Editing Refractive index (section)

==Microscopic explanation==
[[File:Thin section scan crossed polarizers Siilinjärvi R636-105.90.jpg|thumb|In [[optical mineralogy]], [[thin section]]s are used to study rocks. The method is based on the distinct refractive indices of different [[mineral]]s.]]
{{Main|Ewald–Oseen extinction theorem}}
At the atomic scale, an electromagnetic wave's phase velocity is slowed in a material because the [[electric field]] creates a disturbance in the charges of each atom (primarily the [[electron]]s) proportional to the [[electric susceptibility]] of the medium. (Similarly, the [[magnetic field]] creates a disturbance proportional to the [[magnetic susceptibility]].) As the electromagnetic fields oscillate in the wave, the charges in the material will be "shaken" back and forth at the same frequency.<ref name = Hecht />{{rp|67}} The charges thus radiate their own electromagnetic wave that is at the same frequency, but usually with a [[phase (waves)|phase delay]], as the charges may move out of phase with the force driving them (see [[Harmonic oscillator#Sinusoidal driving force|sinusoidally driven harmonic oscillator]]). The light wave traveling in the medium is the macroscopic [[superposition principle|superposition (sum)]] of all such contributions in the material: the original wave plus the waves radiated by all the moving charges. This wave is typically a wave with the same frequency but shorter wavelength than the original, leading to a slowing of the wave's phase velocity. Most of the radiation from oscillating material charges will modify the incoming wave, changing its velocity. However, some net energy will be radiated in other directions or even at other frequencies (see [[scattering]]).

Depending on the relative phase of the original driving wave and the waves radiated by the charge motion, there are several possibilities:
* If the electrons emit a light wave which is 90° out of phase with the light wave shaking them, it will cause the total light wave to travel slower. This is the normal refraction of transparent materials like glass or water, and corresponds to a refractive index which is real and greater than 1.<ref name="Feynman, Richard P. 2011">{{cite book |last= Feynman |first= Richard P. |title= Mainly Mechanics, Radiation, and Heat |series= Feynman Lectures on Physics |volume= 1 |edition= The New Millenium |publisher= Basic Books |date= 2011 |isbn= 978-0-465-02493-3}}</ref>{{page needed|date= August 2023}}
* If the electrons emit a light wave which is 270° out of phase with the light wave shaking them, it will cause the wave to travel faster. This is called "anomalous refraction", and is observed close to absorption lines (typically in infrared spectra), with [[X-ray]]s in ordinary materials, and with radio waves in Earth's [[ionosphere]]. It corresponds to a [[permittivity]] less than 1, which causes the refractive index to be also less than unity and the [[phase velocity]] of light greater than the [[speed of light|speed of light in vacuum]] {{math|c}} (note that the [[signal velocity]] is still less than {{math|c}}, as discussed above). If the response is sufficiently strong and out-of-phase, the result is a negative value of [[permittivity]] and imaginary index of refraction, as observed in metals or plasma.<ref name="Feynman, Richard P. 2011"/>{{page needed|date= August 2023}}
* If the electrons emit a light wave which is 180° out of phase with the light wave shaking them, it will destructively interfere with the original light to reduce the total light intensity. This is [[absorption (electromagnetic radiation)|light absorption in opaque materials]] and corresponds to an [[imaginary number|imaginary]] refractive index.
* If the electrons emit a light wave which is in phase with the light wave shaking them, it will amplify the light wave. This is rare, but occurs in [[laser]]s due to [[stimulated emission]]. It corresponds to an imaginary index of refraction, with the opposite sign to that of absorption.
For most materials at visible-light frequencies, the phase is somewhere between 90° and 180°, corresponding to a combination of both refraction and absorption.