INSTITUTO ARGENTINO DE MATEMATICA ALBERTO CALDERON
Unidad Ejecutora - UE
The Parallel refractor
CRISTIAN GUTIERREZ; FEDERICO TOURNIER
Developments in Mathematics
The problem considered in this paper is the following. Suppose we have a domain Rn1 and a domain contained in an n 1 dimensional surface in Rn ; is referred as the target domain or screen to be illuminated (for the practical application, one can think that n = 3). Let n1 and n2 be the indexes of refraction of two homogeneous and isotropic media I and II, respectively, and suppose that from the region surrounded by medium I, radiation emanates in the direction en with intensity f(x) for x 2 , and is surrounded by media II. That is, all emanating rays from are collimated. We seek an optical surface R interface between media I and II, such that all rays refracted by R into medium II are received at the surface , and the prescribed radiation intensity received at each point p 2 is g(p). Of course some conditions on the relative position of and and are needed so rays can be refracted to , see conditions (A) and (B) below. Assuming no loss of energy in this process, we have the conservation of energy equation R f(x) dx = R g(p) dp.