# Two-mirror optical cavity

Contributor: Stas Fainer

This is a simulation of rays inside an optical cavity with two mirrors. Given the length of the cavity is $$d$$, and the radius of curvature of its mirrors is $$R_1$$ and $$R_2$$ respectively (with the convention that $$R>0$$ for a concave mirror), then the optical cavity is stable (meaning that for each ray that emanates from one of the mirrors towards the other mirror, a non-divergent trajectory is guaranteed for sufficiently high mirrors), if and only if $$0\leq (1-\frac {d}{R_1})(1-\frac {d}{R_2})\leq 1$$. In this simulation we assume that the mirrors are ideal curved mirrors, meaning that $$f=\frac{R}{2}$$, rendering the previous stability condition to $$0\leq (1-\frac {d}{2f_1})(1-\frac {d}{2f_2})\leq 1$$. Here is a similar simulation with spherical mirrors, where the first stability condition holds in the paraxial approximation.