Correct equations and common approximations for calculating Rayleigh scatter in pure gases and mixtures and evaluation of differences.
Equations for Rayleigh scattering in a mixture of gases are derived and compared to frequent approximations in the literature. The traditional Rayleigh scattering equation as modified by King for scatter from a pure gas is correct, whereas another version sometimes appearing in modern literature is erroneous. Use of a mixture's refractive index, which is equivalent to assuming the isotropic molecular polarizabilities of the component gases are identical, is an approximation. Another common approximation is using only number-density weighting of the King factors. Approximation errors can be large when the major components of a mixture have disparate optical properties. Fortunately, the errors for Earth's air are much smaller and comparable to errors from other sources.
Eberhard
Wynn L
WL
National Oceanic and Atmospheric Administration Earth System Research Laboratory, 325 Broadway, Boulder, Colorado 80305, USA. wynn.eberhard@noaa.gov