High-precision numerical methods are used to find the transmitted and reflected fluxes for conservative isotropic scattering and Rayleigh scattering, for a wide range of slab thicknesses. Idealized models are then used to derive simple analytical expressions. These expressions are evaluated numerically, and the results are compared against the earlier calculations. The fluxes from all models are in excellent agreement with the high-precision calculations for all optical thicknesses from zero to fifty, indicating that the formulas derived provide very good approximations to the diffusely reflected fluxes. It is also shown that the external fluxes are virtually independent of the nature of the local scattering law for the cases considered. The conservative nature of the scattering indicates that none of the energy is truly absorbed but is ultimately reflected or transmitted. The ratio of reflected to transmitted flux is shown to be dependent on the optical thickness and the direction of illumination, but very insensitive to the phase function. 40 pp. Refs.
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