Calculations by using the general Mie theory are rather complicated, even for the case of spherical particles, and the numerical results are often not simple for understanding. Fortunately, in some limiting cases, the scattering problem is simplified and it can be considered in terms of approximate theoretical models. A detailed discussion of various regimes of light scattering by homogeneous spherical particles has been presented by van de Hulst (1957). Following the recent monograph by Dombrovsky and Baillis (2010), we consider only the most important particular cases that appeared to be useful for analysis of the properties of disperse systems in numerous applications, namely, Rayleigh scattering, the Rayleigh-Gans scattering, geometrical optics approximation, and anomalous diffraction.
Dombrovsky, L. A. and Baillis, D., Thermal Radiation in Disperse Systems: An Engineering Approach, Begell House, Redding, CT, and New York, 2010.
van de Hulst, H. C., Light Scattering by Small Particles, Wiley, Hoboken, NJ, 1957 (also Dover Publ., 1981).