The problem of electromagnetic scattering by a sphere on a layered substrate is treated and numerical results are presented. Initially, the Rayleigh limit, where the sphere radius is small compared to the wavelength, is considered. Closed-form expressions for the far-zone scattered fields are derived from the radiation of the induced dipoles in the sphere in the presence of the substrate, and these incorporate in a rather explicit manner the various parameters of the problem. The general case, where the ratio sphere radius/wavelength is arbitrary, is also considered. A rigorous formulation is used based on the Mie solution for the scattering by a sphere in a homogeneous medium and an extension of Weyl's method for dipole radiation in the presence of a flat surface. Numerical results obtained using the rigorous formulation for electrically small spheres are in very good agreement with those obtained using the Rayleigh approximate method
