Determination of complex refractive index using prism composed of absorbing medium

Abstract

In light refraction between two transparent media, Snell’s law describes the relationship between the incident angle and refraction angle. The refractive index is usually determined from Snell’s law using the minimum deviation angle through a prism. A medium that partially absorbs light has complex permittivity (or permeability), and its refractive index has an imaginary part. Because of the imaginary part, Snell's law does not hold for light-absorbing media. Accordingly, other methods are required to determine the complex value of the refractive index in a light-absorbing medium. The exact solution of Maxwell’s equations was obtained for light passing through a prism composed of a light-absorbing medium. Thereby the optical path was determined. The difference of optical paths between light-absorbing medium and transparent medium was calculated numerically. The difference is very large in the neighborhood of perfect reflection area of transparent medium. We found two methods to determine the complex value of the refractive index using the optical path. Both methods analyzed the solutions in detail for two specific incident angles. The deviation angles corresponding to the two incident angles determined the complex value of the prism’s refractive index. Of course, the obtained refractive index depends only on the material making up the prism, not on the apex angle of the prism.