Chapter 33, Problem 53P

SSM WWW ILW in Fig. 33-53, a ray is incident on one face of a triangular glass prism in air. The angle of incidence θ is chosen so that the emerging ray also mates the same angle θ with the normal to the other face. Show that the index of refraction n of the glass prism is given by

$n=\frac{\sin \frac{1}{2}\left(\psi +\varphi \right)}{\sin \frac{1}{2}\varphi },$

where ϕ is the vertex angle of the prism and ψ is the deviation angle, the total angle through which the beam is turned in passing through the prism. (Under these conditions the deviation angle ψ has the smallest possible value, which is called the angle of minimum deviation.)

Figure 33-53 Problem 53.