title: Two solvable problems of planar geometrical optics.
abstract: In the framework of geometrical optics we consider a two-dimensional transparent inhomogeneous isotropic medium (dispersive or not). We show that (i) for any family belonging to a certain class of planar monoparametric families of monochromatic light rays given in the form f(x,y)=c of any definite color and satisfying a differential condition, all the refractive index profiles n=n(x,y) allowing for the creation of the given family can be found analytically (inverse problem) and that (ii) for any member of a class of two-dimensional refractive index profiles n=n(x,y) satisfying a differential condition, all the compatible families of light rays can be found analytically (direct problem). We present appropriate examples.
authors.affiliation: Dipartimento di Matematica e Informatica, Università di Cagliari, Italy. gbozis@auth.gr
authors.forename: Francesco
authors.initials: F
authors.lastname: Borghero
authors.forename: George
authors.initials: G
authors.lastname: Bozis