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Spectrometer- Determination of Cauchy's constants
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## Aim:

To determine the CauchyÃƒÂ¢Ã¢â€šÂ¬Ã¢â€žÂ¢s constant of the given prism.

## Apparatus:

Spectrometer, prism, prism clamp, Magnifying glass, mercury vapor lamp, etc.

## Theory:

Cauchy's equation is an empirical relationship between the refractive index and wavelength of light for a particular transparent material. It is named for the mathematician Augustin-Louis Cauchy, who defined it in 1836.

Augustin-Louis Cauchy
(1789-1857)

The most general form of Cauchy's equation is

. . . . .. . . (1)

where n is the refractive index, ÃƒÅ½Ã‚Â» is the wavelength, B, C, D, etc., are coefficients that can be determined for a material by fitting the equation to measured refractive indices at known wavelengths.

The refractive index n of the material of the prism for a wavelength ÃƒÅ½Ã‚Â» is given by.

. . . . ..  .. ..(2)

Where A and B are called CauchyÃƒÂ¢Ã¢â€šÂ¬Ã¢â€žÂ¢s constants for the prism.

If the refractive indices n1 and n2 for any two known wavelength ÃƒÅ½Ã‚Â»1 and ÃƒÅ½Ã‚Â»2 are determined by a spectrometer, the CauchyÃƒÂ¢Ã¢â€šÂ¬Ã¢â€žÂ¢s constants A and B can be calculated from the above equation.

*The theory of light-matter interaction on which Cauchy based this equation was later found to be incorrect. In particular, the equation is only valid for regions of normal dispersion in the visible wavelength region. In the infrared, the equation becomes inaccurate, and it cannot represent regions of anomalous dispersion.

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