Light scattering from a sphere behind a surface

The light scattered by a sphere behind a plane surface is solved with an extension of Mie theory. I solve the boundary conditions at the sphere and at the surface simultaneously and develop the scattering amplitude and Mueller scattering matrices. This approach involves the multiplication of the fields in the half-space region not including the sphere by an appropriate Fresnel reflection coefficient and the projection of these fields onto the half-space region including the sphere. The scattered fields from the sphere, reflecting off the surface and interacting with the sphere, are assumed to be incident upon the surface at near-normal incidence. The exact scatter approaches this limit when (1) the sphere is at a large distance from the surface, (2) the sphere radius is small compared with the incident wavelength, or (3) the difference between the refractive indices of the two half-space regions is either small or great.