The problem of scattering of spherical waves by a bounded obstacle is considered. General scattering theorems are proved. These relate the far-field patterns due to scattering of waves from a point source put in any two different locations. The scatterer can have any of the usual properties, penetrable or impenetrable. The optical theorem is recovered as a corollary. Mixed scattering relations are also established, relating the scattered fields due to a point source and a plane wave.

The problem of scattering of spherical electromagnetic waves by a bounded chiral obstacle is considered. General scattering theorems, relating the far-field patterns due to scattering of waves from a point source put in any two different locations (the reciprocity principle, the optical theorem, etc), and mixed scattering relations (relating the scattered fields due to a point source and a plane wave) are established. Further, in the case of a spherical chiral scatterer, the exact Green's function and the electric far-field pattern of the problem are constructed.