Numerical evaluation of the escape time of a classical point particle from an annular billiard

Abstract

A two-dimensional annular billiard consisting of a region confined within two concentric circumferences, the outer of radius R and the inner of radius r, is considered. The escape time of a point particle projected at a given angle within this billiard is numerically evaluated in terms of the size of the opening in the billiard. The problem is solved by means of classical mechanics and can be of interest for advanced high school physics students or undergraduate college physics students

The path of a light ray in a semicircular cavity

“…The same pattern is repeated over and over. After a certain number of reflections, light might escape the cavity in a given time T, which depends both on θ 0 and on the relative size of the opening S [11].…”