Rayleigh scattering

Rayleigh scattering (named after Lord Rayleigh) is the scattering of light by particles much 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 an early approximation of the reason for why the light from the sky is blue.

Related Topics:
Lord Rayleigh - Scattering - Light - Wavelength - Light from the sky - Blue

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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. Scattering from particles larger than about a tenth of the illuminating wavelength is handled by Mie theory.

Related Topics:
Scattering coefficient - Mie theory

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The intensity I of light scattered by a single small particle from a beam of light of wavelength λ and intensity I0 is given by:

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: I = I_0 rac{ (1+cos^2 heta) }{2 R^2} left( rac{ 2 pi }{ lambda } ight)^4 left( rac{ n^2-1}{ n^2+2 } ight)^2 left( rac{d}{2} ight)^6

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where R is the distance to the particle, θ is the scattering angle, n is the refractive index of the particle, and d is the diameter of the particle.

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The angular distribution of Rayleigh scattering, governed by the (1+cos2 θ) term, is symmetric in the plane normal to the incident direction of the light, and so the forward scatter equals the backwards scatter. Integrating over the sphere surrounding the particle gives the Rayleigh scattering cross section σs:

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: sigma_s = rac{ 2 pi^5}{3} rac{d^6}{lambda^4} left( rac{ n^2-1}{ n^2+2 } ight)^2

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The Rayleigh scattering coefficient for a group of scattering particles is the number of particles per unit volume N times the cross-section.

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The strong wavelength dependence of the scattering (~λ-4) 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. It should be noted that, despite the use of the term photon, Rayleigh scattering was developed prior to the invention of quantum mechanics and is not based fundamentally in modern theory about the interaction of light with matter. Nevertheless, Rayleigh scattering is a fair approximation to the manner in which light scattering occurs within various media.

Related Topics:
Blue - Red - Photons

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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.

Related Topics:
Sunrise - Sunset

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If the size of particles are larger than 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.

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