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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.
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Many oils (such as [[olive oil]]) and [[ethanol]] are examples of liquids that are more refractive, but less dense, than water, contrary to the general correlation between density and refractive index.
For air, {{math|''n'' - 1}} is proportional to the density of the gas as long as the chemical composition does not change.<ref>{{cite web | url = http://emtoolbox.nist.gov/Wavelength/Documentation.asp | first1 = Jack A. | last1 = Stone | first2 = Jay H. | last2 = Zimmerman | date = 2011-12-28 | website = Engineering metrology toolbox | publisher = National Institute of Standards and Technology (NIST) | title = Index of refraction of air | access-date = 2014-01-11 | url-status = live | archive-url = https://web.archive.org/web/20140111155252/http://emtoolbox.nist.gov/Wavelength/Documentation.asp | archive-date = 2014-01-11 }}</ref> This means that it is also proportional to the pressure and inversely proportional to the temperature for [[ideal gas law|ideal gases]]. For liquids the same observation can be made as for gases, for instance, the refractive index in alkanes increases nearly perfectly linear with the density. On the other hand, for carboxylic acids, the density decreases with increasing number of C-atoms within the homologeous series. The simple explanation of this finding is that it is not density, but the molar concentration of the chromophore that counts. In homologeous series, this is the excitation of the C-H-bonding. August Beer must have intuitively known that when he gave Hans H. Landolt in 1862 the tip to investigate the refractive index of compounds of homologeous series.<ref>{{Cite journal |last=Landolt |first=H. |date=January 1862 |title=Ueber die Brechungsexponenten flüssiger homologer Verbindungen |url=https://onlinelibrary.wiley.com/doi/10.1002/andp.18621931102 |journal=Annalen der Physik |language=en |volume=193 |issue=11 |pages=353–385 |doi=10.1002/andp.18621931102 |bibcode=1862AnP...193..353L |issn=0003-3804|url-access=subscription }}</ref> While Landolt did not find this relationship, since, at this time dispersion theory was in its infancy, he had the idea of molar refractivity which can even be assigned to single atoms.<ref>{{Cite journal |last=Landolt |first=H. |date=January 1864 |title=Ueber den Einfluss der atomistischen Zusammensetzung C, H und O-haltiger flüssiger Verbindungen auf die Fortpflanzung des Lichtes |url=https://onlinelibrary.wiley.com/doi/10.1002/andp.18641991206 |journal=Annalen der Physik |language=en |volume=199 |issue=12 |pages=595–628 |doi=10.1002/andp.18641991206 |bibcode=1864AnP...199..595L |issn=0003-3804|url-access=subscription }}</ref> Based on this concept, the refractive indices of organic materials can be calculated.
=== Bandgap ===
[[File:Annotated Eg vs n.png|thumb|A scatter plot of bandgap energy versus optical refractive index for many common IV, III-V, and II-VI semiconducting elements / compounds. ]]
The optical refractive index of a semiconductor tends to increase as the [[Band gap|bandgap energy]] decreases. Many attempts<ref>{{Cite journal |last1=Gomaa |first1=Hosam M. |last2=Yahia |first2=I. S. |last3=Zahran |first3=H. Y. |date=2021-11-01 |title=Correlation between the static refractive index and the optical bandgap: Review and new empirical approach |url=https://www.sciencedirect.com/science/article/abs/pii/S0921452621004208 |journal=Physica B: Condensed Matter |volume=620 |pages=413246 |doi=10.1016/j.physb.2021.413246 |bibcode=2021PhyB..62013246G |issn=0921-4526|url-access=subscription }}</ref> have been made to model this relationship beginning with T. S. Moses in 1949.<ref>{{Cite journal |last=Moss |first=T S |date=1950-03-01 |title=A Relationship between the Refractive Index and the Infra-Red Threshold of Sensitivity for Photoconductors |url= |journal=Proceedings of the Physical Society. Section B |volume=63 |issue=3 |pages=167–176 |doi=10.1088/0370-1301/63/3/302 |bibcode=1950PPSB...63..167M |issn=0370-1301}}</ref> Empirical models can match experimental data over a wide range of materials and yet fail for important cases like InSb, PbS, and Ge.<ref>{{Cite book |last=Moss |first=T. S. |title=October 1 |chapter-url=https://www.degruyter.com/document/doi/10.1515/9783112495384-003/html |chapter=Relations between the Refractive Index and Energy Gap oi Semiconductors |date=1985-12-31 |publisher=De Gruyter |isbn=978-3-11-249538-4 |pages=415–428 |doi=10.1515/9783112495384-003}}</ref>
This negative correlation between refractive index and bandgap energy, along with a negative correlation between bandgap and temperature, means that many semiconductors exhibit a positive correlation between refractive index and temperature.<ref>{{Cite journal |last1=Bertolotti |first1=Mario |last2=Bogdanov |first2=Victor |last3=Ferrari |first3=Aldo |last4=Jascow |first4=Andrei |last5=Nazorova |first5=Natalia |last6=Pikhtin |first6=Alexander |last7=Schirone |first7=Luigi |date=1990-06-01 |title=Temperature dependence of the refractive index in semiconductors |url=https://opg.optica.org/josab/abstract.cfm?uri=josab-7-6-918 |journal=JOSA B |language=EN |volume=7 |issue=6 |pages=918–922 |doi=10.1364/JOSAB.7.000918 |bibcode=1990JOSAB...7..918B |issn=1520-8540|url-access=subscription }}</ref> This is the opposite of most materials, where the refractive index decreases with temperature as a result of a decreasing material density.
===Group index===
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\end{align}</math>
The momentum of photons in a medium of refractive index {{mvar|n}} is a complex and [[Abraham–Minkowski controversy|controversial]] issue with two different values having different physical interpretations.<ref>{{Cite journal |last1=Milonni |first1=Peter W. |last2=Boyd |first2=Robert W. |date=2010-12-31 |title=Momentum of Light in a Dielectric Medium |url=https://opg.optica.org/aop/abstract.cfm?uri=aop-2-4-519 |journal=Advances in Optics and Photonics |language=en |volume=2 |issue=4 |pages=519 |doi=10.1364/AOP.2.000519 |bibcode=2010AdOP....2..519M |issn=1943-8206|url-access=subscription }}</ref>
The refractive index of a substance can be related to its [[polarizability]] with the [[Lorentz–Lorenz equation]] or to the [[molar refractivity|molar refractivities]] of its constituents by the [[Gladstone–Dale relation]].
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==Applications==
The refractive index is an important property of the components of any [[optical instrument]]. It determines the focusing power of lenses, the dispersive power of prisms, the reflectivity of [[anti-reflective coating|lens coatings]],<ref>{{Cite book |last=Willey |first=Ronald R. |url=https://www.spiedigitallibrary.org/ebooks/FG/Field-Guide-to-Optical-Thin-Films/eISBN-9780819478221/10.1117/3.668269 |title=Field Guide to Optical Thin Films |date=2006-01-27 |publisher=SPIE |isbn=978-0-8194-7822-1 |doi=10.1117/3.668269}}</ref> and the light-guiding nature of [[optical fiber]].<ref>{{Cite journal |last=Takeo |first=Takashi |last2=Hattori |first2=Hajime |date=1982-10-01 |title=Optical Fiber Sensor for Measuring Refractive Index |url=https://iopscience.iop.org/article/10.1143/JJAP.21.1509 |journal=Japanese Journal of Applied Physics |volume=21 |issue=10R |pages=1509 |doi=10.1143/JJAP.21.1509 |issn=0021-4922|url-access=subscription }}</ref> Since the refractive index is a fundamental physical property of a substance, it is often used to identify a particular substance, confirm its purity, or measure its concentration. The refractive index is used to measure solids, liquids, and gases. It can be used, for example, to measure the concentration of a solute in an [[aqueous solution]].<ref>{{Cite journal |last=Warren |first=John R. |last2=Gordon |first2=Julius A. |date=January 1966 |title=On the Refractive Indices of Aqueous Solutions of Urea |url=https://pubs.acs.org/doi/abs/10.1021/j100873a507 |journal=The Journal of Physical Chemistry |language=en |volume=70 |issue=1 |pages=297–300 |doi=10.1021/j100873a507 |issn=0022-3654|url-access=subscription }}</ref> It can also be used as a useful tool to differentiate between different types of gemstone, due to the unique [[Chatoyancy|chatoyance]] each individual stone displays. A [[refractometer]] is the instrument used to measure the refractive index. For a solution of sugar, the refractive index can be used to determine the sugar content (see [[Brix]]).
==See also==
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