Validity of effective-medium theory in Mie scattering calculation of hollow dielectric sphere

The effective-medium theory is extended to calculate the equivalent dielectric constants of hollow spheres. The Maxwell-Garnett, inverted Maxwell-Garnett, and Monecke rules are adopted to investigate the hollow ice spheres. Compared with P. Yang's paper, very different Maxwell-Garnett and inverted Maxwell-Garnett formulas but identical mean permittivity values are presented. In order to verify the validity of effective-medium theory in Mie scattering calculation of hollow dielectric spheres, n-layered Mie solution is adopted to calculate the scattering of hollow ice spheres. The mean permittivity values are used in common Mie scattering calculation of uniform sphere. By comparison, it is evident that the effective-medium theory is suitable for small size parameters. For size parameter is about ten, the effective theory is suitable for a very thin hollow ice sphere. At last, it is pointed out that the effective-medium theory make Mie scattering calculation of hollow spheres easier, and can be extended further to non-uniform and eccentric hollow spheres.