Theory of Transparency of the Eye

Abstract

The present work relates the turbidity of the eye to microscopic spatial fluctuations in its index of refraction. Such fluctuations are indicated in electron microscope photographs. By examining the superposition of phases of waves scattered from each point in the medium, we provide a mathematical demonstration of the Bragg reflection principle which we have recently used in the interpretation of experimental investigations: namely, that the scattering of light is produced only by those fluctuations whose fourier components have a wavelength equal to or larger than one half the wavelength of light in the medium. This consideration is applied first to the scattering of light from collagen fibers in the normal cornea. We demonstrate physically and quantitatively that a limited correlation in the position of near neighbor collagen fibers leads to corneal transparency. Next, the theory is extended to predict the turbidity of swollen, pathologic corneas, wherein the normal distribution of collagen fibers is disturbed by the presence of numerous lakes-regions where collagen is absent. A quantitative expression for the turbidity of the swollen cornea is given in terms of the size and density of such lakes. Finally, the theory is applied to the case of the cataractous lens. We assume that the cataracts are produced by aggregation of the normal lens proteins into an albuminoid fraction and provide a formula for the lens turbidity in terms of the molecular weight and index of refraction of the individual albuminoid macromolecules. We provide a crude estimate of the mean albuminoid molecular weight required for lens opacity.