Walker, Halliday & Resnick — Electromagnetic Waves: Problem 13

13 In Fig. 33-34, a ray is incident on one face of a triangular glass prism in air. The angle of incidence \(\theta\) is chosen so that the emerging ray also makes the same angle \(\theta\) with the normal to the other face. Show that the index of refraction \(n\) of the glass prism is given by \[ n = \frac{\sin \frac{1}{2}(\psi + \phi)}{\sin \frac{1}{2}\phi} \] where \(\phi\) is the vertex angle of the prism and \(\psi\) is the deviation angle, the total angle through which the beam is turned in passing through the prism. (Under these conditions the deviation angle \(\psi\) has the smallest possible value, which is called the angle of minimum deviation.)