Certain Transmission and Reflection Theorems (Classic Reprint)

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Excerpt from Certain Transmission and Reflection Theorems In this paper we treat certain theorems which are of interest in connection with the scattering and reflection of electromagnetic and acoustic waves. In Section 2, which serves primarily to introduce notation, we consider the scattering of a plane wave by a cylinder of arbitrary cross-section and arbitrary physical constants. 'we present the well-known relation, that the real part of the forward scattered amplitude is proportional to the total energy cross-section per unit length of cylinder, which is defined as the power the cylinder dissipates as heat and as scattered radiation per unit length. We then derive a corollary of this theorem and apply it to obtain an approximate transmission coefficient for a uniform planar distribution of identical cylinders. In Section 3 we consider the analogous reflection problem for an arbitrary cylindrical protuberance on a smooth perfectly reflecting plane. We derive a theorem stating that the total cross-section is proportional to the real part of the scattering amplitude in the direction of specular reflection of the plane. 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.