Chapter 30, Problem 58P

Show that a three-dimensional corner reflector (three mutually perpendicular mirrors, or a solid cube in which total internal reflection occurs) turns an incident light ray through 180°. (Hint: Let $\bar{\text{q}}$ = ${\text{q}}_{\text{x}}\hat{\text{i}}\text{ + }{\text{q}}_{\text{y}}\hat{\text{j}}\text{ + }{\text{q}}_{\text{z}}\hat{\text{k}}$ be a vector in the propagation direction. How does this vector get changed on reflection by a mirror in a plane defined by two of the coordinate axes?)