  For a congruence of straight lines defined by a hypersurface in $R^{n+1}, n
\geq 1,$ and a field of reflected directions created by a point source we
define the notion of intensity in a tangent direction and introduce elementary
symmetric functions $S_m, m=1, 2,...,n,$ of {\it principal intensities}. The
problem of existence and uniqueness of a closed hypersurface with prescribed
$S_n$ is the "reflector problem" extensively studied in recent years. In this
paper we formulate and give sufficient conditions for solvability of an
analogous problem in which the mean intensity $S_1$ is a given function.
