Intensity and Polarization for Single Scattering by Polydisperse Spheres: A Comparison of Ray Optics and Mie Theory

The intensity and polarization for single scattering by large spherical particles are computed using both the exact Mie theory and the approximation of ray optics. It is found that the ray-tracing method can yield accurate results for particle size parameters in the range of interest for some meteorological applications, where the size parameter is the ratio of the particle circumference to the wavelength of the incident light. Since this method is practical for application to nonspherical particles, it should be of use in studies of cloud microstructure. The ray-optics method is also useful in the case of spherical particles because it provides a physical explanation for features which occur in the exact theory. The ray-optics calculations include Fraunhofer diffraction as well as geometrical reflection and refraction; rays undergoing one or two internal reflections, which give rise to the observable rainbows, are also included. Calculations are made for non-absorbing and absorbing spheres for several refractive indices in the range 1.1 ≤ nr ≤ 2.0. Comparisons between the ray-optics approximation and the exact Mie theory are made for nr = 1.33 and 1.50. It is found that the two methods are in close agreement, if the particle size parameter is ≳400. It is also shown that, to a good approximation, the ray-optics solution may often be used to obtain the entire phase matrix for single scattering.