Two mirrors are placed in the first quadrant of the xyplane (perpendicular to the plane). The first mirror along the line y = bx (for some b > 0) and facing the point (0,0). The second mirror along the line y = mx (where m > 0) and facing the point (b,0). A light source at point (a,0), 0 < a < b, shoots a beam of light into the first quadrant parallel to the first mirror. Find m such that when the beam is reflected exactly once by each mirror, it passes through the original light source at point (a,0).
Experiment with GSP gives the following table, of b/a vs. m:
b/a m
2 3
3 5
4 7
5 9
6 11
which seems to indicate m = 2b/a  1.
As to a proof, I don't know.

Posted by Charlie
on 20061008 13:04:40 