A plot of refactive index vs. wavelength for BK7 glass. Over the visible region (red shading), Cauchy's equation (blue line) agrees well with the more accurate Sellmeier plot (green dashed line). It deviates in the ultraviolet and infrared regions.

Cauchy's equation is an empirical relationship between the refractive index n and wavelength of light λ for a particular transparent material. It is named for the mathematician Augustin Louis Cauchy, who defined it in 1836. In science, an empirical relationship is one based on observation rather than theory: that is, there is no theoretical reason to believe that a relationship should be as claimed; only data that indicates it is. ... Jump to: navigation, search The refractive index of a material is the factor by which the phase velocity of electromagnetic radiation is slowed relative to vacuum. ... Jump to: navigation, search The wavelength is the distance between repeating units of a wave pattern. ... Jump to: navigation, search This article needs to be cleaned up to conform to a higher standard of quality. ... Augustin Louis Cauchy Augustin Louis Cauchy (August 21, 1789 – May 23, 1857) was a French mathematician. ... 1836 was a leap year starting on Friday (see link for calendar). ...

The general form of Cauchy's equation is:

where A, B, and C are coefficients (usually quoted for λ in micrometres) that can be determined for a material by fitting the equation to measured refractive indices at three wavelengths. Jump to: navigation, search In mathematics, a coefficient is a multiplicative factor of a certain object such as a variable (for example, the coefficients of a polynomial), a basis vector, a basis function and so on. ... A micrometre (American spelling: micrometer), symbol µm, is an SI unit of length. ...

Usually, it is sufficient to use a two-term form of the equation:

where A and B are coefficients as before.

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. 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 cannot represent regions of anomalous dispersion. Despite this, its mathematical simplicity makes it useful in some applications. In optics, dispersion is a phenomenon that causes the separation of a wave into spectral components with different frequencies, due to a dependence of the waves speed on its frequency. ... The optical spectrum (light or visible spectrum) is the portion of the electromagnetic spectrum that is visible to the human eye. ... Jump to: navigation, search Image of a small dog taken in mid-infrared (thermal) light (false color) Infrared (IR) radiation is electromagnetic radiation of a wavelength longer than visible light, but shorter than microwave radiation. ...

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. Jump to: navigation, search A plot of the refractive index vs. ... Jump to: navigation, search Ultraviolet (UV) radiation is electromagnetic radiation of a wavelength shorter than that of the visible region, but longer than that of soft X-rays. ...

References

• F.A. Jenkins and H.E. White, Fundamentals of Optics, 4th ed., McGraw-Hill, Inc. (1981).