Enigma 1532 — Just reflecting

by Bob Walker

Take six plane mirrors and set each of them up vertically so that viewed from above they form a regular hexagon, with small gaps at the vertices. Shine a laser beam through one gap so that it emerges from the gap opposite.

By how much should the laser beam be rotated so that it once again emerges from the opposite gap, but by first reflecting just once off each of the mirrors?