Volume scattering function of light for a mixture of polydisperse small particles with various optical properties

Scattering of electromagnetic waves by a polydisperse system of small spherical hydrosol particles in the scalar approximation is considered. The equation for the scattering cross-section which generalizes the well-known Rayleigh-Gans-Rocar formula for a scattering medium containing particles characterized by continuous distributions in their dielectric permittivities at any given size is derived. For a natural situation, such as a coastal environment, the difference between volume scattering functions proposed in this paper and conventionally derived scattering functions can be as large as 50% for the particle size distributions with the maximum size of particles less than ten wavelengths of light.