An approximate, analytical solution is developed for the intensity of electromagnetic radiation resulting from a line or cylindrical source located within and normal to the boundaries of an infinite slab of purely scattering material. The source strength is allowed to vary arbitrarily along the line or cylinder, and the slab is considered to have one absorbing (or open) surface and one partially reflecting surface. The problem represents an idealization of the attenuation of thermal radiation from a nuclear fireball within a layer of fog or a dispersion of oil particles. The six-flux resolution of scattered energy proposed by Chu and Churchill is utilized. In general, machine computations are needed to obtain numerical results. Approximations are suggested for use in the indicated computations. Illustrative numerical results are presented.