Excerpt from The Inverse Scattering Problem in Geometrical Optics and the Design of Reflectors: January, 1958 1. Introduction When radiation of any type is incident upon an object some of the radiation is scattered in all directions by the object. The direct problem of the theory of scattering is that of determining the intensity of the radiation scattered in each direction when the properties of the incident radiation as well as those of the object are known. The inverse scattering problem is that of determining the properties of the scattering object when the incident radiation and the intensity of the radiation scattered in each direction are known. This latter problem has been studied extensively in atomic and nuclear physics by the methods of quantum mechanics and, to some extent, by classical mechanics. The classical mechanical solution is also applicable to the scattering of light (or other radiation obeying the laws of geometrical optics) by a region in which the index of refraction varies in any continuous spherically symmetric manner. We now propose to consider the inverse problem in geometrical optics when the scatterer is an opaque object, such as a piece of metal, with a definite boundary. We will call an object of this type a reflector or mirror. However the reflector may be placed so that either its concave or convex side is exposed to the incident radiation. When the incident radiation is a cylindrical wave a one parameter family of different reflectors is found. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.