Refractive index: Difference between revisions

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The refractive index may vary with wavelength. This causes white light to split into constituent colors when refracted. This is called [[dispersion (optics)|dispersion]]. This effect can be observed in [[Prism (optics)|prisms]] and [[rainbow]]s, and as [[chromatic aberration]] in lenses. Light propagation in [[Absorption (electromagnetic radiation)|absorbing]] materials can be described using a [[complex number|complex]]-valued refractive index.<ref name="Attwood">{{cite book|title=Soft X-rays and extreme ultraviolet radiation: principles and applications|author=Attwood, David |page=60|isbn=978-0-521-02997-1|year=1999|publisher=Cambridge University Press }}</ref> The [[Imaginary number|imaginary]] part then handles the [[attenuation]], while the [[Real number|real]] part accounts for refraction. For most materials the refractive index changes with wavelength by several percent across the visible spectrum. Consequently, refractive indices for materials reported using a single value for {{mvar|n}} must specify the wavelength used in the measurement.

The concept of refractive index applies across the full [[electromagnetic spectrum]], from [[X-ray]]s to [[radio wave]]s. It can also be applied to [[wave]] phenomena such as [[sound]]. In this case, the [[speed of sound]] is used instead of that of light, and a reference medium other than vacuum must be chosen.<ref name=Kinsler>{{cite book | last = Kinsler | first = Lawrence E. | title = Fundamentals of Acoustics | url = https://archive.org/details/fundamentalsacou00kins_265 | url-access = limited | publisher = John Wiley | year = 2000 | isbn = 978-0-471-84789-2 | page = [https://archive.org/details/fundamentalsacou00kins_265/page/n151 136]}}</ref> Refraction also occurs in oceans when light passes into the [[Halocline|halocline]] where salinity has impacted the density of the water column.

For [[lens]]es (such as [[eye glasses]]), a lens made from a high refractive index material will be thinner, and hence lighter, than a conventional lens with a lower refractive index. Such lenses are generally more expensive to manufacture than conventional ones.

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=== 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 |issn=0921-4526}}</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 |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 |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===