D. Refraction in prisms

Glass prisms are often used to bend light in a given direction as well as to bend it back again (retroreflection). The process of refraction in prisms is understood easily with the use of light rays and Snell’s law. Look at Figure 3-11a. When a light ray enters a prism at one face and exits at another, the exiting ray is deviated from its original direction. The prism shown is isosceles in cross section with apex angle A = 30° and refractive index n = 1.50. The incident angle θ and the angle of deviation δ are shown on the diagram.

Figure 3-11b shows how the angle of deviation Ő changes as the angle Ɵ of the incident ray changes. The specific curve shown is for the prism described in Figure 3-11a. Note that Ő goes through a minimum value, about 23° for this specific prism. Each prism material has its own unique minimum angle of deviation.

1. Minimum angle of deviation.It turns out that we can determine the refractive index of a transparent material by shaping it in the form of an isosceles prism and then measuring its minimum angle of deviation. With reference to Figure 3-11a, the relationship between the refractive index n, the prism apex angle A, and the minimum angle of deviation Őm is given by

where both A and Őm are measured in degrees.

The derivation of Equation 3-4 is straightforward, but a bit tedious. Details of the derivation— making use of Snell’s law and geometric relations between angles at each refracting surface— can be found in most standard texts on geometrical optics. (See suggested references at the end of the module.) Let’s show how one can use Equation 3-4 in Example 4 to determine the index of refraction of an unknown glass shaped in the form of a prism.

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