The scattering of light by gases was first treated quantitatively by
Lord Rayleigh in 1871 in an effort to explain the blue colour of the sky
and the red colour of the sunset.
There are numerous ways of arriving at the equation which governs
Rayleigh scattering.
Classical EM theory can be employed using the far-field solution while
retaining only the dipole term (*e.g.*: Jackson, 1962).
Quantum mechanical perturbation theory
for two-photon elastic processes provides both a powerful and elegant
means (*e.g.*: Craig and Thirunamachandran, 1984).

In order for Rayleigh scattering to be valid, the size of the
particle must be much smaller than the wavelength of the incident
radiation, both inside and outside of the particle. These conditions
can be expressed as,

where

The route adopted herein is to consider the limiting case of Mie
scattering.
When equation (2.46) is valid, only the *n*=1 term in the
Mie scattering functions need be retained so that,

(3.48) | |||

(3.49) |

where , and . Furthermore, if equation (2.47) is valid, then and hence,

Using equation (2.32), the Rayleigh scattering matrix has the form

and from equation (2.39), the Rayleigh scattering cross-section is,

(3.54) |

where the approximation has been made, , and