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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: : 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 Line s (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 Glass es. For example, Flint Glass es 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. Alternate definitions of the Abbe number are used in some contexts. The value ''V''d is given by: : which defines the Abbe number with respect to the yellow Fraunhofer d (or D3) Helium line at 587.6 nm wavelength. It can also be defined at the blue Iron e-line at 438.4 nm: : 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 ''V''d of a material versus its refractive index ''n''d. 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 . Abbe numbers are used to calculate the necessary Focal Length s of achromatic doublet Lenses to minimize Chromatic Aberration . SEE ALSO |
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