# What is Abbe Number?

Jan. 08, 2021

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) in relation to the refractive index, with high values of V indicating low dispersion (low chromatic aberration). It is named after Ernst Abbe (1840–1905), the German physicist who defined it.

The Abbe number, V, of a material is defined as

V=（nd-1）/（nF-nC）

where nd, nF and nC are the refractive indices of the material at the wavelengths of the Fraunhofer d-, F- and C- spectral lines (587.6 nm, 486.1 nm and 656.3 nm respectively).

Abbe numbers are used to classify glass and other optically transparent materials. For example, flint glass has V<50 and crown glass has V>50. Typical values of V range from around 20 for very dense flint glass, around 30 for polycarbonate plastics, and 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.

Alternate definitions of the Abbe number are used in some contexts. The value Vd is given by

Vd=（nd-1）/（nF-nC）

which defines the Abbe number with respect to the yellow Fraunhofer d (or D3) helium line at 587.5618  nm wavelength. It can also be defined at the green mercury E-line at 546.073 nm:

Ve=（ne-1）/（nF’-nC’）

where F' and C' are the blue and red cadmium lines at 480.0 nm and 643.8 nm, respectively.

An Abbe diagram is produced by plotting the Abbe number Vd of a material versus its refractive index nd. Glass can then be categorised by their composition and position on the diagram. This can be a letter-number code, as used in the CGGlass catalogue, or a 6-digit glass code.

Abbe numbers are used to calculate the necessary focal lengths of achromatic doublet lenses to minimize chromatic aberration.

The following table lists standard wavelengths at which n is usually determined, indicated by subscripts. For example, nD is measured at 589.3 nm:

 λ in nm Fraunhofer's symbol Light source Color 365.01 i Hg UV 404.66 h Hg violet 435.84 g Hg blue 479.99 F' Cd blue 486.13 F H blue 546.07 e Hg green 587.56 d He yellow 589.3 D Na yellow 643.85 C' Cd red 656.27 C H red 706.52 r He red 768.2 A' K IR 852.11 s Cs IR 1013.98 t Hg IR