Abbe number

In physics and optics, the Abbe number, also known as the V-number or constringence of a transparent material is a measure of the material's dispersion (variation of refractive index with wavelength). It is named for Ernst Abbe (1840-1905), the German physicist who defined it.

The Abbe number V of a material is defined as:

V={\frac {n_{D}-1}{n_{F}-n_{C}}}

where n_D, n_F and n_C are the refractive indices of the material at the wavelengths of the Fraunhofer D-, F- and C- spectral lines (589.2 nm, 486.1 nm and 656.3 nm respectively). Low dispersion materials have high values of V.

Abbe numbers are used to classify glasses. For example, flint glasses have V<50 and crown glasses have V >50. Typical values of V range from around 20 for very dense flint glasses, up to 65 for very light crown glass, and up to 85 for fluor-crown glass. Abbe numbers are only a useful measure of dispersion for visible light, and for other wavelengths, or for higher precision work, the group velocity dispersion is used.

An Abbe diagram is produced by plotting the Abbe number of a material verses its refractive index at 587.6 nm wavelength (the yellow Fraunhofer D₃ line). Glasses can then be categorised by their composition and position on the diagram.

See also