Determination of Cauchy’s constant by dispersive method

To determine the Cauchy’s constant of the given prism.

The angle of the prism A and the angle of minimum deviation D for different wave length are determined. From this the refractive index n for these colours are calculated. Taking the value of λ from the mathematical table, the Cauchy’s constants A and B are calculated for different pairs of spectral colours using the equation.

The Cauchy’s constants can also be determined graphically. A graph is drawn with n along the y-axis and 1/λ2 along x-axis with zero as the origin for both axes. The graph is a straight line. The Y intercept gives A and the slope gives B.

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. 

 The most general form of Cauchy's equation is

   . . . . .. . . (1)

where n is the refractive index, λ 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 λ is given by.

                               . . . . ..  .. ..(2)

 Where A and B are called Cauchy’s constants for the prism.

If the refractive indices n1 and n2 for any two known wavelength λ1 and λ2 are determined by a spectrometer, the Cauchy’s constants A and B can be calculated from the above equation.