More on patterns in Mie scattering

The powerlaw patterns in Mie scattering (the normalized light intensity I( θ)/ I(0) vs. the dimensionless qR where q=4 πλ ^-1sin{θ}/{2} is the magnitude of the wave vector transfer at the scattering angle θ for wavelength λ, and R is the radius of the nonabsorbing sphere with a relative refractive index m>1) are analyzed using the geometrical optics approximation for particles of a large size parameter. The ( qR) ^-4 powerlaw regime is shown to be present only in Mie scattering of soft particles. The ( qR) ^-2 powerlaw regime occurs at the scattering angles of the p=1 geometrical ray (refracted without internal reflections) from the portion of the incident beam with an incidence angle around π/4 upon the particle. The ( qR) ^-2 powerlaw regimes from particles sharing one common relative refractive index but differing in size parameters are collinear. Simple analytical expressions are derived to describe these powerlaw regimes of Mie scattering.