From AMS Glossary
Approximate theory for electromagnetic scattering by small particles named for Lord Rayleigh (John William Strutt, 1842–1919), who in 1871 showed that the blue color of the clear sky is explained by the scattering of light by molecules in the atmosphere.
The Rayleigh approximation to the more complex Mie theory requires that the particles be very small in comparison to the wavelength of the radiation. The range of applicability of the Rayleigh theory depends on the refractive index of the particles. For water drops the criterion is usually stated as D < λ/10, where D is the drop diameter and λ is the wavelength of the incident radiation. Characteristics of Rayleigh scattering are that the scattering cross section of a sphere of diameter D is proportional to D6/λ4 and that the phase function is proportional to (1 + cos2θ), where θ is the scattering angle. In radar, Rayleigh scattering theory is usually employed to interpret the observations of echoes from precipitation, even though the Rayleigh criterion is not satisfied by raindrops for wavelengths much shorter than 10 cm or by hailstones for even longer wavelengths. Corrections based on Mie theory are sometimes applied to observations at wavelengths shorter than 3 cm. Large raindrops and hailstones can deviate from spherical shape; radar scattering by nonspherical particles has been approximated by the Gans theory for small ellipsoids.
Bohren, C. F., and D. R. Huffman 1983. Absorption and Scattering of Light by Small Particles. Wiley, New York, . 3–223.
McCartney, E. J. 1976. Optics of the Atmosphere. Wiley, New York, . 176–262.