Ray Deflection through a Medium Having a Continuously Varying Refractive Index

Abstract

A method is outlined for computing the ray deflection through a medium having a continuously varying refractive index. General equations are developed by applying the calculus of variations to Fermat’s principle of optics. These equations are applied to the case of a dielectric material having a linear variation with distance in its refractive index and also to the case of a foam dielectric having a linear variation in density. A set of universal curves is presented for the case of a plane dielectric sheet having a linearly varying dielectric constant. The general equations presented here can also be applied to the design of lenses and optical devices having a continuously varying refractive index.