
Diffraction
The bending of waves (including light waves) around obstacles is calleddiffraction. Light has a very short
wavelength, but it is possible to observe diffraction in light waves without too much trouble.
One such experiment involves a setup similar to Young’s experiment, but using onlyoneslit. Light from
one part of the slit will interfere with light coming from another part of the slit, creating adiffraction pattern
as the light waves coming from different parts of the slit interfere with each other. This phenomenon is called
single-slit diffraction. The positions of thedarkfringes in single-slit diffraction are given by
asinDm .mD1;2;3;:::/ .dark fringes/ (52.1)whereais the slit width,is the angle between the midpoint of the slit and them-th order dark fringe, and
is the wavelength of light.
In a real Young’s experiment, you observeboththe interference pattern (due to the two slits)andsingle-
slit diffraction (due to the finite width of the slits): you will see the interference pattern modulated by an
“envelope” of single-slit diffraction.
A similar diffraction effect may be observed when light is incident on acircularaperture. In this case, the
resulting diffraction pattern is a single central bright circle, surrounded by alternating dark and light rings.
The radius of the first dark ring (which can be taken as the radius of the central maximum) subtends an angle
rD1:22
D; (52.2)
whereris inradians, is the wavelength of the light, andDis the diameter of the aperture.^1
52.1 The Rayleigh Criterion.
Single-slit diffraction limits the resolving power of astronomical instruments: that is, it places limits on how
close two point sources of light can be to each other and still be distinguished as separate points of light.
For example, suppose an astronomical telescope is used to observe two stars that are close together. Each
star is essentially a point source of light, and will produce a single-slit diffraction pattern as seen through
the telescope aperture. If the two diffraction patterns are far apart, you will see two stars. But if the two
diffraction patterns are too close together, they will overlap and the image will blur together and look like a
single star (Fig. 52.1).
There is a threshold where the stars will be as close together as they can be, and still be distinguished
as two separate stars. This threshold is given by theRayleigh criterion. It states that theminimumangular
(^1) The coefficient 1.22 in this equation is the first zero of the Bessel functionJ 1 .x/, divided by. A closer value is 1.2196698912665.