The Obedient Ray

Two mirrors, A and B, are joined at a fixed angle at point O, and a ray of light is shone into the angle between them, parallel to mirror A. It bounces a number of times on mirrors B and A, strikes one mirror at right angles at a point X on the mirror, and then re-emerges along its original path. What is the distance between the original ray and mirror A, in terms of the angle between the mirrors and the distance OX? (Solve for X on either A or B).

Source: The Penguin Book of Curious and Interesting Puzzles, David Wells, 1992, #378. Used as Ken's POTD 3/29/95.

Mail to Ken