**The Harmonic Interchangeability Variance of Cauchy Constant’s Value: A and B**

Rawand H. Abdullah and Farmesk J. Abubaker

University of Sulaimani, College of Education, Physics Department. Zanko Street, Sulaimani, Kurdistan Region Iraq

**Abstarct**

The strong relationship of refractive index of a material with wavelengths dates back to more than a century especially where Sellmeier’s equation was invented by Wolfgang Sellmeier in 1871 and then developed by Cauchy for visible region of electromagnetic waves. In this work, we studied the interchangeability of Cauchy constants A and B for a glass prism by using inert gas light sources such as He and Ne and metal vapor light sources as Hg, Cd, HgCd, and Na. Cauchy formula represents this dependence where A and B are Cauchy constants and their value are harmonically interchangeable. We investigated that each light sources have a different value of A and B and does not follow the same pattern of graphical representation. From this result, one can notice that Cauchy constants have a crucial role on this dependence of refractive indices on the wavelength of the light sources. The novelty of this work is the combination of Geometrical Optics and Wave Optics, then formulating a new

equation, which is exactly geometrical measurements.

**Keywords**: Cauchy Formula, Gratings, Prism, Inert Gases and Metal Vapor Light Sources, Deviation Angle, Spectral Width.

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