Theoretical Investigations on the Light Scattering of Spheres. XVI. Range of Practical Validity of the Rayleigh Theory

Abstract

The errors committed on using the Rayleigh equations of light scattering at finite α values were evaluated numerically for spherical nonabsorbing particles using exact Mie data as the reference. The errors considered are Δα, Δα′, Δτ, and ΔI. Considering an error of 2% as the tolerable maximum, the upper limiting particle diameters which may be evaluated by means of the Rayleigh equations are, expressed in units relative to the wavelength (in the medium) used, 0.124 and 0.207 at m=1.00 and 1.30, respectively. These data which apply to the use of lateral scattering differ little from the limiting data obtained for diameters derived from turbidity. The errors committed on evaluating turbidity or lateral scattering from the Rayleigh equations are distinctly larger at identical true α values, and at identical m values. The interesting fact that the Rayleigh equations perform better the larger m—as long as m<∼1.8—opens up the possibility of using these equations for the evaluation of relative large particle diameters provided m is sufficiently large. Thus at m=1.63±0.2, particle diameters, dimensionally one-third the wavelength in the medium, are obtainable from the Rayleigh equations with 100% theoretical accuracy. This `.second'' range of validity of the Rayleigh theory appears to be of major meteorological and astrophysical interest.

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Affiliated Institutions

• Wayne State University US

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