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Added a section on relationship between refractive index and bandgap in semiconductors. |
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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}}</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}}</ref> Based on this concept, the refractive indices of organic materials can be calculated.
=== Bandgap ===
The optical refractive index of a semiconductor tends to increase as the [[Band gap|bandgap energy]] decreases. Many attempts<ref>{{Cite journal |last=Gomaa |first=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 |issn=0921-4526}}</ref> have been made to fit this relationship to a theory, 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 |issn=0370-1301}}</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 |last=Bertolotti |first=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 |issn=1520-8540}}</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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