Editing Refractive index (section)

===Refractive index below unity===
According to the [[theory of relativity]], no information can travel faster than the speed of light in vacuum, but this does not mean that the refractive index cannot be less than 1. The refractive index measures the [[phase velocity]] of light, which does not carry [[information]].<ref name=Als-Nielsen2011>{{cite book |last1=Als-Nielsen |first1=J. |last2=McMorrow |first2=D. |date=2011 |title=Elements of Modern X-ray Physics |publisher=Wiley-VCH |isbn=978-0-470-97395-0 |url=https://archive.org/details/elementsmodernxr00alsn |url-access=limited |page=[https://archive.org/details/elementsmodernxr00alsn/page/n38 25]}}</ref>{{efn|
One consequence of the real part of {{mvar|n}} being less than unity is that it implies that the phase velocity inside the material, {{sfrac|{{math|c}}|{{mvar|n}}}}, is larger than the velocity of light, {{math|c}}. This does not, however, violate the law of relativity, which requires that only signals carrying information do not travel faster than {{math|c}}. Such signals move with the group velocity, not with the phase velocity, and it can be shown that the group velocity is in fact less than {{math|c}}.<ref name=Als-Nielsen2011/>}} The phase velocity is the speed at which the crests of the wave move and can be faster than the speed of light in vacuum, and thereby give a refractive index {{nobr|below 1.}} This can occur close to [[resonance frequency|resonance frequencies]], for absorbing media, in [[plasma (physics)|plasmas]], and for [[X-ray]]s. In the X-ray regime the refractive indices are lower than but very {{nobr|close to 1}} (exceptions close to some resonance frequencies).<ref name=CXRO>{{cite web |last= Gullikson |first= Eric |title= X-Ray interactions with matter |department=Optical constants |website= The Center for X-Ray Optics |publisher= [[Lawrence Berkeley Laboratory]] |url = http://henke.lbl.gov/optical_constants/ |access-date= 2011-08-30 |url-status= live |archive-url= https://web.archive.org/web/20110827214322/http://henke.lbl.gov/optical_constants/ |archive-date= 2011-08-27 }}</ref>
As an example, water has a refractive index of {{nobr|{{val|0.99999974}} {{=}}}} {{nobr|1 − {{val|2.6|e=-7}}}} for X-ray radiation at a photon energy of {{val|30|ul=keV}} ({{val|0.04|u=nm}} wavelength).<ref name=CXRO/>

An example of a plasma with an index of refraction less than unity is Earth's [[ionosphere]].  Since the refractive index of the ionosphere (a [[Plasma (physics)|plasma]]), is less than unity, electromagnetic waves propagating through the plasma are bent "away from the normal" (see [[Geometric optics]]) allowing the radio wave to be refracted back toward earth, thus enabling long-distance radio communications.  See also [[Radio Propagation]] and [[Skywave]].<ref>{{cite book |last1=Lied |first1=Finn |date=1967 |title=High Frequency Radio Communications with Emphasis on Polar Problems |publisher=The Advisory Group for Aerospace Research and Development |pages=1–7}}</ref>