Rayleigh scattering (named after Lord Rayleigh) is the elastic scattering of light or other electromagnetic radiation by particles much smaller than the wavelength of the light. It can occur when light travels in transparent solids and liquids, but is most prominently seen in gases. Rayleigh scattering of sunlight in clear atmosphere is the main reason why the sky is blue. Rayleigh and cloud-mediated scattering contribute to diffuse light (direct light being sunrays).
Figure showing the more intense scattering of blue light by the atmosphere relative to red light.
The size of a scattering particle is parameterized by the ratio x of its characteristic dimension r and wavelength ?:
Rayleigh scattering can be defined as scattering in small size parameter regime X<<1. 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 for small size parameter inversely with the fourth power of the wavelength. Scattering from larger spherical particles is explained by the Mie theory for arbitrary size parameter x including small size parameter - in this case Mie theory reduces to Rayleigh approximation.
The intensity I of light scattered by a single small particle from a beam of unpolarized light of wavelength ? and intensity I0 is given by:
where R is the distance to the particle, ? is the scattering angle, n is the refractive index of the particle, and d is the diameter of the particle.
The angular distribution of Rayleigh scattering, governed by the (1+cos2?) 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
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, in incoherent scattering the scattered powers add arithmetically, while in 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.
Rayleigh scattering from molecules
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A 5 mW green laser pointer is visible at night due to Rayleigh scattering and airborne dust.
Rayleigh scattering from molecules is also possible. An individual molecule does not have a well-defined refractive index and diameter. Instead, a molecule has a polarizability a, which describes how much electrical charges on the molecule will move in an electric field. In this case, the Rayleigh scattering intensity for a single particle is given by
The amount of Rayleigh scattering from a single particle can also be expressed as a cross section s. For example, the major constituent of the atmosphere, nitrogen, has a Rayleigh cross section of 5.1×10-31 m2 at a wavelength of 532 nm (green light). This means that at atmospheric pressure, about a fraction 10-5 of light will be scattered for every meter of travel.
The strong wavelength dependence of the scattering (~?-4) means that blue light is scattered much more than red light. In the atmosphere, this results in blue wavelength being scattered to a greater extent than longer wavelengths, and so one sees blue light coming from all regions of the sky. Direct radiation (from definition) is coming directly from the Sun. Rayleigh scattering is a good approximation to the manner in which light scattering occurs within various media for which scattering particles have small size parameter. |
