Editing Refractive index (section)

===Group index===
{{Redirect distinguish|Group index|Index of a subgroup}}
Sometimes, a "group velocity refractive index", usually called the ''group index'' is defined:{{citation needed|date=June 2015}}
<math display="block">n_\mathrm{g} = \frac{\mathrm{c}}{v_\mathrm{g}},</math>
where {{math|''v''{{sub|g}}}} is the [[group velocity]]. This value should not be confused with {{mvar|n}}, which is always defined with respect to the [[phase velocity]]. When the [[dispersion (optics)|dispersion]] is small, the group velocity can be linked to the phase velocity by the relation<ref name=bornwolf>{{cite book | title=[[Principles of Optics]] | publisher=CUP Archive | edition=7th expanded | last1=Born | first1=Max | author-link1=Max Born | last2=Wolf | first2=Emil | author-link2=Emil Wolf | page=[https://archive.org/details/principlesofopti0006born/page/22 22] | isbn=978-0-521-78449-8 | date=1999 }}</ref>{{rp|22}}
<math display="block">v_\mathrm{g} = v - \lambda\frac{\mathrm{d}v}{\mathrm{d}\lambda},</math>
where {{mvar|λ}} is the wavelength in the medium. In this case the group index can thus be written in terms of the wavelength dependence of the refractive index as
<math display="block">n_\mathrm{g} = \frac{n}{1 + \frac{\lambda}{n}\frac{\mathrm{d}n}{\mathrm{d}\lambda}}.</math>

When the refractive index of a medium is known as a function of the vacuum wavelength (instead of the wavelength in the medium), the corresponding expressions for the group velocity and index are (for all values of dispersion)<ref>{{Cite journal |last1= Bor |first1= Z. |last2=  Osvay |first2= K. |last3= Rácz |first3= B. |last4= Szabó |first4= G. |date= 1990 |title= Group refractive index measurement by Michelson interferometer |journal= Optics Communications |pages= 109–112 |volume= 78 |doi= 10.1016/0030-4018(90)90104-2 |bibcode= 1990OptCo..78..109B |issue= 2 }}</ref>
<math display="block">\begin{align}
v_\mathrm{g} &= \mathrm{c}\!\left(n - \lambda_0 \frac{\mathrm{d}n}{\mathrm{d}\lambda_0}\right)^{-1}\!, \\
n_\mathrm{g} &= n - \lambda_0 \frac{\mathrm{d}n}{\mathrm{d}\lambda_0},
\end{align}</math>
where {{math|''λ''{{sub|0}}}} is the wavelength in vacuum.