Light Traps

In the February 1992 issue of the American Mathematical Monthly, J. E. Connett [1] asked whether it is possible to construct a 'light trap': a re ective-sided container with the property that a beam of light, shone into it from an appropriate direction, would be re ected inside it over and over again and never escape. Connett suggests that such a trap might be of value as a device to store light rays; however, the market for escape-proof golf holes might be even more lucrative! In order to make the problem interesting, we should insist that the container be of nite size, and that the walls of the container be smooth everywhere, or at least everywhere where the beam of light hits. It is not su cient to focus the beam of light to a spot on the wall of the container where the container fails to be smooth, and hence where the re ection of the beam is not well-de ned. Rather, the beam must be re ected in such a way that it can keep traveling forever without leaving the container.