Editing Refractive index (section)

===Relative permittivity and permeability===
The refractive index of electromagnetic radiation equals
<math display="block">n = \sqrt{\varepsilon_\mathrm{r} \mu_\mathrm{r}},</math>
where {{math|''ε''{{sub|r}}}} is the material's [[relative permittivity]], and {{math|''μ''{{sub|r}}}} is its [[Permeability (electromagnetism)|relative permeability]].<ref name = bleaney>{{cite book | last1 = Bleaney| first1 = B.| author-link1 = Brebis Bleaney |last2 = Bleaney |first2 = B.I. | title = Electricity and Magnetism | publisher = [[Oxford University Press]] | edition = Third | date = 1976 | isbn = 978-0-19-851141-0 }}</ref>{{rp|229}} The refractive index is used for optics in [[Fresnel equations]] and [[Snell's law]]; while the relative permittivity and permeability are used in [[Maxwell's equations]] and electronics. Most naturally occurring materials are non-magnetic at optical frequencies, that is {{math|''μ''{{sub|r}}}} is very close to 1, therefore {{mvar|n}} is approximately {{math|{{sqrt|''ε''{{sub|r}}}}}}.<ref>{{cite book |last1=Andrews |first1=David L. |title=Photonics, Volume 2: Nanophotonic Structures and Materials |date=24 February 2015 |publisher=John Wiley & Sons |isbn=978-1-118-22551-6 |page=54 |url=https://books.google.com/books?id=EYRVBgAAQBAJ |language=en}}</ref> In this particular case, the complex relative permittivity {{math|{{uu|''ε''}}{{sub|r}}}}, with real and imaginary parts {{math|''ε''{{sub|r}}}} and {{math|''ɛ̃''{{sub|r}}}}, and the complex refractive index {{math|{{uu|''n''}}}}, with real and imaginary parts {{mvar|n}} and {{mvar|κ}} (the latter called the "extinction coefficient"), follow the relation
<math display="block">\underline{\varepsilon}_\mathrm{r} = \varepsilon_\mathrm{r} + i\tilde{\varepsilon}_\mathrm{r} = \underline{n}^2 = (n + i\kappa)^2,</math>

and their components are related by:<ref>{{cite book|first=Frederick|last=Wooten|title=Optical Properties of Solids|page=49|publisher=[[Academic Press]]|location=New York City|year= 1972|isbn=978-0-12-763450-0}}[http://www.lrsm.upenn.edu/~frenchrh/download/0208fwootenopticalpropertiesofsolids.pdf  (online pdf)] {{webarchive|url=https://web.archive.org/web/20111003034948/http://www.lrsm.upenn.edu/~frenchrh/download/0208fwootenopticalpropertiesofsolids.pdf |date=2011-10-03 }}</ref>
<math display="block">\begin{align}
\varepsilon_\mathrm{r} &= n^2 - \kappa^2\,, \\
\tilde{\varepsilon}_\mathrm{r} &= 2n\kappa\,,
\end{align}</math>

and:

<math display="block">\begin{align}
n &= \sqrt{\frac{|\underline{\varepsilon}_\mathrm{r}| + \varepsilon_\mathrm{r}}{2}}, \\
\kappa &= \sqrt{\frac{|\underline{\varepsilon}_\mathrm{r}| - \varepsilon_\mathrm{r}}{2}}.
\end{align}</math>

where <math>|\underline{\varepsilon}_\mathrm{r}| = \sqrt{\varepsilon_\mathrm{r}^2 + \tilde{\varepsilon}_\mathrm{r}^2}</math> is the [[modulus of complex number|complex modulus]].