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.
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