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Chapter 2:
General Prisms and Reflectors

The equilateral prism is one of the most available and most widely known of the prism types. It is normally used as a dispersing prism, separating white light into its component visible colors. The prism has three planar surfaces at equal 60-deg angles (Fig. 2.1) and is commercially available in optical glass or plastic, with specified surface and angular accuracies.

A multispectral light ray entering surface 1 at angle of incidence I1 is refracted at angle I1, incident on surface 2 at angle I2, and refracted at angle I2. The refraction angles vary for each wavelength λ in the light ray according to Snell's law, and the exiting beam is dispersed into the familiar visible spectrum. The resulting deviation angle δ(λ) is the change in direction of the exit beam from the entrance beam.

There is an allowable range of incident angles for which the rays refracted at surface 1 hit surface 2 and are refracted into a dispersed beam. In particular, if I2 exceeds the critical angle at surface 2, then the ray undergoes total internal reflection (TIR). For BK7 glass with nd = 1.5168 (λ = 587.3 nm), the critical value I2crit = arcsin(1 = nd) = 41.25 deg. The resultant minimum allowable value of I1 = 29.19 deg is calculated using Eqs. (2.1a) to (2.1c). Rays that undergo TIR at surface 2 will exit through surface 3 as a nondispersed ray. The maximum allowable value of I1 is 90 deg, or close to grazing. Also, some of the internally refracted rays might directly hit surface 3 and undergo TIR. These rays are refracted by surface 2 and are not dispersed. These specific cases are well described by Southall.1

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