Single-scattering properties of Platonic solids in geometrical-optics regime

We investigate the single-scattering properties of the Platonic solids with size parameters in the geometrical-optics regime at wavelengths 0.66 and 11 μm using the geometrical-optics method. The comparisons between the results for the Platonic solids and four types of spherical equivalence show that the equal-surface-area spherical equivalence has the smallest errors in terms of the extinction cross section at both wavelengths. At a wavelength of 0.66 μm, all the spherical equivalences substantially overestimate the asymmetry factors of the Platonic solids; and in the case of strong absorption, they underestimate the single-scattering albedo. The comparisons also show that the spherical equivalences cannot be used to describe the spatial distribution of scattered intensity associated with a prismatic polyhedron.