Cauchy's equation

In optics, Cauchy's transmission 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 originally defined it in 1830 in his article "The refraction and reflection of light".

[1] The most general form of Cauchy's equation is where n is the refractive index, λ is the wavelength, A, B, C, etc., are coefficients that can be determined for a material by fitting the equation to measured refractive indices at known wavelengths.

A table of coefficients for common optical materials is shown below: The theory of light-matter interaction on which Cauchy based this equation was later found to be incorrect.

The Sellmeier equation is a later development of Cauchy's work that handles anomalously dispersive regions, and more accurately models a material's refractive index across the ultraviolet, visible, and infrared spectrum.

Refractive index vs. wavelength for BK7 glass . Red crosses show measured values. Over the visible region (red shading), Cauchy's equation (blue line) agrees well with the measured refractive indices and the Sellmeier plot (green dashed line). It deviates in the ultraviolet and infrared regions.