Estimate of Errors in Measurements of Refractive Index by Modified Prism Methods

Goniometric methods of measuring the refractive index of optically transparent materials based on the refraction of light by a triangular prism are studied. A modified minimum deviation method and 3 modified constant deviation methods are examined which make it possible to determine the refractive indices of triangular prisms with unknown refracting angles. According to the modified prism methods the deflection angles of the light by the prism are measured with a goniometer, while the refractive index of the material and the refraction angles of the prism are determined by solving systems of equations. Thus, there is no need for preliminary measurement of the prism angles, which would require special autocollimation goniometers. In addition, in the modified prism methods, light reflected from the faces of the prism is not used, which makes it possible to extend the spectral range of a measurement of the refractive index to the infrared and ultraviolet ranges. The errors in measurements of the refractive index by these methods are compared for the example of a prism with a refractive index of 1.5 and a refraction angle of 60 degrees. It is shown that the modified minimum deviation method has the smallest error among all the prism methods, so it can be recommended for high-precision measurements of the refractive index in those cases where the refractive angles of the prism are unknown or it is technically difficult to measure them. The modified methods examined here can be used for measuring the refractive index of triangular prisms made of optically transparent materials, as well as of liquids poured into hollow prisms with plane-parallel transparent windows. Practical implementation of methods of this type should be useful in the optical, chemical, and food industries for monitoring the composition and properties of optically transparent materials.