Elementary results for scattering by finite cones whose length and base dimensions are large compared to wavelength are obtained by approximating the surface fields in the integral representation by their geometrical-optics values. Both singly and doubly truncated cones are considered. A general expression is obtained for the location of the “specular beam” (i.e., the surface generated by the geometrically reflected rays), and simple results for the field on and off the “beam” are developed. In particular, it is shown that for many practical purposes a universal curve exists for the scattering pattern. This curve, which depends on a parameter involving the cone’s length and half-angle, falls more or less between the Fraunhofer “aperture” patterns for the strip and disk, and differs essentially in that the minima are not zero. Numerical illustrations are given.
J. E. BURKE, L. MOWER, and V. TWERSKY, "Elementary Results for Scattering by Large Cones," J. Opt. Soc. Am. 52, 1093-1104 (1962)