thumb|300x300px|Rayleigh scattering causes the blue color of the sky at large angles to the direction of solar rays and yellow or orange colors for light from the direction of the Sun.
Rayleigh scattering ( ) is the scattering or deflection of light, or other electromagnetic radiation, by particles with a size much smaller than the wavelength of the radiation. For light frequencies well below the resonance frequency of the scattering medium (normal dispersion regime), the amount of scattering is inversely proportional to the fourth power of the wavelength (e.g., a blue color is scattered much more than a red color as light propagates through air). The phenomenon is named after the 19th-century British physicist Lord Rayleigh (John William Strutt).
thumb|300x300px|Due to Rayleigh scattering, red and orange colors are more visible during sunset because the blue and violet light has been scattered out of the direct path. This can yield [[Atmospheric_optics#Sky coloration|dramatically colored skies and monochromatic rainbows.]]
Rayleigh scattering results from the electric polarizability of the particles. The oscillating electric field of a light wave acts on the charges within a particle, causing them to move at the same frequency. The particle, therefore, becomes a small radiating dipole whose radiation we see as scattered light. The particles 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 of sunlight in Earth's atmosphere causes diffuse sky radiation. Since blue light wavelengths scatter more, the diffuse sky seen in daytime is blue. At twilight the sunlight on the horizon is missing the scattered blue light wavelengths giving a yellowish to reddish hue to the low Sun. He conjectured that a similar scattering of sunlight gave the sky its blue hue, but he could not explain the preference for blue light, nor could atmospheric dust explain the intensity of the sky's color. In 1881, with the benefit of James Clerk Maxwell's 1865 proof of the electromagnetic nature of light, he showed that his equations followed from electromagnetism. In 1899, he showed that they applied to individual molecules, with terms containing particulate volumes and refractive indices replaced with terms for molecular polarizability.
It was this paper that established the basic scientific model for the color of the sky.) and the whole surface re-radiates with the same phase. Because the particles are randomly positioned, the scattered light arrives at a particular point with a random collection of phases; it is incoherent and the resulting intensity is just the sum of the squares of the amplitudes from each particle and therefore proportional to the inverse fourth power of the wavelength and the sixth power of its size. The wavelength dependence is characteristic of dipole scattering
<math display="block"> I_s = I_0 \frac{ 1+\cos^2 \theta }{2 R^2} \left( \frac{ 2 \pi }{ \lambda } \right)^4 \left( \frac{ n^2-1}{ n^2+2 } \right)^2 r^6</math>
where R is the observer's distance to the particle and θ is the scattering angle. Averaging this over all angles gives the Rayleigh scattering cross-section of the particles in air:
<math display="block"> \sigma_\text{s} = \frac{ 8 \pi}{3} \left( \frac{2\pi}{\lambda}\right)^4 \left( \frac{ n^2-1}{ n^2+2 } \right)^2 r^6 .</math>
Here n is the refractive index of the spheres that approximate the molecules of the gas; the index of the gas surrounding the spheres is neglected, an approximation that introduces an error of less than 0.05%. Over the length of one meter the fraction of light scattered can be approximated from the product of the cross-section and the particle density, that is number of particles per unit volume. For air at atmospheric pressure there are about molecules per cubic meter, and the fraction scattered will be 10<sup>−5</sup> for every meter of travel.
From molecules
thumb|Figure showing the greater proportion of blue light scattered by the atmosphere relative to red light
The expression above can also be written in terms of individual molecules by expressing the dependence on refractive index in terms of the molecular polarizability α, proportional to the dipole moment induced by the electric field of the light. In this case, the Rayleigh scattering intensity for a single particle is given in CGS-units by
<math display="block">I_s = I_0 \frac{8\pi^4\alpha^2}{\lambda^4 R^2}(1+\cos^2\theta)</math>
and in SI-units by
<math display="block">I_s = I_0 \frac{\pi^2\alpha^2}