Page 141 - Modern Optical Engineering The Design of Optical Systems

124 Chapter Seven

Figure 7.1 The deviation of a ray
by a refracting prism.

To compute the deviation produced by the prism we can readily
determine the angles in Eq. 7.2 by Snell’s law (Eq. 1.3) as follows
(where n is the prism index):
1
sin I′ sin I (7.3)
1 1
n
I A I′ (7.4)
2 1
sin I′ n sin I (7.5)
2 2
While it is ordinarily much more convenient to calculate the deviation
step by step, using the equations above, it is possible to combine them
into a single expression for D, in terms of I 1 , A, and n as follows:
2
2
D I A arcsin [(n sin I ) 1/2 sin A cos A sin I ] (7.6)
1 1 1
It is apparent that the deviation is a function of the prism index and
that the deviation will be increased as the index is raised. For optical
materials, the index of refraction is higher for short wavelengths (blue
light) than for long wavelengths (red light). Therefore, the deviation
angle will be greater for blue light than red, as indicated in Fig. 7.2.
This variation of the deviation angle with wavelength is called the dis-
persion of the prism. An expression for the dispersion can be found by

Figure 7.2 The dispersion of white light into its component
wavelengths by a refracting prism (highly exaggerated).