IAM   02674
INSTITUTO ARGENTINO DE MATEMATICA ALBERTO CALDERON
Unidad Ejecutora - UE
artículos
Título:
The Parallel refractor
Autor/es:
CRISTIAN GUTIERREZ; FEDERICO TOURNIER
Revista:
Developments in Mathematics
Editorial:
Springer
Referencias:
Año: 2011
ISSN:
1389-2177
Resumen:
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.