Radiation transport and internal reflection in a sphere

We construct an integral equation for the flux intensity in a scattering and absorbing medium using the integro-differential form of the radiative transfer equation in a sphere. The sphere is uniformly irradiated by an external source of arbitrary angular distribution. The Fresnel boundary conditions, which incorporate reflection and refraction, are used. For the special cases of a non-scattering medium, and in the limit of an optically transparent medium, we obtain exact solutions for specular and diffuse refection. Some numerical examples are given which give qualitative agreement with some recent work of Tian and Chiu (JQSRT, 2005).