Editing Refraction (section)

== General explanation ==
[[File:Refraction animation.gif|thumb|When a wave moves into a slower medium the wavefronts get compressed. For the wavefronts to stay connected at the boundary the wave must change direction.]]

Refraction involves two related parts, both a result of the wave nature of light: a reduced speed in an optical medium and a change in angle when a wave front crosses between different media at an angle.

# Light slows as it travels through a medium other than vacuum (such as air, glass or water). This is not because of scattering or absorption. Rather it is because, as an [[electromagnetic wave|electromagnetic oscillation]], light itself causes other [[electrical charge|electrically charged]] particles such as [[electron]]s, to oscillate. The oscillating electrons emit their own electromagnetic waves  which interact with the original light. The resulting combined wave has a lower speed. When light returns to a vacuum and there are no electrons nearby, this slowing effect ends and its speed returns to {{mvar|c}}.
# When light enters a slower medium at an angle, one side of the [[wavefront]] is slowed before the other. This asymmetrical slowing of the light causes it to change the angle of its travel. Once light is within the new medium with constant properties, it travels in a straight line again.

===Slowing of light===

As described above, the [[speed of light]] is slower in a medium other than vacuum. This slowing applies to any medium such as air, water, or glass, and is responsible for phenomena such as refraction. On the other side of the medium its speed will again be the speed of light in vacuum, {{mvar|c}}.

A correct explanation rests on light's nature as an [[electromagnetic wave]].<ref>[https://m.youtube.com/watch?v=CUjt36SD3h8 Why does light slow down in water?] - [[Fermilab]]</ref> Because light is an oscillating electrical/magnetic wave, light traveling in a medium causes the electrically charged [[electron]]s of the material to also oscillate. (The material's [[proton]]s also oscillate but as they are around 2000 times more massive, their movement and therefore their effect, is far smaller). A moving [[electrical charge]] emits electromagnetic waves of its own. The electromagnetic waves emitted by the oscillating electrons interact with the electromagnetic waves that make up the original light, similar to water waves on a pond, a process known as [[constructive interference]]. When two waves interfere in this way, the resulting "combined" wave may have wave packets that pass an observer at a slower rate. The light has effectively been slowed. When the light leaves the material, this interaction with electrons no longer happens, and therefore the wave packet rate (and therefore its speed) return to normal.

===Bending of light===

Consider a wave going from one material to another where its speed is slower as in the figure. If it reaches the interface between the materials at an angle one side of the wave will reach the second material first, and therefore slow down earlier. With one side of the wave going slower the whole wave will pivot towards that side. This is why a wave will bend away from the surface or toward the [[Normal (geometry)|normal]] when going into a slower material. In the opposite case of a wave reaching a material where the speed is higher, one side of the wave will speed up and the wave will pivot away from that side.

Another way of understanding the same thing is to consider the change in wavelength at the interface. When the wave goes from one material to another where the wave has a different speed {{mvar|v}}, the [[frequency]] {{mvar|f}} of the wave will stay the same, but the distance between [[wavefront]]s or [[wavelength]] {{math|1= ''λ'' = ''v''/''f''}} will change. If the speed is decreased, such as in the figure to the right, the wavelength will also decrease. With an angle between the wave fronts and the interface and change in distance between the wave fronts the angle must change over the interface to keep the wave fronts intact. From these considerations the relationship between the [[Angle of incidence (optics)|angle of incidence]] {{math|''θ''{{sub|1}}}}, angle of transmission {{math|''θ''{{sub|2}}}} and the wave speeds {{math|''v''{{sub|1}}}} and {{math|''v''{{sub|2}}}} in the two materials can be derived. This is the [[law of refraction]] or Snell's law and can be written as<ref name="Hecht">{{cite book|author=Hecht, Eugene|title=Optics|publisher=Addison-Wesley|year=2002|isbn=0-321-18878-0|page=101}}</ref>

<math display="block">\frac{\sin\theta_1}{\sin\theta_2} = \frac{v_1}{v_2} \,.</math>

The phenomenon of refraction can in a more fundamental way be derived from the 2 or 3-dimensional [[wave equation]]. The boundary condition at the interface will then require the tangential component of the [[wave vector]] to be identical on the two sides of the interface.<ref>{{cite web|url=https://www.rp-photonics.com/refraction.html|title=Refraction|author=<!--Not stated-->|website=RP Photonics Encyclopedia|publisher=RP Photonics Consulting GmbH, Dr. Rüdiger Paschotta|access-date=2018-10-23|quote=It results from the boundary conditions which the incoming and the transmitted wave need to fulfill at the boundary between the two media. Essentially, the tangential components of the wave vectors need to be identical, as otherwise the phase difference between the waves at the boundary would be position-dependent, and the wavefronts could not be continuous. As the magnitude of the wave vector depends on the refractive index of the medium, the said condition can in general only be fulfilled with different propagation directions.}}</ref> Since the magnitude of the wave vector depend on the wave speed this requires a change in direction of the wave vector.

The relevant wave speed in the discussion above is the [[phase velocity]] of the wave. This is typically close to the [[group velocity]] which can be seen as the truer speed of a wave, but when they differ it is important to use the phase velocity in all calculations relating to refraction.

A wave traveling perpendicular to a boundary, i.e. having its wavefronts parallel to the boundary, will not change direction even if the speed of the wave changes.

===Dispersion of light===
[[File:Hetch Hetchy Releases (5910591819).jpg|thumb|Rainbows are formed by dispersion of light, in which the refraction angle depends on the light's frequency.]]
Refraction is also responsible for [[rainbow]]s and for the splitting of white light into a rainbow-spectrum as it passes through a glass [[triangular prism (optics)|prism]]. Glass and water have higher refractive indexes than air. When a beam of white light passes from air into a material having an index of refraction that varies with frequency (and wavelength), a phenomenon known as [[dispersion (optics)|dispersion]] occurs, in which different coloured components of the white light are refracted at different angles, i.e., they bend by different amounts at the interface, so that they become separated. The different colors correspond to different frequencies and different wavelengths.