Editing Abbe number (section)

== Abbe diagram ==
[[Image:Abbe-diagram 2.svg|right|thumb|380px|An Abbe diagram, also known as 'the glass veil',  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-en.svg|250px|thumb|Influences of selected [[glass]] component additions on the Abbe number of a specific base glass.<ref>{{cite web |first = Alexander |last = Fluegel |date = 2007-12-07 |title = Abbe number calculation of glasses |website = Statistical Calculation and Development of Glass Properties (glassproperties.com) |url = http://glassproperties.com/abbe_number/ |access-date = 2022-01-16}}</ref>]]
An '''Abbe diagram''', also called 'the glass veil', is produced by plotting the Abbe number <math>V_\mathsf d</math> of a material versus its refractive index <math>n_\mathsf d .</math> Glasses can then be categorised and selected according to their positions on the diagram. This can be a letter-number code, as used in the [[Schott Glass]] catalogue, or a 6&nbsp;digit [[glass code]].

Glasses' Abbe numbers, along with their mean refractive indices, are used in the calculation of the required [[refractive power]]s of the elements of [[achromatic lens]]es in order to cancel [[chromatic aberration]] to first order. These two parameters which enter into the equations for design of achromatic doublets are exactly what is plotted on an Abbe diagram.

Due to the difficulty and inconvenience in producing sodium and hydrogen lines, alternate definitions of the Abbe number are often substituted ([[ISO]] 7944).<ref>{{cite report |last=Meister |first=Darryl |date=12 April 2010 |title=Understanding reference wavelengths |type=memo |publisher=Carl Zeiss Vision |website=opticampus.opti.vision |url=http://opticampus.opti.vision/files/memo_on_reference_wavelengths.pdf |archive-url=https://ghostarchive.org/archive/20221009/http://opticampus.opti.vision/files/memo_on_reference_wavelengths.pdf |archive-date=2022-10-09 |url-status=live |access-date=2013-03-13}}</ref> For example, rather than the standard definition given above, that uses the refractive index variation between the F and C [[Fraunhofer lines#Naming|hydrogen lines]], one alternative measure using the subscript "e" for [[mercury (element)|mercury]]'s e&nbsp;line compared to [[cadmium]]'s {{prime|F}} and {{prime|C}}&nbsp;lines is
:<math> V_\mathsf e = \frac{ n_\mathsf e - 1 }{\ n_\mathsf{F'} - n_\mathsf{C'}\ } ~.</math>
This alternate takes the difference between cadmium's blue ({{prime|F}}) and red ({{prime|C}}) refractive indices at wavelengths 480.0&nbsp;nm and 643.8&nbsp;nm, relative to <math>\ n_\mathsf e\ </math> for mercury's e&nbsp;line at 546.073&nbsp;nm, all of which are close by, and somewhat easier to produce than the C, F, and e&nbsp;lines. Other definitions can similarly be employed; the following table lists standard wavelengths at which <math>\ n\ </math> is commonly determined, including the [[Fraunhofer lines|standard subscripts]] used.<ref>{{cite book |first1=L.D. |last1=Pye |first2=V.D. |last2=Frechette |first3=N.J. |last3=Kreidl |year=1977 |title=Borate Glasses |publisher=Plenum Press |place=New York, NY}}</ref>

{| class="wikitable"
|-
! {{mvar|λ}}<br/>(nm) !! [[Fraunhofer lines|Fraunhofer's<br/>symbol]] !! Light<br/>source !! Color
|-
| 365.01 ||align=center| i  ||  [[Mercury (element)|Hg]]  || [[Ultraviolet light|UV-A]]
|-
| 404.66 ||align=center| h  ||  [[Mercury (element)|Hg]] || violet
|-
| 435.84 ||align=center| g  ||  [[Mercury (element)|Hg]] || blue
|-
| 479.99 ||align=center| {{prime|F}} ||  [[Cadmium|Cd]] || blue
|-
| 486.13 ||align=center| F  ||  [[Hydrogen|H]] || blue
|-
| 546.07 ||align=center| e  ||  [[Mercury (element)|Hg]] || green
|-
| 587.56 ||align=center| d  ||  [[Helium|He]]  || yellow
|-
| 589.3  ||align=center| D  ||  [[Sodium|Na]]  || yellow
|-
| 643.85 ||align=center| {{prime|C}} ||  [[Cadmium|Cd]]  || red
|-
| 656.27 ||align=center| C  ||  [[Hydrogen|H]] || red
|-
| 706.52 ||align=center| r  ||  [[Helium|He]]  || red
|-
| 768.2  ||align=center| {{prime|A}} ||  [[Potassium|K]]  || [[Infrared light|IR-A]]
|-
| 852.11 ||align=center| s  ||  [[Cesium|Cs]]  || [[Infrared light|IR-A]]
|-
| 1013.98 ||align=center| t  ||  [[Mercury (element)|Hg]]  || [[Infrared light|IR-A]]
|}