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Abbe Number

Definition: a measure for the chromatic dispersion of a transparent material

Alternative terms: V-number, constringence

German: Abbe-Zahl

Category: general optics

Formula symbol: νD

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The Abbe number of a transparent optical material, named after the German physicist Ernst Abbe, is defined as

Abbe number

It is also sometimes called the V-number VD or the constringence.

The definition refers to refractive indices at three different reference wavelengths in the visible spectral region:

The middle one (from the sodium D line) lies in the region of maximum sensitivity of the human eye.

In some cases, somewhat different wavelength values corresponding to other Fraunhofer lines are used, e.g., 480.0 nm (F' line), 587.6 nm (d line) and 643.9 nm (C' line); this leads to the modified Abbe number νd. All those wavelengths can be obtained from common gas discharge lamps.

Relation to the Chromatic Dispersion of Lenses

With the Abbe number, one can easily estimate the change of focal length of a simple optical lens made from a material:

focal length mismatch from Abbe number

The formula is not exact, because it is based on a Taylor expansion, but it is normally good enough for practical purposes. It shows that the mismatch of focal length values between the blue and red spectral regions is inversely proportional to the Abbe number.

Abbe Diagram

A good overview over different glass types can be obtained with an n−ν diagram (Abbe diagram), where each glass is represented by a point, where the coordinates are the Abbe number and the refractive index n:

Abbe diagram
Figure 1: Abbe diagram with a couple of optical glasses from Schott.

Glasses with a relatively low Abbe number of less than 50 (i.e., with relatively strong dispersion) are called flint glasses, whereas glasses with a higher Abbe number are crown glasses. Typically, flint glasses have relatively high refractive indices, whereas crown glasses exhibit lower values.

See also: chromatic dispersion, achromatic optics, optical glasses
and other articles in the category general optics

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