[[Image:Abbe-diagram.png|right|thumb|380px|An Abbe diagram plots the Abbe number against refractive index for a range of different glasses (red dots). Glasses are classified using the Schott Glass letter-number code to reflect their composition and position on the diagram.]]

[[Image:SpiderGraph_Abbe_Number.gif|250px|thumb|Influences of selected [[glass]] component additions on the Abbe number of a specific base glass.<ref>[http://glassproperties.com/abbe_number/ Abbe number calculation of glasses]</ref>]]

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 (optics)|dispersion]] (variation of [[refractive index]] with wavelength) in relation to the [[refractive index]]. It is named for [[Ernst Abbe]] ([[1840]]–[[1905]]), the German physicist who defined it.

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

:<math>V = \frac{ n_D - 1 }{ n_F - n_C },</math>

where ''n''_D, ''n''_F and ''n''_C are the [[refractive index|refractive indices]] of the material at the wavelengths of the [[Fraunhofer lines|Fraunhofer]] D-, F- and C- [[spectral line]]s (589.2 [[nanometre|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 and other optically transparent materials. For example, [[flint glass]]es have ''V''<50 and [[crown glass (optics)|crown glasses]] have ''V'' >50. Typical values of ''V'' range from around 20 for very dense flint glasses, around 30 for [[polycarbonate]] plastics, and up to 65 for very light crown glass, and up to 85 for [[fluorite|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 [[dispersion (optics)|group velocity dispersion]] is used.

Alternate definitions of the Abbe number are used in some contexts. The value ''V''_d is given by
:<math> V_d = \frac{n_d-1}{ n_F - n_C }</math>
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 (element)|mercury]] E-line at 546.073 nm:
:<math> V_e = \frac{n_e-1}{ n_{F'} - n_{C'}}</math>
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 lens|achromatic doublet]] [[lens (optics)|lenses]] to minimize [[chromatic aberration]].

The following table lists standard wavelengths at which n is usually determined, indicated by subscripts.<ref>L. D. Pye, V. D. Frechette, N. J. Kreidl: "Borate Glasses"; Plenum Press, New York, 1977</ref> For example, n_D is measured at 589.3 nm:

{| class="wikitable"
|-
! λ in nm
! [[Fraunhofer lines|Fraunhofer's symbol]]
! Light source
! Color
|-
| 365.01
| i
| Hg
| UV
|-
| 404.66
| h
| Hg
| violet
|-
| 435.84
| g
| Hg
| blue
|-
| 479.19
| 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
| red
|-
| 852.11
| s
| Cs
| IR
|-
| 1013.98
| t
| Hg
| IR
|}

==See also==
*[[Abbe prism]]
*[[Abbe refractometer]]
*[[Calculation of glass properties]], including Abbe number
*[[Fraunhofer lines]]

==References==
{{reflist}}

[[Category:Dimensionless numbers]]
[[Category:Optics]]

[[cs:Abbeovo číslo]]
[[de:Abbesche Zahl]]
[[el:Αριθμός Abbe]]
[[fr:Nombre d'Abbe]]
[[he:מספר Abbe]]
[[ja:アッベ数]]
[[pl:Liczba Abbego]]
[[sk:Abbeho číslo]]
[[sl:Abbejevo število]]
[[zh:阿贝数]]