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# Rayleigh scattering

Rayleigh scattering (named after Lord Rayleigh) is the scattering of light by particles smaller than the wavelength of the light. It occurs when light travels in transparent solids and liquids, but is most prominently seen in gases. Rayleigh scattering of sunlight from particles in the atmosphere is the reason why the light from the sky is blue.

The amount of Rayleigh scattering that occurs to a beam of light is dependent upon the size of the particles and the wavelength of the light; in particular, the scattering coefficient[?], and hence the intensity of the scattered light, varies inversely with the fourth power of the wavelength, a relation known as the Rayleigh law. The angular intensity polarization relationships for Rayleigh scattering are conveniently simple. For particles not larger than the Rayleigh limit, there is complete symmetry of scattering about a plane normal to the direction of the incident radiation, so that the forward scatter equals the backward scatter. The Rayleigh scattering coefficient ks is

$k_s = \frac {2 \pi^6} {3} n \left( \frac {m^2 - 1} {m^2 + 2} \right)^2 \frac {d^5} {\lambda^4}$

where n is the number of scatters of diameter d; m is the index of refraction; and λ is the wavelength of the radiation.

This means that blue light is scattered much more than red light. In the atmosphere, this results in blue photons being scattered across the sky to a greater extent than photons of a longer wavelength, and so one sees blue light coming from all regions of the sky whereas the rest is still mainly coming directly from the Sun.

A notable exception occurs during sunrise and sunset, when the Sun's light must pass through a much greater thickness of the atmosphere to reach an observer on the ground. This extra distance causes multiple scatterings of blue light, but relatively little scattering of red light; this is seen as a pronounced red-hued sky in the direction towards the sun.

If the size of particles are larger then the wavelength of light, light is not separated and all wavelengths are scattered as by a cloud which appears white, as do salt and sugar. For scattering by particles similar to or larger than a wavelength, see the article on Mie scattering.

See also: Optical phenomenon

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