  We present an abstract method in the setting of compact metric spaces which
is applied to solve a number of problems in geometric optics. In particular, we
solve the one source near field refraction problem. That is, we construct
surfaces separating two homogenous media with different refractive indices that
refract radiation emanating from the origin into a target domain contained in
an n-1 dimensional hypersurface. The input and output energy are prescribed.
This implies the existence of lenses focusing radiation in a prescribed manner.
