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The finite sum of the squares of the Mie coefficients is very useful foraddressing problems of classical light scattering. An approximate formulaavailable in the literature, and still in use today, has been developed todetermine a priori the number of the most significant terms needed to evaluatethe scattering cross section. Here we obtain an improved formula, whichincludes the number of terms needed for determining the scattering crosssection within a prescribed relative error. This is accomplished using extendedprecision computation, for a wide range of commonly used size parameters andindexes of refraction. The revised formula for the finite number of terms canbe a promising and valuable approach for efficient modeling light scatteringphenomena.

Effect of finite terms on the truncation error of Mie series