Approximate Formula for the Total Scattering of Electromagnetic Radiation by Spheres

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Abstract
A semiempirical formula is given for the total scattering efficiency of electromagnetic radiation (light) by dielectric spheres of refractive index from 1 to 2. The formula neglects the “ripple” and gives a smooth curve Qs, which is much easier to apply to practical problems than the “unsmoothed” true function Qext, which is obtained from the exact Mie theory. The formula based on the theory of geometrical optics is asymptotic, approaching the true formula from the large-particle side. The ripple structure has been analyzed and it seems likely that the ripple arises from the interference between the reflected wave and surface waves travelling round the sphere, partly on the surface and partly along a series of “short cuts” through the interior.

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