Editing Abbe number (section)

{{Short description|Material dispersion property}}
In [[optics]] and [[lens design]], the '''Abbe number''', also known as the '''Vd-number''' or '''constringence''' of a [[Transparency (optics)|transparent]] material, is an approximate measure of the material's [[dispersion (optics)|dispersion]] (change of [[refractive index]] versus wavelength), with high values of ''Vd'' indicating low dispersion. It is named after [[Ernst Abbe]] (1840–1905), the German physicist who defined it. The term Vd-number should not be confused with the [[Normalized frequency (fiber optics)|normalized frequency in fibers]].

[[File:Abbe_number_calculation.svg|right|thumb|300px|Refractive index variation for SF11 flint glass, BK7 borosilicate crown glass, and fused quartz, and calculation for two Abbe numbers for SF11.]]
The Abbe number,<ref>{{cite book |title=The Properties of Optical Glass |year=1998 |series=Schott Series on Glass and Glass Ceramics |language=en |publisher=[[Schott Glass]] |doi=10.1007/978-3-642-57769-7 |isbn=978-3-642-63349-2 |url=https://link.springer.com/book/10.1007/978-3-642-57769-7 |editor1=Bach, Hans |editor2=Neuroth, Norbert }}</ref> <math> V_\mathsf d\ ,</math> of a material is defined as

:<math> V_\mathsf d \equiv \frac{ n_\mathsf d - 1 }{\ n_\mathsf F - n_\mathsf C\ }</math>,

where <math>n_\mathsf C,</math> <math>n_\mathsf d,</math> and <math>n_\mathsf F</math> are the [[refractive indices]] of the material at the wavelengths of the [[Fraunhofer lines|Fraunhofer's]] C, d, and F [[spectral line]]s (656.3&nbsp;[[nanometre|nm]], 587.56&nbsp;nm, and 486.1&nbsp;nm respectively). This formulation only applies to the [[visible spectrum|human vision]]. Outside this range requires the use of different spectral lines. For non-visible spectral lines the term "V-number" is more commonly used. The more general formulation defined as,

:<math> V \equiv \frac{ n_\mathsf{center} - 1 }{ n_\mathsf{short} - n_\mathsf{long} }</math>,

where <math>n_\mathsf{short},</math> <math>n_\mathsf{center},</math> and <math>n_\mathsf{long},</math> are the refractive indices of the material at three different wavelengths. The shortest wavelength's index is <math>n_\mathsf{short}</math>, and the longest's is <math>n_\mathsf{long}</math>.

Abbe numbers are used to classify [[glass]] and other optical materials in terms of their [[chromaticity]]. For example, the higher dispersion [[flint glass]]es have relatively small Abbe numbers <math>V < 55</math> whereas the lower dispersion [[crown glass (optics)|crown glass]]es have larger Abbe numbers. Values of <math>V_\mathsf d</math> range from below 25 for very dense flint glasses, around 34 for [[polycarbonate]] plastics, up to 65 for common crown glasses, and 75 to 85 for some fluorite and phosphate crown glasses.

[[File:Eyesensitivity.svg|thumb|Most of the human eye's wavelength sensitivity curve, shown here, is bracketed by the Abbe number reference wavelengths of 486.1&nbsp;nm (blue) and 656.3&nbsp;nm (red)]]
Abbe numbers are used in the design of [[achromatic lens]]es, as their [[reciprocal (mathematics)|''reciprocal'']] is proportional to dispersion (slope of refractive index versus wavelength) in the wavelength region where the human eye is most sensitive (see graph). For different wavelength regions, or for higher precision in characterizing a system's chromaticity (such as in the design of [[apochromat]]s), the full dispersion relation (refractive index as a function of wavelength) is used.