Scattering functions have been calculated for a homogeneous sphere surrounded by a concentric spherical shell. The scattering is insensitive to radial variation of the refractive index in the shell. The scattering from the radially varying case can be approximated by a sphere with a homogeneous concentric shell whose refractive index is intermediate between the internal and the external media.
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Kerker et al. (1966) studied this question.
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