Rayleigh scattering refers to the scattering of light off of the molecules of the air, and can be extended to scattering from particles up to about a tenth of the wavelength of the light. The most common example is blueness of the sky.
For particle sizes larger than a wavelength, Mie scattering predominates and it is not strongly wavelength dependent. The best example is white glare around the sun, where the air is dusty. Mie scattering, also populalrly known as, Mie theory provides rigorous solutions for light scattering by an isotropic sphere embedded in a homogeneous medium.
The best way to understand between these two scattering phenomena, the given figure may suffice.
Unfortunately, this rigorous solution is not easily available in any textbook. The following literature are the best resources:
– Mie, G., Ann.Physik,  25, 377(1908).
– van de Hulst, H.C., “Light Scattering by Small Particles,” Chapters 9 and 10, Wiley, New York, 1957.
– Kerker, M., “The Scattering of Light and Other Electromagnetic Radiation,” Chapters 3 and 4, Academic Press, New York, 1969.
– Bohren, C.F. and Huffman, D.R., “Absorption and Scattering of Light by Small Particles”, Wiley, New York, 1983.
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