In this paper, with the aid of invariant imbedding, we discuss the mathematical model of a searchlight on a target of turbid plane-parallel atmosphere, bounded below by a diffuse reflector. In the real physical situation, the faint background light illuminating the top is considered. However in this paper, for the sake of simplicity, the angular distribution of radiation emergent from the top with a point source is considered, by imbedding the problem within a family of parameters.