  Due to dispersion, light with different wavelengths, or colors, is refracted
at different angles. Our purpose is to determine when is it possible to design
a lens made of a single homogeneous material so that it refracts light
superposition of two colors into a desired fixed final direction. Two problems
are considered: one is when light emanates in a parallel beam and the other is
when light emanates from a point source. For the first problem, and when the
direction of the parallel beam is different from the final desired direction,
we show that such a lens does not exist; otherwise we prove the solution is
trivial, i.e., the lens is confined between two parallel planes. For the second
problem we prove that is impossible to design such a lens when the desired
final direction is not among the set of incident directions. Otherwise, solving
an appropriate system of functional equations we show that a local solution
exists.
