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Two Mirrors (Posted on 2006-10-08) Difficulty: 2 of 5
Two mirrors are placed in the first quadrant of the xy-plane (perpendicular to the plane). The first mirror along the line y = b-x (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).

See The Solution Submitted by Bractals    
Rating: 2.5000 (4 votes)

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Starting thoughts | Comment 1 of 4
If x is near the origin, then m should be near infinite.
If x is near (b,0), then m should be near 1.

Also the eqn of the first beam of light is y=a-x
The light reflects off the second mirror at the intersection of:
    y=mx and y=a-x which is point P {(a/(m+1)), (m*a/(m+1))}

Edited on October 8, 2006, 11:06 am
  Posted by Larry on 2006-10-08 11:03:56

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