Enigma 1039: Mirror, mirror
26 October 2018
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From New Scientist #2195, 17th July 1999 [link]
George has fitted two mirrors inside a rectangular box, the first on one of the long sides, and the other across a diagonal. He shines a narrow beam of light through a small hole which he has drilled through the side of the box and the mirror on that side. It enters perpendicular to the side of the box, is reflected five times by the mirrors and emerges perpendicular to the end of the box through another hole, as shown.
The box is exactly one metre long. You can calculate the width if you wish, but that is not George’s problem. He wants to know how far the beam travels while it is inside the box.
Can you help him?