A note on the expansion coefficient of geometrical optics

Abstract

Abstract : The expansion coefficient of geometrical optics is a measure of the cross section os, New York U., N. Y. A NOTE ON THE EXPANSION COEFFICIENT OF GEOMETRICAL OPTICS, by Morris Kline. 1961, 12p. (Research rept. no. EM-166) (Contract AF 19(604)5238) Unclassified report DESCRIPTORS: *Optics, *Electromagnetic theory, *Differential geometry, Light, Electron optics, Series, Geometry. The expansion coefficient of geometrical optics is a measure of the cross section of a tube of rays and has the physical significance of measuring the intensity of the light propagating along the tube. Strictly, it is a point concept and measures the intensity along an individual ray. This paper presents a convenient expression for the expansion coefficient. The mathematics involved is merely an application of known differential geometry but the expression derived seems to be new and is apparently unknown to workers in electromagnetic theory. The new feature of this paper is that the formula given for the variation of the expansion coefficient holds in inhomogeneous isotropic media and reduces immediately to the widely known expression for the expansion coefficient in homogeneous media, which involves the Gauss curvature of the wave front. (Author)