Plane wave diffraction from a small half-sphere mounted on a large conducting body

Using image theory and the scattering solution for a sphere, the plane wave scattering by a small, perfectly conducting half-sphere on a conducting plane is obtained first. The scattered field can then be identified as that radiated from a combination of electric and magnetic dipoles on the plane. Equating these dipole fields to the corresponding radiation dipoles, we can solve for the induced scattering dipole moments. These moments can now be used to obtain the scattering of a small half-sphere mounted, for example, on large cones spheres, cylinders etc., provided the simpler problem of radiation dipoles on the large bodies has been solved first.