A study is made of the directional transmittance of an isothermal dielectric surrounded by air. The dielectric sheet studied is assumed to be infinite in extent but of finite thickness much greater than one wavelength with plane parallel reflecting surfaces. The dielectric-air interfaces are assumed to be smooth, and therefore, reflect specularly according to Fresnel’s law. Interference is not considered in the solution. The approach to the problem is through the solution of the transport equation with boundary conditions considering refraction, total reflection beyond the critical angle, and directional irradiance. The results are plotted as the directional monochromatic transmittance for various optical depths with diffuse irradiance. The same curves may be read at a discrete direction to determine the monochromatic transmittance for mondirectional irradiance. The same procedure is followed to determine the directional emittance.
JOHN E. FRANCIS and TOM J. LOVE, JR., "Effect of Optical Thickness on the Directional Transmittance and Emittance of a Dielectric," J. Opt. Soc. Am. 56, 779-780 (1966)