Degree and class of caustics by reflection for a generic source

TL;DR

This paper investigates the properties of caustics formed by reflection of algebraic curves, proving the birationality of the caustic map and providing formulas for the degree and class of these caustics.

Contribution

It introduces simple formulas for the degree and class of caustics by reflection for any irreducible algebraic curve of degree at least 2, and proves the birationality of the caustic map.

Findings

Proves the birationality of the caustic map for a generic light position.

Provides formulas for the degree and class of caustics by reflection.

Applicable to any irreducible algebraic curve of degree at least 2.

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.