Photon

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Here is a nice little puzzle.

A gigantic structure consisting of two planes is set up so that the planes have a 1-degree between them (see below). A photon is sent into the structure parallel to the bottom plane, 2617 meters above it. The planes have a mirror-like surface so that each time the photon hits the structure it bounces off with the degree of incidence equal to the degree of reflection. Assuming that the experiment takes place in an empty space, please answer the following:

1) how many times will the photon hit the surface of the structure before it flies off for good?
2) how long will the photon be inside the structure (between the first and last hit)?

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1) 179 times
2) Approximately 1 millisecond

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1) that is the answer I got
2) I haven’t got that far yet – care to share the inner workings?

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The drawing below shows the idea, with angles of 45 degrees for simplicity. We can represent the path of the foton as a straight line, and mirror the mirrors instead of the foton.

If the angle is 45 degrees, the foton passes (i.e. is reflected by) a mirror 180 /45 -1 = 3 times.
If the angle is 30 degrees, the foton is reflected 180 / 30 – 1 = 5 times.
If the angle is 1 degree, the foton is reflected 180 / 1 – 1 = 179 times.

The distance between the first ‘hit’ and the last one is 2x. We can compute x from tan(1

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