The diffraction of plane electromagnetic waves by a perfectly reflecting sphere

Abstract

Introduction. -The problem of the diffraction of electromagnetic waves by a perfectly conducting sphere is of interest both from the point of view of wireless and from that of physical optics. Two cases may be considered: (1) when the source of the waves is a Hertzian oscillator on the surface of the sphere; and (2) when the waves are plane. The formal series solution of both these problems has been given by several writers, including Sir J. J. Thomson, the late Lord Rayleigh, and Prof. H. M. Macdonald. For a sphere of which the radius is small compared with the wave-length the series converge rapidly and are suitable for computation, but for a large sphere the important terms are far on in the series and the latter must be transformed in order to get formula which may be of use. For case (1) this problem has been attacked by Macdonald, Poincare, J. W. Nicholson, A. E. H. Love and several others, but case (2) has not attracted nearly so much attention. This paper, then, deals with case (2).