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The exact homogenized probability density function, for a photon making astep of length $s$ has been analytically derived for a binary(isotropic-Poisson) statistical mixture with unmatched refractive indexes. Thecompanions, exact, homogenized probability density function for a photon tochange direction (``scatter'') with an angle $\vartheta$, and the homogenizedalbedo, have also been obtained analytically. These functions also hold even inthe case of negative refractive indexes and allow one to reduce hundreds of MCsimulations of photon propagation in complex binary (isotropic-Poisson)statistical mixtures, to only one MC simulation, for an equivalent homogeneousmedium. Note, that this is not an approximate approach, but a mathematicallyequivalent and exact result. Additionally, some tutorial examples ofhomogenized MC simulations are also given.

Probability density functions for photon propagation in a binary  (isotropic-Poisson) statistical mixture with unmatched positives/negatives  refractive indexes