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The exact spheroidal-function series solution for the scattering of a plane wave by a penetrable spheroid is used to obtain explicit low-frequency (long-wavelength) approximations in ascending powers of k = 2π/λ, where λ is the wavelength. The farfield scattering amplitude is given to the sixth power of k, and the fields near and inside the spheroid are given to the second and first power, respectively. The results are valid for prolate and oblate spheroids and arbitrary angles of incidence and observation.
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J. E. Burke (1968) studied this question.
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