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.
© 2006 Optical Society of America
Original Manuscript: February 21, 2006
Revised Manuscript: June 14, 2006
Manuscript Accepted: June 16, 2006
Francesco Borghero and George Bozis, "Two solvable problems of planar geometrical optics," J. Opt. Soc. Am. A 23, 3133-3138 (2006)