Physics for Geologists, Second edition

52 Optics
Diffraction
If you shine a small light on the edge of an opaque disc above a piece of
paper, the shadow is not sharp. Some light rays passing near the edge are
apparently bent. If you can examine the edge of the shadow, you will find
that it is not just a diffused light, but consists of dark and light bands. This
is diffraction. Diffraction is also the breaking up of light into dark and light
patterns, or colours, when it passes through a grating or discontinuous solid
(such as a crystal) in which the dimensions of the obstacles are not very much
larger than the wavelength of the light.
The theory (due to Fresnel, and later to Huygens) is that each element
of a wave-front acts as a source of vibration itself, sending out secondary
waves. When a wave-front reaches an obstacle, some of these secondary
sources of vibration are destroyed. The remaining sources - some in phase
and so reinforcing each other; others out of phase - interfere with each other,
giving the diffraction pattern of alternating light and dark bands. The width
of these bands is proportional to the wavelength, so red light has wider bands
than blue. White light leads to superimposed bands and a spectrum results.
Mother of Pearl owes its colouring to diffraction of ordinary light due to
very fine striations on the shell.
Diffraction gratings
Monochromatic light (i.e. of a single wavelength) passing through a trans-
parent plate with many fine lines ruled onto it takes several paths:
straight ahead, as if there were no lines, and
a scattering of paths, as if the lines were the source of the radiation.
In Figure 4.5, the diffracted ray or beam travels farther than that above
by a distance a = d sin cp, where d is the distance between rays or rulings.
But the beams only reinforce each other when a is an exact multiple of the
wavelength 1. So the grating equation is
nh = d sin cp, (4.5)
where n is an integer and cp is the angle of diffraction. There will also be
a symmetrical pattern diffracted upwards, and there is another solution for
the supplement of cp, 180 - cp. Note that if d < X, Equation 4.5 can only
have the solution n = 0, that is, cp = 0 or 180". This is not quite what it
seems to be. It is not that all the radiation goes straight through: there is new
radiation going in the same direction, and in the opposite direction.
Polychromatic light (many colours, many wavelengths) will fan out into
spectra on either side of the normal to the grating (Figure 4.6). If we have
a grating with lines at 5 p,m spacing, a first-order radiation of 400 nm (just
visible violet) will be diffracted through 4.59" (n = 1 in Equation 4.5), as
will second-order radiation of 200 nm (n = 2 in Equation 4.5), third-order
Copyright 2002 by Richard E. Chapman