A peculiar discontinuity in the intensity of light reflected by a plane-parallel atmosphere

A peculiar discontinuity in the intensity of light reflected by a plane-parallel atmosphere for horizontal directions of incidence and reflectance is uncovered. A formula is derived describing this discontinuity as a function of the albedo of single scattering and the phase (scattering) function, both at the top of the atmosphere, and the manner in which the directions of incidence and emergence become horizontal. This formula holds for atmospheres that are homogeneous or inhomogeneous, semi-infinite or finite with or without a reflecting surface underneath. Some illustrative examples and sample applications are also discussed.