Reflectance of an Isotropically Scattering Coating on a Black Substrate

The influences of the medium\u27s refractive index on the radiation transfer through an absorbing-isotropically scattering finite medium on a black substrate were examined for the case when the incident radiation on the upper interface is diffuse. Approximate but closed-form solution to the governing radiative transfer equation was used to generate simple algebraic expressions for the intensity and flux distribution through the medium. Results are presented for the apparent hemispherical directional and hemispherical reflectances as a function of the medium\u27s refractive index, scattering albedo and optical thickness. Non-gray behavior can be evaluated readily by utilizing the proposed solution