Reflections on Refraction (Geometrical Optics)

. Consider an optical system made of an unknown number N of layers of homogeneous transparent plates with different unknown refraction indices. Observing beams of monochromatic light through the system, find the number N of plates together with their respective indices and their thicknesses. The mathematical analysis of the problem involves the so-called Hadamard quotient of two power series. We shall also discuss fractal optical systems consisting of infinitely many infinitely thin plates. If the index of refraction varies in an erratic way there may be multiple refraction. These systems could be called “refractals". We conclude the paper with independent considerations on a general system consisting of one plate with continuous varying index n ( x , y ) ≥ 1. To determine the function seems to be a difficult problem. Our contribution to solving it is thus very modest.