Link between the laws of geometrical optics and the radiative transfer equation in media with a spatially varying refractive index

We proposed in a previous paper [J.-M. Tualle, E. Tinet, Opt. Commun. 228 (2003) 33] a modified radiative transfer equation to describe radiative transfer in a medium with a spatially varying refractive index. The present paper is devoted to the demonstration that this equation perfectly works in the non-absorbing/non-scattering limit, what was contested by Martí-López and coworkers [L. Martí-López, J. Bouza-Domínguez, R.A. Martínez-Celorio, J.C. Hebden, Opt. Commun. 266 (2006) 44]. The assertion that this equation would imply a zero divergence of the rays is also commented.