The animated .gif above was created by calculating the scattering of visible light by a spherical water drop for 1, 10 and 100 micrometer diameters. The 1 um particle produces a fog bow (white region in center) and a corona (pale yellow region to the right). The 10 um particle produces a rainbow with supernumeraries (center pale spectral colors with stripes). The 100 um produces a rainbow (center spectra colors).

The MIE formulation for the scattering of light from a spherical particle is an exact calculation of the far-field scattering. In principle, the MIE formulation may be used for all particle sizes and wavelengths. In practice, MIE theory fills the gap between simple theories like Rayleigh scattering for particles small compared to wavelength and geometric optics for structures large compared to the wavelength of interest. The MIE formulation preserves interference effects (not generally handled by Rayliegh theory or ray-tracing) while also preserving the polarization effects. The following set of formulas is a summary of the results of the MIE formulation.

The scattering cross section equals

.

The coefficients are

The Riccati-Bessel functions are

The size parameter, which is the ratio of circumference to wavelength, is

.

The argument y is

where the ratio of the indices of refraction m is given by

the relative wavelength is

the angular functions are

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