The propagation of photons in complex media, such as K-colored (isotropic-Poisson) statistical mixture, is typically investigated through Monte Carlo methods, which are inherently time-consuming. In this article, we show that under the Lambertian illumination hypothesis and thanks to a generalized invariance property, the K-colored statistical mixture can be fully described by an equivalent homogeneous medium characterized by a homogeneous refractive index. This greatly simplifies the implementation of Monte Carlo codes. To illustrate our findings, we present Monte Carlo simulations carried out on various tutorial examples.