Caustics and wavefronts by multiple reflections in a circular surface

Abstract

A caustic by reflection at an arbitrary surface is commonly known as a catacaustic. We study the formation of the catacaustic by multiple reflections in a reflecting circular surface by considering a point light source placed at an arbitrary point on the optical axis. The geometrical wavefront associated with multiple reflections for a paraxial approximation occurs for arbitrary locations of the source. Simple relations for the catacaustic and its wavefront are given.