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.
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.
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. Glasses can then be categorised by their composition and position on the diagram. This can be a letter-number code, as used in the Schott Glass catalogue, or a 6-digit glass code.
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|
- Abbe number calculation of glasses
- Hovestadt, H. (1902). Jena Glass and Its Scientific and Industrial Applications. London: Macmillan and Co. pp. 1–81.
- Bergmann, Ludwig; Clemens Schaefer (1999). Optics of Waves and Particles. Berlin: Walter de Gruyter. pp. 198–201. ISBN 3-11-014318-6.
- Meister, Darryl. "Understanding Reference Wavelengths". Carl Zeiss Vision. Retrieved 2013-03-13.
- L. D. Pye, V. D. Frechette, N. J. Kreidl: "Borate Glasses"; Plenum Press, New York, 1977