# Abbe number

The **Abbe number** (also called the V-number or constringence) is a single dimensionless number that quantifies the dispersion of a transparent optical material, defined as the ratio of its refractivity to its principal dispersion:

\[ \nu_{\mathrm{D}} = \frac{n_{\mathrm{D}} - 1}{n_{\mathrm{F}} - n_{\mathrm{C}}} \]

Here \( n_{\mathrm{D}} \), \( n_{\mathrm{F}} \), and \( n_{\mathrm{C}} \) are the refractive indices at three standard spectral lines in the visible region: the blue Fraunhofer F line of hydrogen at 486.1 nm, the orange Fraunhofer D line of sodium at 589.2 nm, and the red Fraunhofer C line of hydrogen at 656.3 nm<sup>[1](https://www.rp-photonics.com/abbe_number.html)</sup>. The numerator, \( n_{\mathrm{D}} - 1 \), is called the refractivity; the denominator, \( n_{\mathrm{F}} - n_{\mathrm{C}} \), is the principal dispersion<sup>[1](https://www.rp-photonics.com/abbe_number.html)</sup>. The number was created in the late 1800s by the German physicist [Ernst Abbe](https://www.edgepedia.org/ernst-abbe), a colleague of [Carl Zeiss](https://www.edgepedia.org/carl-zeiss), as a measure of the magnitude of chromatic dispersion over the visible spectrum<sup>[2](https://eyewiki.aao.org/Lens_Material_Properties)</sup>.

| Key fact | Detail |
|---|---|
| Definition | \( \nu_{\mathrm{D}} = (n_{\mathrm{D}} - 1)/(n_{\mathrm{F}} - n_{\mathrm{C}}) \), the ratio of refractivity to principal dispersion<sup>[1](https://www.rp-photonics.com/abbe_number.html)</sup> |
| Reference wavelengths | F 486.1 nm (hydrogen), D 589.2 nm (sodium), C 656.3 nm (hydrogen); the standard \( \nu_{\mathrm{d}} \) uses d 587.6 nm, F 486.1 nm, and C 656.3 nm<sup>[1](https://www.rp-photonics.com/abbe_number.html)</sup><sup> • </sup><sup>[15](https://www.edmundoptics.com/knowledge-center/application-notes/optics/optical-glass/)</sup> |
| Crown vs. flint | Glasses with \( \nu \) below 50 are flint glasses (strong dispersion, typically high index); higher values are crown glasses<sup>[1](https://www.rp-photonics.com/abbe_number.html)</sup> |
| Example values | N-BK7: \( n_{\mathrm{d}} = 1.51680 \), \( \nu_{\mathrm{d}} = 64.17 \), glass code 517642; F2: \( \nu_{\mathrm{d}} = 36.37 \)<sup>[3](https://www.rp-photonics.com/optical_glasses.html)</sup><sup> • </sup><sup>[4](https://media.schott.com/api/public/content/63b62a0d73a640efa8c6fde92f2ad5c2?v=97a6a05a)</sup> |
| Focal-length color error | For a simple lens, \( f_{\mathrm{F}} - f_{\mathrm{C}} = -f_{\mathrm{D}}/\nu_{\mathrm{D}} \); the blue-to-red focal mismatch is inversely proportional to the Abbe number<sup>[1](https://www.rp-photonics.com/abbe_number.html)</sup> |
| Delivery tolerances | ISO 12123 grades for the Abbe number run from ±0.8% (grade 8) down to ±0.1% (grade 1)<sup>[5](https://www.frontiersin.org/articles/10.1515/aot-2015-0047/pdf)</sup> |
| Standardization | ISO 7944:2024 (edition 3, published November 2024) specifies the reference wavelengths and defines the associated Abbe numbers for optical materials, systems, and ophthalmic lenses<sup>[6](https://committee.iso.org/cms/live/live/en/sites/isoorg/contents/data/standard/08/58/85865.html?browse=ics)</sup> |

## What the number measures

Dispersion is the variation of refractive index with wavelength. Because the index of a glass changes across the visible spectrum, a simple lens focuses blue light closer to the lens than red light, producing chromatic aberration<sup>[2](https://eyewiki.aao.org/Lens_Material_Properties)</sup>. The Abbe number condenses this behavior into one figure: a high Abbe number means low dispersion, and a low Abbe number means high dispersion<sup>[2](https://eyewiki.aao.org/Lens_Material_Properties)</sup>. For most glasses, dispersion increases with increasing refractive index<sup>[7](https://store.astm.org/c1648-12r18.html)</sup>, so designers usually trade one against the other.

The number has direct design use. From the lensmaker relation, the change in focal length of a simple thin lens between the F and C wavelengths is approximately

\[ f_{\mathrm{F}} - f_{\mathrm{C}} = -\frac{f_{\mathrm{D}}}{\nu_{\mathrm{D}}} \]

so a lens of focal length 100 mm made of glass with \( \nu_{\mathrm{D}} = 50 \) shifts focus by about 2 mm between blue and red. The formula comes from a Taylor expansion and is not exact, but is adequate for practical purposes<sup>[1](https://www.rp-photonics.com/abbe_number.html)</sup>.

## Crown and flint glasses

Glasses are conventionally divided by Abbe number. Glasses with a relatively low Abbe number, below 50, are called flint glasses and have relatively strong dispersion; those with higher values are crown glasses. Typically, flint glasses have relatively high refractive indices, while crown glasses have lower values<sup>[1](https://www.rp-photonics.com/abbe_number.html)</sup>. Edmund Optics uses a slightly different split, treating glasses with an Abbe number greater than 55 as crowns and those below 50 as flints<sup>[8](https://www.edmundoptics.com/knowledge-center/application-notes/optics/understanding-optical-specifications/)</sup>.

The six-digit glass code encodes both quantities: the first three digits give \( n_{\mathrm{d}} \) to three decimals and the second three give \( \nu_{\mathrm{d}} \) to one decimal. N-BK7, with \( n_{\mathrm{d}} = 1.51680 \) and \( \nu_{\mathrm{d}} = 64.17 \), carries the code 517642<sup>[3](https://www.rp-photonics.com/optical_glasses.html)</sup>. A survey of the whole catalog of glass types is given by the Abbe diagram, an \( n \)-\( \nu \) plot in which each glass appears as a point<sup>[1](https://www.rp-photonics.com/abbe_number.html)</sup>.

## Achromatic correction

The Abbe number enters directly into the design of color-corrected lenses. An achromatic doublet, a positive low-index crown element cemented to a negative high-index flint element, cancels primary axial color when the powers and Abbe numbers of the two components satisfy

\[ f_1 \nu_1 + f_2 \nu_2 = 0 \]

so the large dispersion of the flint compensates the dispersion of the crown<sup>[1](https://www.rp-photonics.com/abbe_number.html)</sup>. Compared with a singlet, such a doublet gives much reduced variation of focus position with wavelength, along with better correction of spherical aberration and coma<sup>[9](https://www.edmundoptics.com/knowledge-center/application-notes/optics/why-use-an-achromatic-lens)</sup>.

## Measurement and tolerances

Because the Abbe number is a ratio of small index differences, its accuracy is set by the accuracy of the refractive index measurements. ASTM guide C1648 notes that for \( \nu \)-values accurate to 1 to 4%, index measurements must be accurate to \( 1 \times 10^{-4} \), so citing \( \nu \)-values from less accurate test methods may not be useful<sup>[7](https://store.astm.org/c1648-12r18.html)</sup>. Suitable methods include Abbe-type and Pulfrich-type critical angle refractometers, V-block refractometers, and the prism spectrometer<sup>[7](https://store.astm.org/c1648-12r18.html)</sup>; the V-block method of ISO 21395-2 reaches an accuracy within \( 3 \times 10^{-5} \) over 365 nm to 2,400 nm<sup>[10](https://www.sis.se/en/produkter/image-technology/optical-equipment/iso-21395-22022/)</sup>, and the prism goniometer method provides an uncertainty of about \( 1 \times 10^{-6} \)<sup>[5](https://www.frontiersin.org/articles/10.1515/aot-2015-0047/pdf)</sup>.

Manufacturers deliver glass to stated tolerances in both index and Abbe number. Under ISO 12123, the Abbe number tolerance grades are ±0.8%, ±0.5%, ±0.3%, ±0.2%, and ±0.1%<sup>[5](https://www.frontiersin.org/articles/10.1515/aot-2015-0047/pdf)</sup>; a typical general tolerance for polished optical glass is ±0.5% in Abbe number alongside ±0.0003 in refractive index<sup>[11](https://www.shimadzu.com/opt/products/ref/ref-app01.html)</sup>. Measured values for common glasses agree closely with catalog data: a BK7-equivalent crown gave \( n_{\mathrm{d}} \) 1.516763 and \( \nu_{\mathrm{d}} \) 64.10, and an F2-equivalent flint gave 1.619942 and 36.34<sup>[11](https://www.shimadzu.com/opt/products/ref/ref-app01.html)</sup>.

## Beyond a single number

Three wavelengths give only a crude summary of dispersion. Early refinements used relative partial dispersions, ratios of index differences for other wavelength pairs such as \( P_{\mathrm{g,F}} = (n_{\mathrm{g}} - n_{\mathrm{F}})/(n_{\mathrm{F}} - n_{\mathrm{C}}) \), which are listed in glass catalogs and estimate index differences at additional wavelengths<sup>[1](https://www.rp-photonics.com/abbe_number.html)</sup>. For most commonly available glasses the relative partial dispersion varies nearly linearly with Abbe number, and glasses lying off this normal line are said to show anomalous partial dispersion<sup>[12](https://www.synopsys.com/content/dam/synopsys/optical-solutions/documents/whitepapers/application-specific-design.pdf)</sup>. Modern dispersion characterization instead relies on derivatives of wavenumbers, such as group delay dispersion, calculated from Sellmeier equations fitted to index data<sup>[1](https://www.rp-photonics.com/abbe_number.html)</sup>.

The Abbe number also appears outside classical glass optics. In ophthalmic lenses it predicts the colored fringes wearers may see at high powers; among commonly used materials, polycarbonate has the worst chromatic aberration with an Abbe value of 30, and higher-index lens materials generally carry lower Abbe numbers<sup>[13](https://www.opterio.com/learn/abbe-value-chromatic-aberration-abo)</sup>. [Intraocular lens](https://www.edgepedia.org/intraocular-lens) materials span a similar range: one study measured hydrophobic IOLs at Abbe numbers below 41 and hydrophilic IOLs above 50, with the hydrophobic materials showing the larger dispersion<sup>[14](https://pubmed.ncbi.nlm.nih.gov/32304541/)</sup>.

## References

1. [Abbe Number, RP Photonics Encyclopedia](https://www.rp-photonics.com/abbe_number.html)
2. [Lens Material Properties, EyeWiki (American Academy of Ophthalmology)](https://eyewiki.aao.org/Lens_Material_Properties)
3. [Optical Glasses, RP Photonics Encyclopedia](https://www.rp-photonics.com/optical_glasses.html)
4. [SCHOTT Technical Information, glass data table](https://media.schott.com/api/public/content/63b62a0d73a640efa8c6fde92f2ad5c2?v=97a6a05a)
5. [P. Hartmann: Optical glass standards, Advanced Optical Technologies 4(5-6): 377–388 (2015)](https://www.frontiersin.org/articles/10.1515/aot-2015-0047/pdf)
6. [ISO 7944:2024, Optics and photonics — Reference wavelengths, ISO](https://committee.iso.org/cms/live/live/en/sites/isoorg/contents/data/standard/08/58/85865.html?browse=ics)
7. [ASTM C1648, Standard Guide for Choosing a Method for Determining the Index of Refraction and Dispersion of Glass](https://store.astm.org/c1648-12r18.html)
8. [Understanding Optical Specifications, Edmund Optics](https://www.edmundoptics.com/knowledge-center/application-notes/optics/understanding-optical-specifications/)
9. [Why Use an Achromatic Lens?, Edmund Optics](https://www.edmundoptics.com/knowledge-center/application-notes/optics/why-use-an-achromatic-lens)
10. [ISO 21395-2:2022, V-block refractometer method, SIS](https://www.sis.se/en/produkter/image-technology/optical-equipment/iso-21395-22022/)
11. [Refractive index and dispersion of optical glass, Shimadzu Corporation](https://www.shimadzu.com/opt/products/ref/ref-app01.html)
12. [Application-Specific Design white paper, Synopsys Optical Solutions](https://www.synopsys.com/content/dam/synopsys/optical-solutions/documents/whitepapers/application-specific-design.pdf)
13. [Abbe Value and Chromatic Aberration, Opterio](https://www.opterio.com/learn/abbe-value-chromatic-aberration-abo)
14. [On the Chromatic Dispersion of Hydrophobic and Hydrophilic Intraocular Lenses, PubMed](https://pubmed.ncbi.nlm.nih.gov/32304541/)
15. [edmundoptics.com](https://www.edmundoptics.com/knowledge-center/application-notes/optics/optical-glass/)

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*Topic: Encyclopedia › Physical world and mathematics › Physics › Classical physics › Waves and optics › Geometrical optics and imaging › Prisms and dispersive elements › Dispersive materials: crown and flint glasses*

*Initially written Sep 17, 2026 · Reviewed: Sep 17, 2026; Sep 30, 2026; Oct 15, 2026 · Edited: Sep 17, 2026; Sep 30, 2026; Oct 15, 2026 · Last review: Oct 15, 2026*

*Copyright 2026 EdgeChat AI, a subsidiary of Biostate AI.*

License: Edgepedia Community License 1.0, https://www.edgepedia.org/edgepedia/license