Determination of Complex Refractive Index using Maximum Deviation Angle through Prism

TL;DR

This paper presents a method to determine the complex refractive index of light-absorbing materials using the maximum deviation angle in a prism, which is sensitive to both real and imaginary parts of the index.

Contribution

It introduces a novel approach based on the local maximum deviation angle to accurately measure complex refractive indices of absorbing materials.

Findings

The deviation angle has a local maximum sensitive to the complex refractive index.

The method allows easy determination of complex refractive index from measured angles.

The technique can be used for material identification with liquids in a prism.

Abstract

Light-absorbing materials are widely used, and their optical properties are an important factor. Snell's law does not hold in materials that partially absorb light. Hence, the optical path in refraction is calculated from Maxwell's law. We used it to obtain the deviation angle when a light passes through a prism made of light absorbing material. As a result, the deviation angle has a local maximum point. The deviation angle near the local maximum is sensitive to the real and imaginary parts of the refractive index. The local maximum deviation angle and its incident angle are used to determine the complex index of refraction. This measurement has the same advantages as measuring the minimum deviation angle of a transparent prism. That is, when the optical bench is slightly rotated and the measurement light is observed, the moving direction of the light-spot is reversed at the extreme value. The detection is easy. Then, it is necessary to determine the complex refractive index from the measured local maximum deviation angle and its incident angle. These two angles are plotted parametrically by varying the real part of the refractive index under a fixed imaginary part. The similar curves are drawn under the fixed real parts. Each curve has a fixed value for the real or imaginary parts of the refractive index. Drawings of these many curves are made prior to measurement. Then we select the four curves that are closest to the local maximum deviation angle and its incident angle. Four fixed values attached to each of the four curves determine the complex index of refraction. Various liquids can be put in a prism container made of parallel plate glass and their local maximum deviation angles are measured. The method in this paper can easily determine the complex refractive index and can be used for material identification