Editing Optics (section)

====Superposition and interference====
{{Main|Superposition principle|Interference (optics)}}

In the absence of [[nonlinear optics|nonlinear]] effects, the superposition principle can be used to predict the shape of interacting waveforms through the simple addition of the disturbances.{{sfnp|Young|Freedman|2020|pp=1187–1188}} This interaction of waves to produce a resulting pattern is generally termed "interference" and can result in a variety of outcomes. If two waves of the same wavelength and frequency are ''in [[phase (waves)|phase]]'', both the wave crests and wave troughs align. This results in [[constructive interference]] and an increase in the amplitude of the wave, which for light is associated with a brightening of the waveform in that location. Alternatively, if the two waves of the same wavelength and frequency are out of phase, then the wave crests will align with wave troughs and vice versa. This results in [[destructive interference]] and a decrease in the amplitude of the wave, which for light is associated with a dimming of the waveform at that location. See below for an illustration of this effect.{{sfnp|Young|Freedman|2020|p=512, 1189}}

{|
|-
|'''combined<br> waveform'''
|colspan="2" rowspan="3"|[[File:Interference of two waves.svg|class=skin-invert-image]]
|-
|'''wave 1'''
|-
|'''wave 2'''
|-
|
|'''Two waves in phase'''
|'''Two waves 180° out <br>of phase'''
|}

[[File:Dieselrainbow.jpg|thumb|right|upright=1.35|When oil or fuel is spilled, colourful patterns are formed by thin-film interference.]]
Since the Huygens–Fresnel principle states that every point of a wavefront is associated with the production of a new disturbance, it is possible for a wavefront to interfere with itself constructively or destructively at different locations producing bright and dark fringes in regular and predictable patterns.{{sfnp|Young|Freedman|2020|pp=1191–1192}} [[Interferometry]] is the science of measuring these patterns, usually as a means of making precise determinations of distances or [[angular resolution]]s.<ref name=interferometry>{{cite book|author=P. Hariharan|title=Optical Interferometry|edition=2nd|publisher=Academic Press|place=San Diego, US|year=2003|url=http://www.astro.lsa.umich.edu/~monnier/Publications/ROP2003_final.pdf|isbn=978-0-12-325220-3|url-status=live|archive-url=https://web.archive.org/web/20080406215913/http://www.astro.lsa.umich.edu/~monnier/Publications/ROP2003_final.pdf|archive-date=2008-04-06}}</ref> The [[Michelson interferometer]] was a famous instrument which used interference effects to accurately measure the speed of light.<ref>{{cite book|author=E.R. Hoover|title=Cradle of Greatness: National and World Achievements of Ohio's Western Reserve|place=Cleveland|publisher=Shaker Savings Association|year=1977}}</ref>

The appearance of [[Thin film optics|thin films and coatings]] is directly affected by interference effects. [[Antireflective coating]]s use destructive interference to reduce the reflectivity of the surfaces they coat, and can be used to minimise glare and unwanted reflections. The simplest case is a single layer with a thickness of one-fourth the wavelength of incident light. The reflected wave from the top of the film and the reflected wave from the film/material interface are then exactly 180° out of phase, causing destructive interference. The waves are only exactly out of phase for one wavelength, which would typically be chosen to be near the centre of the visible spectrum, around 550&nbsp;nm. More complex designs using multiple layers can achieve low reflectivity over a broad band, or extremely low reflectivity at a single wavelength.

Constructive interference in thin films can create a strong reflection of light in a range of wavelengths, which can be narrow or broad depending on the design of the coating. These films are used to make [[dielectric mirror]]s, [[interference filter]]s, [[heat reflector]]s, and filters for colour separation in [[colour television]] cameras. This interference effect is also what causes the colourful rainbow patterns seen in oil slicks.{{sfnp|Young|Freedman|2020|pp=1198–1200}}