On caustics by reflection of algebraic surfaces

Alfrederic Josse (1) , Françoise Pene (1)

1 LM - Laboratoire de mathématiques de Brest

Given a point S (the light position) in P^3 and an algebraic surface Z (the mirror) of P^3, the caustic by reflection of Z from S is the Zariski closure of the envelope of the reflected lines got by reflection of the incident lines (Sm) on Z at m in Z. We use the ramification method to identify the caustic by reflection with the Zariski closure of the image, by a rational map, of an algebraic 2-covering space of Z. We also give a general formula for the degree (with multiplicity) of caustics (by reflection) of algebraic surfaces.

Mots clés: caustic; surfaces; plucker formulas

Domaines: Géométrie algébrique [math.AG]

Alfrederic Josse, Françoise Pene. On caustics by reflection of algebraic surfaces. 2013. ⟨hal-00812963v2⟩