Editing Refractive index (section)

==Dispersion==
[[File:WhereRainbowRises.jpg|thumb|150px|alt=A rainbow|Light of different colors has slightly different refractive indices in water and therefore shows up at different positions in the [[rainbow]].]]
[[File:Prism-rainbow.svg|thumb|left|alt=A white beam of light dispersed into different colors when passing through a triangular prism|In a triangular [[Prism (optics)|prism]], [[Dispersion (optics)|dispersion]] causes different colors to refract at different angles, splitting [[White|white light]] into a [[rainbow]] of colors. The blue color is more deviated (refracted) than the red color because the refractive index of blue is higher than that of red. ]]
[[File:Mplwp dispersion curves.svg|right|thumb|320px|alt=A graph showing the decrease in refractive index with increasing wavelength for different types of glass|The variation of refractive index with wavelength for various glasses. The shaded zone indicates the range of visible light.]]
{{Main|Dispersion (optics)}}

The refractive index of materials varies with the wavelength (and [[frequency]]) of light.<ref name=dispersion_ELPT>{{cite encyclopedia |last= Paschotta |first= Rüdiger |title= Chromatic Dispersion |url=https://www.rp-photonics.com/chromatic_dispersion.html |archive-url= https://web.archive.org/web/20150629012047/http://www.rp-photonics.com/chromatic_dispersion.html |archive-date= 2015-06-29 |url-status= live |encyclopedia= [[RP Photonics Encyclopedia]] |access-date= 2023-08-13}}</ref> This is called dispersion and causes [[prism (optics)|prisms]] and [[rainbow]]s to divide white light into its constituent spectral [[color]]s.<ref name=hyperphysics_dispersion>{{cite web |last= Nave |first= Carl R. |date= 2000 |title= Dispersion |url= http://hyperphysics.phy-astr.gsu.edu/hbase/geoopt/dispersion.html |archive-url= https://web.archive.org/web/20140924222742/http://hyperphysics.phy-astr.gsu.edu/hbase/geoopt/dispersion.html |archive-date= 2014-09-24 |website= [[HyperPhysics]] |publisher= Department of Physics and Astronomy, Georgia State University |url-status= live |access-date= 2023-08-13}}</ref> As the refractive index varies with wavelength, so will the refraction angle as light goes from one material to another. Dispersion also causes the [[focal length]] of [[Lens (optics)|lenses]] to be wavelength dependent. This is a type of [[chromatic aberration]], which often needs to be corrected for in imaging systems. In regions of the spectrum where the material does not absorb light, the refractive index tends to {{em|decrease}} with increasing wavelength, and thus {{em|increase}} with frequency. This is called "normal dispersion", in contrast to "anomalous dispersion", where the refractive index {{em|increases}} with wavelength.<ref name=dispersion_ELPT/> For visible light normal dispersion means that the refractive index is higher for blue light than for red.

For optics in the visual range, the amount of dispersion of a lens material is often quantified by the [[Abbe number]]:<ref name=hyperphysics_dispersion/>
<math display="block">V = \frac{n_\mathrm{yellow} - 1}{n_\mathrm{blue} - n_\mathrm{red}}.</math>
For a more accurate description of the wavelength dependence of the refractive index, the [[Sellmeier equation]] can be used.<ref>{{cite encyclopedia |last= Paschotta |first= Rüdiger |title= Sellmeier formula |url= https://www.rp-photonics.com/sellmeier_formula.html |archive-url= https://web.archive.org/web/20150319205203/http://www.rp-photonics.com/sellmeier_formula.html |archive-date= 2015-03-19 |url-status= live |encyclopedia= [[RP Photonics Encyclopedia]] |access-date= 2014-09-08}}</ref> It is an empirical formula that works well in describing dispersion. ''Sellmeier coefficients'' are often quoted instead of the refractive index in tables.

===Principal refractive index wavelength ambiguity===
Because of dispersion, it is usually important to specify the vacuum wavelength of light for which a refractive index is measured. Typically, measurements are done at various well-defined spectral [[emission line]]s.

Manufacturers of optical glass in general define principal index of refraction at yellow spectral line of helium ({{val|587.56|u=nm}}) and alternatively at a green spectral line of mercury ({{val|546.07|u=nm}}), called {{mvar|d}} and {{mvar|e}} lines respectively. [[Abbe number]] is defined for both and denoted {{mvar|V<sub>d</sub>}} and {{mvar|V<sub>e</sub>}}. The spectral data provided by glass manufacturers is also often more precise for these two wavelengths.<ref>{{cite web |author= Schott Company |date= <!-- undated --> |title= Interactive Abbe Diagram |url= https://www.schott.com/en-pl/interactive-abbe-diagram |access-date= 2023-08-13 |website= Schott.com}}</ref><ref>{{cite web |author= Ohara Corporation |date= <!-- undated --> |title= Optical Properties |url= https://www.oharacorp.com/o2.html |access-date= 2022-08-15 |website= Oharacorp.com }}</ref><ref>{{cite web |author= Hoya Group |date= <!-- undated --> |title= Optical Properties |url= https://www.hoya-opticalworld.com/english/technical/002.html |access-date= 2023-08-13 |website=Hoya Group Optics Division}}</ref><ref>{{cite book |last1= Lentes |first1= Frank-Thomas |last2= Clement |first2= Marc K. Th. |last3= Neuroth |first3= Norbert |last4= Hoffmann |first4= Hans-Jürgen |last5= Hayden |first5= Yuiko T. |last6= Hayden |first6= Joseph S. |last7= Kolberg |first7= Uwe |last8= Wolff |first8= Silke |editor-last1= Bach |editor-first1= Hans |editor-last2= Neuroth |editor-first2= Norbert |date= 1998 |title=The Properties of Optical Glass |chapter= Optical Properties |series=Schott Series on Glass and Glass Ceramics |page= 30 |language=en |doi= 10.1007/978-3-642-57769-7 |isbn= 978-3-642-63349-2 }}</ref>

Both, {{mvar|d}} and {{mvar|e}} spectral lines are singlets and thus are suitable to perform a very precise measurements, such as spectral goniometric method.<ref>{{cite conference |last1= Krey |first1= Stefan |last2= Off |first2= Dennis |last3= Ruprecht |first3= Aiko |editor-last1= Soskind |editor-first1= Yakov G. |editor-last2= Olson |editor-first2= Craig |date= 2014-03-08 |title= Measuring the Refractive Index with Precision Goniometers: A Comparative Study |url= https://www.spiedigitallibrary.org/conference-proceedings-of-spie/8992/89920D/Measuring-the-refractive-index-with-precision-goniometers--a-comparative/10.1117/12.2041760.full |conference=  SPIE OPTO, 2014 |location= San Francisco, California |book-title= Proc. SPIE 8992, Photonic Instrumentation Engineering |publisher= SPIE |volume= 8992 |pages= 56–65 |doi= 10.1117/12.2041760 |bibcode= 2014SPIE.8992E..0DK |s2cid= 120544352 |url-access= subscription }}</ref><ref>{{Cite book |last1=Rupp |first1=Fabian |last2=Jedamzik |first2=Ralf |last3=Bartelmess |first3=Lothar |last4=Petzold |first4=Uwe |title=Optical Fabrication, Testing, and Metrology VII |chapter=The modern way of refractive index measurement of optical glass at SCHOTT |journal=Optical Fabrication |editor-first1=Reinhard |editor-first2=Roland |editor-first3=Deitze |editor-last1=Völkel |editor-last2=Geyl |editor-last3=Otaduy |date=2021-09-12 |chapter-url=https://www.spiedigitallibrary.org/conference-proceedings-of-spie/11873/1187308/The-modern-way-of-refractive-index-measurement-of-optical-glass/10.1117/12.2597023.full |publisher=SPIE |volume=11873 |pages=15–22 |doi=10.1117/12.2597023|bibcode=2021SPIE11873E..08R |isbn=9781510645905 |s2cid=240561530 }}</ref>

In practical applications, measurements of refractive index are performed on various refractometers, such as [[Abbe refractometer]]. Measurement accuracy of such typical commercial devices is in the order of 0.0002.<ref>{{Cite web |title=Abbe Refractometer{{!}} ATAGO CO., LTD. |url=https://www.atago.net/en/products-abbe-top.php |access-date=2022-08-15 |website=www.atago.net}}</ref><ref>{{Cite web |title=Abbe Multi-Wavelength Refractometer |url=https://www.novatech-usa.com/1412-DR-M2-1550_2 |access-date=2022-08-15 |website=Nova-Tech International |language=en-US}}</ref> Refractometers usually measure refractive index {{mvar|n<sub>D</sub>}}, defined for sodium doublet {{mvar|D}} ({{val|589.29|u=nm}}), which is actually a midpoint between two adjacent yellow spectral lines of sodium. Yellow spectral lines of helium ({{mvar|d}}) and sodium ({{mvar|D}}) are {{val|1.73|u=nm}} apart, which can be considered negligible for typical refractometers, but can cause confusion and lead to errors if accuracy is critical.

All three typical principle refractive indices definitions can be found depending on application and region,<ref>{{Cite book |url=https://link.springer.com/book/10.1007/978-3-642-57769-7 |title=The Properties of Optical Glass |series=Schott Series on Glass and Glass Ceramics |year=1998 |pages=267 |language=en |doi=10.1007/978-3-642-57769-7|isbn=978-3-642-63349-2 |editor1=Bach, Hans |editor2=Neuroth, Norbert }}</ref> so a proper subscript should be used to avoid ambiguity.