Three-sided goniometric methods for measuring the refractive index

Physica Scripta. 2026. Vol. 101. Article 015501.

Yurin A., Vishnyakov G., Minaev V.

This paper describes goniometric methods for measuring the refractive index (RI) based on measuring the angles of light deviation with a triangular prism made from the material under study. Three-sided goniometric methods (TGM) involving measuring the angles of light deviation on all three faces of a prism and determining the RI by solving a system of equations are considered. The advantages and limitations of such an approach are analyzed. The calculation of the maximum allowable prism angles and measurement errors is given. It is shown that the use of TGM helps to increase the accuracy of RI measurements up to 2 times compared with the widespread minimum deviation method and avoids additional measurements of the prism angles. The limitation of TGM is the phenomenon of total internal reflection, which imposes a condition on the maximum allowable angle of the prism, depending on the value of the RI. This condition limits the measurement range to RI < 2.0. A reference prism set was studied using a high-precision goniometer with a digital autocollimator and the measurement errors were estimated. The calculated absolute error does not exceed ±1•10 -5 , which proves the prospect of using TGM for high-precision RI measurements.

Keywords: refractive index, prism methods, refractive index measurements, goniometry, measurements accuracy analysis

Publication based on the results of: Methods and tools for the development and implementation of digital twins for electronic engineering (2025)