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 separate 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

(7.1)

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

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 substitution in Eq. 7.1, we get

(7.2)

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...