Degree and class of caustics by reflection for a generic source

Abstract

We are interested in the study of caustics by reflection of irreducible algebraic planar curves (in the complex projective plane). We prove the birationality of the caustic map (for a generic light position). We also give simple formulas for the degree and the class of caustics by reflection valid for any irreducible algebraic curve of degree at least 2 and for a generic light position.