Resolving the Refractive Indices of Transparent and Translucent Liquids from the Spacings, Spatial Frequencies, and Directions of Interference Fringes

Abstract

In this work, we present a novel approach to resolve the refractive indices of transparent and translucent liquids from straight interference fringes. The optical path difference between the two arms of the Mach–Zehnder interferometer is first derived by assuming a reference plane wave interfering with a plane wave passing through a rectangular cuvette. The analytic expressions for the liquid refractive indices are then deduced, describing how the refractive index is related to the fringe spacings, spatial frequencies, and directions. The structure coefficients in the above formulas are determined from the fringe spacings and directions of the interference patterns of the empty cuvette and the cuvette filled with a liquid of a known refractive index. The NaCl solution and Coca Cola are adopted as the test examples to show experimentally the validity of the proposed method. There is good agreement between the refractive indices obtained from the fringe spacings and direction of a single interference pattern. The sensitivity and resolution of this method are dependent on the structure of the experimental systems and thus can be adjusted in a controlled manner. The proposed method is simple to implement and can be easily extended to other high precision optical interferometer systems.

Keywords

• Mach–Zehnder interferometer
• refractive index measurement
• fringe spacing
• fringe direction