15.65 If a ray reaches the second surface of a prism at an angle larger than the critical angle. total reflection occurs and the ray is reflected back instead of passing out of the prism. This principle is used in many optical instruments. (a) Show that if n > 1. the condition that at least one ray emerge is that A$ 21, where 2 is the critical angle. (b) Discuss the range of values of the angle of incidence i if the ray is to emerge on the other side. This range is given by the angle a shown in Fig. 15-43. (c) Prove that the range is given by cos * = n sin (A -1). (d) Discuss the variation of a with A