# Rayleigh scattering

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Rayleigh scattering (named after the British physicist Lord Rayleigh) is the elastic scattering of light or other electromagnetic radiation by particles much smaller than the wavelength of the light, which may be individual atoms or molecules. It can occur when light travels through transparent solids and liquids, but is most prominently seen in gases. Rayleigh scattering is a function of the electric polarizability of the particles.

Rayleigh scattering of sunlight in the atmosphere causes diffuse sky radiation, which is the reason for the blue color of the sky and the yellow tone of the sun itself.

Scattering by particles similar to or larger than the wavelength of light is typically treated by the Mie theory or the discrete dipole approximation.

## Contents

### Small size parameter approximation

The size of a scattering particle is parametrized by the ratio x of its characteristic dimension r and wavelength λ:

Rayleigh scattering can be defined as scattering in the small size parameter regime x ≪ 1. Scattering from larger spherical particles is explained by the Mie theory for an arbitrary size parameter x. For small x the Mie theory reduces to the Rayleigh approximation.

The amount of Rayleigh scattering that occurs for a beam of light is dependent upon the size of the particles and the wavelength of the light. Specifically, the intensity of the scattered light varies as the sixth power of the particle size and varies inversely with the fourth power of the wavelength.

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

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.

The Rayleigh scattering coefficient for a group of scattering particles is the number of particles per unit volume N times the cross-section. As with all wave effects, for incoherent scattering the scattered powers add arithmetically, while for coherent scattering, such as if the particles are very near each other, the fields add arithmetically and the sum must be squared to obtain the total scattered power.