Geometric optics of a refringent sphere illuminated by a point source: caustics, wavefronts, and zero phase-fronts for every rainbow “k” order

This study relates to a refringent sphere illuminated by a point source placed at a distance h from its center; for h→∞ the light beam becomes parallel. A selection of variables, principally angular with the center of the sphere as a common point, allows a global, straightforward, and geometrically transparent way to the rays, caustics, and wavefronts, internal as well as external, for every k order, k being the number of internal reflections. One obtains compact formulas for generating the rays and the wavefronts.