Page 140 - Modern Optical Engineering The Design of Optical Systems

Chapter
7

Prism and Mirror Systems

7.1 Introduction
In most optical systems, prisms serve one of two major functions. In
spectral instruments (spectroscopes, spectrographs, spectrophotometers,
etc.) their function is to disperse the light or radiation; that is, to sepa-
rate the different wavelengths. In other applications, prisms are used
to displace, deviate, or reorient a beam of light or an image. In this type
of use, the prism is carefully arranged so that it will not separate the
different colors.

7.2 Dispersing Prisms
In a typical dispersing prism, as shown in Fig. 7.1, a light ray strikes
the first surface at an angle of incidence I 1 and is refracted downward,
making an angle of refraction I′ 1 with the normal to the surface. The
ray is thus deviated through an angle of (I 1 I′ 1 ) at this surface. At
the second surface the ray is deviated through an angle (I′ 2 I 2 ), so
the total deviation of the ray is given by
D (I I′ ) (I′ I ) (7.1)
1 1 2 2
From the geometry of the figure it can be seen that angle I 2 is equal
to (A I′ 1 ), where A is the vertex angle of the prism; making this sub-
stitution in Eq. 7.1, we get

D I I′ A (7.2)
1 2

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