Radiative transfer inside a linearly graded index semi-transparent slab: Gray substrate wall and specular semi-transparent surface

Radiative transfer inside a linearly graded index semi-transparent slab was analyzed. One boundary of the medium is a gray diffuse wall and the other is a specular semi-transparent interface. Curved ray-tracing technique was used to solve the radiative transfer equation and pseudo-source adding method was adopted to obtain the intensity of the gray wall. Based on these, the inner intensities were deduced. The analytical method of this paper can be used to check the correctness of previous work that was based on a multi-layered numerical method. The relative errors show that the previous method is effective in solving such problems.