In the case of uniformly diffuse internal incidence on a plane surface, formulas for the internal reflectance based on Fresnel’s laws have been given by Walsh and Judd. Several investigators of turbid media such as opal glasses have found, however, experimental values smaller than these. A new explanation is given in the present paper based on refraction instead of imperfect diffusion as suggested in the literature. It is verified by a series of observations with two kinds of opal glasses. The only formulas used in this paper are those given long ago by Stokes, adapted for diffuse incidence. A unique solution of the Stokes formulas is given here. The underlying theory is the two-constant Schuster theory, whose shortcomings are also discussed.
FRIEDRICH KOTTLER, "Turbid Media with Plane-Parallel Surfaces," J. Opt. Soc. Am. 50, 483-490 (1960)