The Obedient Reflected Ray

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Two mirrors are joined at a fixed angle at . A ray of light shines into the angle between them, parallel to the horizontal mirror and at a given height. It bounces a number of times. Suppose it strikes the lower mirror at right angles at and then reemerges along the original path. This is called an obedient ray.

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What is the relationship between the distance between the height and the length of ? The answer is given in the Details.

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Contributed by: Izidor Hafner (December 2015)
Open content licensed under CC BY-NC-SA


Snapshots


Details

They are equal.

Reference

[1] D. Wells, The Penguin Book of Curious and Interesting Puzzles, New York: Penguin Books, 1992.



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