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The rigorous theory of the conversion between the scattering of uniform plane electromagnetic wave by a perfectly conducting sphere and the scattering of uniform plane acoustic wave by a rigid sphere is studied in this paper. The conversion formula between these two different scattering based on two calibration curves is derived, which describes the quantitative relationship between acoustic and electromagnetic wave scattering at arbitrary frequencies by spheres of arbitrary sizes. In addition, the scaling relationship of the sizes of those two spheres and the corresponding frequencies are discussed in detail, and an indirect method of measurement of electromagnetic scattering by the spheres is proposed

The derivation of scaling relationship between acoustic and electromagnetic scattering by spheres