An exact theory is presented for calculating electromagnetic scattering by a model heterogeneous particle. The model is a multilayer sphere composed of alternating layers of different dielectric constants in the limit where the number of layers approaches infinity and the layer thickness approaches zero. The scattering analysis for this limiting case is based on a formulation of scattering theory known as the variable-phase method (VPM). A derivation of the VPM formulation is presented. Analytic formulas are derived for the scattering coefficients of the heterogeneous sphere that are generalizations of similar Mie theory formulas for scattering by a homogeneous sphere. The optical properties of the layered heterogeneous mixture are exactly described in this theory by the two effective-media parameters. The solution in the long-wavelength limit is used to derive a new formula for the effective dielectric constant for heterogeneous mixtures.
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