= Rayleigh scattering
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<Rayleigh scattering> is <elastic scattering> of <electromagnetic radiation> by particles much smaller than the incident <wavelength>. In the stationary particle approximation, the scattered <electromagnetic radiation> keeps the incident <frequency>: its direction changes, rather than its color. The incident <electric field> induces an oscillating <electric dipole moment>, which produces <electric dipole radiation>. This is a useful example of how a microscopic response can explain a familiar large-scale sight, <why the sky is blue>. https://farside.ph.utexas.edu/teaching/jk1/lectures/node108.html[Richard Fitzpatrick, Rayleigh Scattering: bound-charge response and wavelength dependence]{ref}.
The smallness condition for <Rayleigh scattering by a small sphere> of <radius> $a$ is $ka\ll1$, where the <wavenumber> is $k=2\pi/\lambda$ and $\lambda$ is the surrounding medium's <wavelength>. For ordinary materials with modest <refractive index>, the incident <electric field> then varies little across the particle, making the <electric-dipole approximation for radiation> useful. For very large <refractive index>, also check the internal size $|m|ka\ll1$ before applying the simple <electric dipole> model. Once these conditions fail, use <Mie scattering> for a <sphere> instead of extrapolating the <Rayleigh scattering wavelength dependence>.
Historically, the 1871 paper https://en.wikisource.org/wiki/Scientific_Papers/Volume_1/On_the_Light_from_the_Sky,_Its_Polarization_and_Colour[Rayleigh, On the Light from the Sky, Its Polarization and Colour: original-paper transcription]{ref} connected the color and <polarization of an electromagnetic wave> of scattered skylight with particles smaller than the <wavelength>. Its <dimensional analysis> anticipates scattered <light intensity> proportional to particle <volume> squared and to $\lambda^{-4}$. The original mechanical picture is historical; the modern explanation uses induced <electric dipole radiation>.
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