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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


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.

KeywordsCauchy Formula, Gratings, Prism, Inert Gases and Metal Vapor Light Sources, Deviation Angle, Spectral Width.


[1] Cowan, R. D. "The Theory of Atomic Structure and Spectra". USA: University of California Press, Berkeley. (1981).

[2] Onorato, P., Malgieri, M, and De Ambrosis, A. "Measuring the hydrogen Balmer series and Rydberg’s constant with a homemade pectrophotometer". European Journal of Physics (IOP). (2015).

[3] Born, M. and Wolf E. "Principles of Optics". UK: Cambridge University Press, 7th Edn. (1999).

[4] Southhall, J. "Mirrors, Prisms and lens: a textbook of geometrical optics". New York: The Macmillian Company. 3rd Edn, pp. 112-137. (1933).

[5] Bass, M. "Handbook of Optics". USA: McGraw-Hill. Vol.2, 2Edn, pp.14.6. (1995).

[6] Nayar, S. K., "Surface Reflection: Physical and Geometrical Perspective". IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 13, No.7. (1991).

[7] Lawrence, G. N. "Integrating Geometrical and Physical Optics with the Lens group Operator Method". Part of the SPIE Conference on Optical Design and Analysis Software. (1999).

[8] Hyder, D., "Physiological Optics and Physical Geometry". Science in Context, Vol. 14, pp 419-456. (2001).

[9] Wyrowski, F. and Hellmann, C. "Geometrical Optics Reloaded: Physical optics modeling with smart rays". WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim: Optik and Photonik. (2015).

[10] Qin, Y. et al. "Comparison between ray-tracing and physical optics for the computation of light absorption in capillaries – the influence of diffraction and interference". Optical Society of America. (2012).

[11] Alphonse, F., "Refractive Index as a Function of Wavelength for Sixty API- NBS Hydrocarbons". Part of the Journal of Research of the National Bureau of Standards. (1950).

[12] Micheal E. "Optical Propagation in Linear Media: Atmospheric Gases and Particles, Solid-State Components, and Water". UK: Oxford University press. pp.78-79, pp.364-372. (2006).

[13] Iizuka, K. "Engineering Optics". USA: Springer, 3rd Edn. (2007).

[14] Ghosh, G. "Handbook of Optical Constants of Solids: Handbook of Thermo-Optic Coefficients of Optical Materials with Applications". Edited by Edward D. Palik. Academic Press, Japan, Vol.5. (1998).
[15] Estey, R. "The Use of AO Spenser Spectrometer". New York: American Optical Company. (1938).

[16] Loyd, D. "Physics Laboratory Manual: Diffraction grating measurement of the wavelength of light". Thomson Brooks/cole. (2008).

[17] Wagh, A. and Rakhecha, V. "Geometric formula for prism deflection". Panama Journal of Physics. India: Vol.63, No.2. (2004).

[18] Chris I., "Teach astronomy, emission lines and bands available from: Teach Astronomy", (accessed 26 April (2016).

[19] Sharma, K. "Optics: Principles and Applications". USA: Elsevier Academic Press. pp. 44-50. (2006).

[20] Bass, M. "Handbook of Optics". USA: McGrawHill. Vol.4. (2010).

[21] Frank, L. and Leno, S. "Introduction to Optics". USA: Prentice-Hall International, 2nd Edn. pp. 349- 351. (1993).

[22] Bach, H. and Neuroth, N. "The Properties of Optical Glass". Springer-Verlag Berlin Heidelberg: New York. 1st Edn. pp. 20-37. (1998).

[23] Francis A., and Harvey, E. "Fundamental of Optics". McGraw-Hill, USA. 4th Edn. (1976).

[24] The Center for Occupational Research and Development, "Laser/Electro-Optics Technology Series", Course 6. Center of Occupational, Third Edition. (1987)

[25] Hawkins, T. "Cauchy and the Spectral Theory of Matrices". Historia Mathematica. Vol. 2, pp.1-29. (1975).

[26] Cauchy, A.L. "Sur la refraction et la refiexion de la lumiere", Bull. des Sc. Math. Vol. 14, pp. 6-10. (1830).

[27] Xi, J.-Q. et al. "Optical thin-film materials with low refractive index for broad- band elimination of Fresnel reflection". Nature photonics: Vol. 1. (2007).

[28] Lesnic, D. et al. "Determination of the index of refraction of antireflection coatings". Mathematics-in- Industry Case Studies Journal, Vol. 2, pp. 155-173. (2010).

[29] Weber, M. "Handbook of optical material". New York: CRC Press.pp. 274. (2003).

[30] Jose V., "Lecture notes on Atom Light interaction". (MSc. Lecture, taken by Farmesk J. Abubaker). (2012).

[31] Cornell, J. A., and Berger, R. D. "Factors that influence the value of the coefficient of determination in simple linear and nonlinear regression models". Phytopathology Vol. 77. pp. 63-70. (1987).

[32] Efron, B. "Regression and ANOVA with zero-one data: measures of residual variation", Journal of the American Statistical Association Vol. 73, pp. 113-121. (1978).