The Calculation of Refractive Indices and Optical Dispersion Using Prism Technique

Abstract

This study aims to calculate the refractive indices and optical dispersion of silicates using a novel small-prism technique. Utilizing prisms with thicknesses of 1-2mm, held by a ceramic sample holder and illuminated by a Hg–Cd light source, we determined the refractive indices at λ = 589.3 nm and for infinite wavelength using the Sellmeier equation. This paper presents the results of these measurements, providing insights into the optical properties of silicates.

Introduction

Accurate refractive indices and optical dispersion are very useful for many purposes that are listed below:

1. The resultant data helps in the determination of theoretical, empirical polarizability and bond: Comparison of theoretically calculated indices with experimentally determined (n) by extrapolation to infinite wavelength is imperitive for the theoretical parameter accuracy assessment.
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   By using values one can find the theoretical n calculations.

2. Electronic polarizability values α are traditionally derived from the relationship between Clausius and Lorentz, which relates to polarizability to and crystalline molar volume.12–14 Extensive and accurate knowledge of refractive indices and their dispersion is necessary for these derivations.
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   One of the aims of this study was to provide a database of refractive indices with accompanying composition, unit cell dimensions, and dielectric properties that could serve as the basis for a set of values for use in deriving a more extensive set of electronic polarizability than there is now.

3. This data importan in the prediction of nonlinear refractive indices of materials used for frequency shifting and harmonic generation. A good relationship between the nonlinear refractive index coefficient() and the linear refractive index(n) magnitude and dispersion can be useful for the estimation of approximate glass and crystalline material values.
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Experiment

The study utilized several silicate samples, as detailed in Table 1 below.

Table 1: List of Silicate Samples Used in the Study

Apparatus

For calculating refractive indices and optical dispersion An optical two-circle goniometer (Stoe Type F 2.13.0) with a polarizing device and microscope optics, was used and vertical circle is eliminated to increase the accuracy of the measurement.In this Experiment the deviation of light is measured in in two symmetric positions by displacement of both the prism and the light source to the both sides Left side as well as right side. This leds to an increase of measurement accuracy by resulting a value of twice the angle of minimum deviation values in 2d instead of d measured the deviation of the light beam

The light source was a Hg–Cd spectral lamp, which emits 8 lines covering the range 643.8–404.7 nm. Although it would have been desirable to extend the dispersion measurements to longer wavelengths, the light source and apparatus did not permit that option. Prisms with faces with 1 mm 3 1 mm cross section give sharp and well-defined lines when they are prepared in the manner described below. Smaller faces result in a broadening of lines, as described by Leiss.

Sample Preparation

Samples were prepared using a MACOR ceramic holder designed for holding eight specimens simultaneously. This holder facilitated the efficient preparation and analysis of multiple samples.

Results

The Sellmeier coefficient, along with the calculated refractive indices at λ = 589.3 nm and for infinite wavelength (λ = ∞), are presented in the following table.

Table 2: Sellmeier Coefficients and Calculated Refractive Indices

The Sellmeier equation was successfully applied to model the dispersion in the visible region, providing a comprehensive understanding of the optical properties of the studied silicates.

Conclusion

The small-prism technique demonstrated in this study offers a precise method for calculating the refractive indices and optical dispersion of silicates. The data obtained provides valuable insights into the materials' optical properties, contributing to the broader knowledge of silicate materials and their applications in optical technologies.

References

1. Wemple, S.H., and DiDomenico, M. Jr., "Behavior of the Electronic Dielectric Constant in Covalent and Ionic Materials." Physical Review B, vol. 3, no. 4, pp. 1338–1351, 1971.
2. Leiss, A., "Methods of Small-Prism Preparation for Optical Measurements." Journal of Applied Crystallography, vol. 22, pp. 546–550, 1989.
3. Schneider, F., "MACOR Machinable Glass Ceramic for High-Precision Optical Components." Ceramics International, vol. 35, no. 2, pp. 849–856, 200