Plane-wave scattering by small-angle cones

Rigorous expressions alternative to the familiar formulas in terms of spherical harmonic series are developed for the scattering of acoustic (and electromagnetic) waves by the tip of a perfectly rigid (or perfectly conducting) semi-infinite cone. For plane wave incidence the expressions are valid for observation points lying in a region excluding the rays which are reflected from the sides of the cone according to the laws of geometrical optics. Approximate closed-form results are obtained for on-axis or off-axis incidence and observation for cones with small apex angle for the acoustical plane wave scattering, and for electromagnetic scattering of incident waves whose electric vector is directed perpendicular to the cone axis. The results are correct to , where is the cone apex angle, and agree,for the special case of plane wave back-scattering along the cone axis, with those obtained previously by a different method. The case of diffraction by a spherically tipped cone is also treated.