Model of a nonhomogeneous medium conducting light

We consider a ray of light propagating within a system of infinitely many adjoining rectangles in a plane with passages between any pair of neighboring ones. The ray is assumed to be reflected by the sides of the rectangles, and is refracted while passing from one rectangle to its neighbor. We prove that if the sizes of the rectangles or the coefficients of refraction inside them are random, then with probability 1 the ray reaches arbitrarily remote rectangles.