The propagation of polarized light through the cornea is affected by the orientations of the corneal lamellae and by the refractive imbalance between the collagen fibrils and the ground substance. Thus, well-designed measurements and analyses of polarized light propagation through the cornea can be used to obtain information regarding the cornea's lamellar and fibrillar structures. This paper shows that, for the rabbit, measured values of the optical parameters strongly suggest that the distribution of lamellae orientations is not random, but has one (or two) preferred orientation directions. Also, there is considerable evidence that collagen is intrinsically anisotropic. The Weiner formula gives the effective birefringence of an assembly of parallel isotropic fibrils and its generalization to the case of anisotropic fibrils is presented. Finally, calculations based on preferred orientation models having lamellae composed of anisotropic fibrils show that comparison with experimental values can yield structural information.