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imported>ShinigamiSenpai Removed the technical notice. I do not think there is much to be simplified, and the basics of what the average person would want to understand has been adequately explained in the initial part of the mechanism section. Any further explanation will require more depth and technical jargon to accurately explain. |
imported>Jerryv64 →Acoustic interferometry: Fixed typo |
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Interference effects can be observed with all types of waves, for example, [[Light wave|light]], [[Radio wave|radio]], [[sound wave|acoustic]], [[surface wave|surface water waves]], [[gravity wave]]s, or [[matter wave]]s as well as in loudspeakers as electrical waves. | Interference effects can be observed with all types of waves, for example, [[Light wave|light]], [[Radio wave|radio]], [[sound wave|acoustic]], [[surface wave|surface water waves]], [[gravity wave]]s, or [[matter wave]]s as well as in loudspeakers as electrical waves. | ||
== | == History == | ||
Around 1800, the word ''interference'' was used by [[Thomas Young (scientist)|Thomas Young]] in developing his theories of acoustics and optics.<ref>{{Cite book|last=Kipnis|first=Nahum|date=1991|title=History of the Principle of Interference of Light|url=https://link.springer.com/book/10.1007/978-3-0348-8652-9|language=en-gb|doi=10.1007/978-3-0348-8652-9|isbn=978-3-0348-9717-4 }}</ref> | |||
== Mechanisms == | == Mechanisms == | ||
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[[File:3D Interference of Laser Light Through 2 Pinholes Animation.webm|thumb|thumbtime=3|Cropped tomography scan animation of laser light interference passing through two pinholes (side edges)]] | [[File:3D Interference of Laser Light Through 2 Pinholes Animation.webm|thumb|thumbtime=3|Cropped tomography scan animation of laser light interference passing through two pinholes (side edges)]] | ||
The [[superposition principle#Wave interference|principle of superposition of waves]] states that when two or more propagating waves of the same type are incident on the same point, the resultant [[amplitude]] at that point is equal to the [[Euclidean vector#Addition and subtraction|vector sum]] of the amplitudes of the individual waves.<ref>Ockenga, Wymke. [ | The [[superposition principle#Wave interference|principle of superposition of waves]] states that when two or more propagating waves of the same type are incident on the same point, the resultant [[amplitude]] at that point is equal to the [[Euclidean vector#Addition and subtraction|vector sum]] of the amplitudes of the individual waves.<ref>Ockenga, Wymke. [https://www.leica-microsystems.com/science-lab/phase-contrast/ Phase contrast]. Leika Science Lab, 09 June 2011. "If two waves interfere, the amplitude of the resulting light wave will be equal to the vector sum of the amplitudes of the two interfering waves."</ref> If a [[Crest (physics)|crest]] of a wave meets a crest of another wave of the same frequency at the same point, then the amplitude is the sum of the individual amplitudes—this is '''constructive interference'''. If a crest of one wave meets a trough of another wave, then the amplitude is equal to the difference in the individual amplitudes—this is known as '''destructive interference'''. In ideal mediums (water, air are almost ideal) energy is always conserved, at points of destructive interference, the wave amplitudes cancel each other out, and the energy is redistributed to other areas. For example, when two pebbles are dropped in a pond, a pattern is observable; but eventually waves continue, and only when they reach the shore is the energy absorbed away from the medium. | ||
[[File:Interference colours in soap film 1.jpg|thumb|Photograph of 1.5cm x 1cm region of soap film under white light. Varying film thickness and viewing geometry determine which colours undergo constructive or destructive interference. Small bubbles significantly affect surrounding film thickness.]] | [[File:Interference colours in soap film 1.jpg|thumb|Photograph of 1.5cm x 1cm region of soap film under white light. Varying film thickness and viewing geometry determine which colours undergo constructive or destructive interference. Small bubbles significantly affect surrounding film thickness.]] | ||
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Interference of light is a unique phenomenon in that we can never observe superposition of the EM field directly as we can, for example, in water. Superposition in the EM field is an assumed phenomenon and necessary to explain how two light beams pass through each other and continue on their respective paths. Prime examples of light interference are the famous [[double-slit experiment]], [[laser speckle]], [[anti-reflective coating]]s and [[interferometer]]s. | Interference of light is a unique phenomenon in that we can never observe superposition of the EM field directly as we can, for example, in water. Superposition in the EM field is an assumed phenomenon and necessary to explain how two light beams pass through each other and continue on their respective paths. Prime examples of light interference are the famous [[double-slit experiment]], [[laser speckle]], [[anti-reflective coating]]s and [[interferometer]]s. | ||
In addition to classical wave model for understanding optical interference, quantum | In addition to the classical wave model for understanding optical interference, quantum matter waves also demonstrate interference. | ||
=== Real-valued wave functions === | === Real-valued wave functions === | ||
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A [[diffraction grating]] can be considered to be a multiple-beam interferometer; since the peaks which it produces are generated by interference between the light transmitted by each of the elements in the grating; see [[interference vs. diffraction]] for further discussion. | A [[diffraction grating]] can be considered to be a multiple-beam interferometer; since the peaks which it produces are generated by interference between the light transmitted by each of the elements in the grating; see [[interference vs. diffraction]] for further discussion. | ||
== Optical wave interference == | |||
[[File:Optical flat interference.svg|thumb|upright=1.55|Creation of interference fringes by an [[optical flat]] on a reflective surface. Light rays from a monochromatic source pass through the glass and reflect off both the bottom surface of the flat and the supporting surface. The tiny gap between the surfaces means the two reflected rays have different path lengths. In addition the ray reflected from the bottom plate undergoes a 180° phase reversal. As a result, at locations '''''(a)''''' where the path difference is an odd multiple of λ/2, the waves reinforce. At locations '''''(b)''''' where the path difference is an even multiple of λ/2 the waves cancel. Since the gap between the surfaces varies slightly in width at different points, a series of alternating bright and dark bands, ''interference fringes'', are seen.]] | [[File:Optical flat interference.svg|thumb|upright=1.55|Creation of interference fringes by an [[optical flat]] on a reflective surface. Light rays from a monochromatic source pass through the glass and reflect off both the bottom surface of the flat and the supporting surface. The tiny gap between the surfaces means the two reflected rays have different path lengths. In addition the ray reflected from the bottom plate undergoes a 180° phase reversal. As a result, at locations '''''(a)''''' where the path difference is an odd multiple of λ/2, the waves reinforce. At locations '''''(b)''''' where the path difference is an even multiple of λ/2 the waves cancel. Since the gap between the surfaces varies slightly in width at different points, a series of alternating bright and dark bands, ''interference fringes'', are seen.]] | ||
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Quantum mechanically the theories of Paul Dirac and Richard Feynman offer a more modern approach. Dirac showed that every quanta or photon of light acts on its own which he famously stated as "every photon interferes with itself". Richard Feynman showed that by evaluating a path integral where all possible paths are considered, that a number of higher probability paths will emerge. In thin films for example, film thickness which is not a multiple of light wavelength will not allow the quanta to traverse, only reflection is possible. | Quantum mechanically the theories of Paul Dirac and Richard Feynman offer a more modern approach. Dirac showed that every quanta or photon of light acts on its own which he famously stated as "every photon interferes with itself". Richard Feynman showed that by evaluating a path integral where all possible paths are considered, that a number of higher probability paths will emerge. In thin films for example, film thickness which is not a multiple of light wavelength will not allow the quanta to traverse, only reflection is possible. | ||
=== Light source requirements === | |||
The discussion above assumes that the waves which interfere with one another are monochromatic, i.e. have a single frequency—this requires that they are infinite in time. This is not, however, either practical or necessary. Two identical waves of finite duration whose frequency is fixed over that period will give rise to an interference pattern while they overlap. Two identical waves which consist of a narrow spectrum of frequency waves of finite duration (but shorter than their coherence time), will give a series of fringe patterns of slightly differing spacings, and provided the spread of spacings is significantly less than the average fringe spacing, a fringe pattern will again be observed during the time when the two waves overlap. | The discussion above assumes that the waves which interfere with one another are monochromatic, i.e. have a single frequency—this requires that they are infinite in time. This is not, however, either practical or necessary. Two identical waves of finite duration whose frequency is fixed over that period will give rise to an interference pattern while they overlap. Two identical waves which consist of a narrow spectrum of frequency waves of finite duration (but shorter than their coherence time), will give a series of fringe patterns of slightly differing spacings, and provided the spread of spacings is significantly less than the average fringe spacing, a fringe pattern will again be observed during the time when the two waves overlap. | ||
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It is also possible to observe interference fringes using white light. A white light fringe pattern can be considered to be made up of a 'spectrum' of fringe patterns each of slightly different spacing. If all the fringe patterns are in phase in the centre, then the fringes will increase in size as the wavelength decreases and the summed intensity will show three to four fringes of varying colour. Young describes this very elegantly in his discussion of two slit interference. Since white light fringes are obtained only when the two waves have travelled equal distances from the light source, they can be very useful in interferometry, as they allow the zero path difference fringe to be identified.<ref name="Born and Wolf">{{cite book |first1=Max |last1=Born |author-link=Max Born |first2=Emil |last2=Wolf |year=1999 |title=[[Principles of Optics]] |publisher=Cambridge University Press |location=Cambridge |isbn=0-521-64222-1 }}</ref> | It is also possible to observe interference fringes using white light. A white light fringe pattern can be considered to be made up of a 'spectrum' of fringe patterns each of slightly different spacing. If all the fringe patterns are in phase in the centre, then the fringes will increase in size as the wavelength decreases and the summed intensity will show three to four fringes of varying colour. Young describes this very elegantly in his discussion of two slit interference. Since white light fringes are obtained only when the two waves have travelled equal distances from the light source, they can be very useful in interferometry, as they allow the zero path difference fringe to be identified.<ref name="Born and Wolf">{{cite book |first1=Max |last1=Born |author-link=Max Born |first2=Emil |last2=Wolf |year=1999 |title=[[Principles of Optics]] |publisher=Cambridge University Press |location=Cambridge |isbn=0-521-64222-1 }}</ref> | ||
=== Optical arrangements === | |||
To generate interference fringes, light from the source has to be divided into two waves which then have to be re-combined. Traditionally, interferometers have been classified as either amplitude-division or wavefront-division systems. | To generate interference fringes, light from the source has to be divided into two waves which then have to be re-combined. Traditionally, interferometers have been classified as either amplitude-division or wavefront-division systems. | ||
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</gallery> | </gallery> | ||
== Quantum interference == | |||
{{See also|Double-slit_experiment|l1=Double-slit experiment|Matter wave}} | {{See also|Double-slit_experiment|l1=Double-slit experiment|Matter wave}} | ||
{{Quantum mechanics|cTopic=Fundamental concepts}} | {{Quantum mechanics|cTopic=Fundamental concepts}} | ||
'''Quantum interference''' – the observed [[matter wave | wave-behavior of matter]]<ref>[[Richard Feynman|Feynman R]], [[Robert B. Leighton|Leighton R]], and [[Matthew Sands|Sands M.]], The Feynman Lectures Website, September 2013.[https://feynmanlectures.caltech.edu/III_toc.html "The Feynman Lectures on Physics, Volume III"] (online edition)</ref> – resembles [[Wave interference#Optical interference|optical interference]]. Let <math>\Psi (x, t)</math> be a [[Wave function|wavefunction]] solution of the [[Schrödinger equation]] for a quantum mechanical object. Then the [[probability amplitude|probability]] of observing the object in the interval <math>[a,b]</math> is <math>P([a,b]) = \int_a^b |\Psi (x, t)|^2 dx = \int_a^b \Psi^* (x, t) \Psi (x, t) dx</math> where * indicates [[complex conjugate|complex conjugation]]. Quantum interference concerns the issue of this probability when the wavefunction is expressed as a sum or [[Quantum superposition|linear superposition]] of two terms <math>\Psi (x, t) = \Psi_A (x, t) + \Psi_B (x, t)</math>: | '''Quantum interference''' – the observed [[matter wave|wave-behavior of matter]]<ref>[[Richard Feynman|Feynman R]], [[Robert B. Leighton|Leighton R]], and [[Matthew Sands|Sands M.]], The Feynman Lectures Website, September 2013.[https://feynmanlectures.caltech.edu/III_toc.html "The Feynman Lectures on Physics, Volume III"] (online edition)</ref> – resembles [[Wave interference#Optical interference|optical interference]]. Let <math>\Psi (x, t)</math> be a [[Wave function|wavefunction]] solution of the [[Schrödinger equation]] for a quantum mechanical object. Then the [[probability amplitude|probability]] of observing the object in the interval <math>[a,b]</math> is <math>P([a,b]) = \int_a^b |\Psi (x, t)|^2 dx = \int_a^b \Psi^* (x, t) \Psi (x, t) dx</math> where * indicates [[complex conjugate|complex conjugation]]. Quantum interference concerns the issue of this probability when the wavefunction is expressed as a sum or [[Quantum superposition|linear superposition]] of two terms <math>\Psi (x, t) = \Psi_A (x, t) + \Psi_B (x, t)</math>: | ||
<math display="block">P([a,b]) = \int_a^b |\Psi (x, t)|^2 = \int_a^b (|\Psi_A (x, t)|^2 + |\Psi_B (x, t)|^2 + \Psi_A^* (x, t) \Psi_B (x, t) + \Psi_A (x, t) \Psi_B^* (x, t)) dx</math> | <math display="block">P([a,b]) = \int_a^b |\Psi (x, t)|^2 = \int_a^b (|\Psi_A (x, t)|^2 + |\Psi_B (x, t)|^2 + \Psi_A^* (x, t) \Psi_B (x, t) + \Psi_A (x, t) \Psi_B^* (x, t)) dx</math> | ||
Usually, <math>\Psi_A (x, t)</math> and <math>\Psi_B (x, t)</math> correspond to distinct situations A and B. When this is the case, the equation <math>\Psi (x, t) = \Psi_A (x, t) + \Psi_B (x, t)</math> indicates that the object can be in situation A or situation B. The above equation can then be interpreted as: The probability of finding the object at <math>x</math> is the probability of finding the object at <math>x</math> when it is in situation A plus the probability of finding the object at <math>x</math> when it is in situation B plus an extra term. This extra term, which is called the ''quantum interference term'', is <math>\Psi_A^* (x, t) \Psi_B (x, t) + \Psi_A (x, t) \Psi_B^* (x, t)</math> in the above equation. As in the [[Wave interference#Mechanisms|classical wave case]] above, the quantum interference term can add (constructive interference) or subtract (destructive interference) from <math>|\Psi_A (x, t)|^2 + |\Psi_B (x, t)|^2</math> in the above equation depending on whether the quantum interference term is positive or negative. If this term is absent for all <math>x</math>, then there is no quantum mechanical interference associated with situations A and B. | Usually, <math>\Psi_A (x, t)</math> and <math>\Psi_B (x, t)</math> correspond to distinct situations A and B. When this is the case, the equation <math>\Psi (x, t) = \Psi_A (x, t) + \Psi_B (x, t)</math> indicates that the object can be in situation A or situation B. The above equation can then be interpreted as: The probability of finding the object at <math>x</math> is the probability of finding the object at <math>x</math> when it is in situation A plus the probability of finding the object at <math>x</math> when it is in situation B plus an extra term. This extra term, which is called the ''quantum interference term'', is <math>\Psi_A^* (x, t) \Psi_B (x, t) + \Psi_A (x, t) \Psi_B^* (x, t)</math> in the above equation. As in the [[Wave interference#Mechanisms|classical wave case]] above, the quantum interference term can add (constructive interference) or subtract (destructive interference) from <math>|\Psi_A (x, t)|^2 + |\Psi_B (x, t)|^2</math> in the above equation depending on whether the quantum interference term is positive or negative. If this term is absent for all <math>x</math>, then there is no quantum mechanical interference associated with situations A and B. | ||
The best known example of quantum interference is the [[double-slit experiment]]. In this experiment, [[matter wave|matter waves]] from electrons, atoms or molecules approach a barrier with two slits in it. | The best known example of quantum interference is the [[double-slit experiment]]. In this experiment, [[matter wave|matter waves]] from electrons, atoms or molecules approach a barrier with two slits in it. The part of the wavefunction going through one slit is associated with <math>\Psi_A (x, t)</math> while the part going through the other slit is associated with <math>\Psi_B (x, t)</math>. The interference pattern occurs on the far side, observed by detectors suitable to the particles originating the [[matter wave]].<ref name="Bach Pope Liou Batelaan 2013 p=033018">{{cite journal | last1=Bach | first1=Roger | last2=Pope | first2=Damian | last3=Liou | first3=Sy-Hwang | last4=Batelaan | first4=Herman | title=Controlled double-slit electron diffraction | journal=New Journal of Physics | publisher=IOP Publishing | volume=15 | issue=3 | date=2013-03-13 | issn=1367-2630 | doi=10.1088/1367-2630/15/3/033018 | article-number=033018 | url=https://iopscience.iop.org/article/10.1088/1367-2630/15/3/033018| arxiv=1210.6243 | bibcode=2013NJPh...15c3018B | s2cid=832961 }}</ref> The pattern matches the optical double slit pattern. | ||
== Applications == | == Applications == | ||
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In [[acoustics]], a '''beat''' is an [[Interference (wave propagation)|interference]] pattern between two [[sound]]s of slightly different [[frequency|frequencies]], ''perceived'' as a periodic variation in [[amplitude (music)|volume]] whose rate is the [[Difference (mathematics)|difference]] of the two frequencies. | In [[acoustics]], a '''beat''' is an [[Interference (wave propagation)|interference]] pattern between two [[sound]]s of slightly different [[frequency|frequencies]], ''perceived'' as a periodic variation in [[amplitude (music)|volume]] whose rate is the [[Difference (mathematics)|difference]] of the two frequencies. | ||
With [[Musical tuning|tuning]] instruments that can produce sustained tones, beats can be readily recognized. Tuning two tones to a [[unison]] will present a peculiar effect: when the two tones are close in pitch but not identical, the difference in frequency generates the beating. The volume varies like in a [[tremolo]] as the sounds alternately interfere constructively and destructively. As the two tones gradually approach unison, the beating slows down and may become so slow as to be imperceptible. As the two tones get further apart, their beat frequency starts to approach the range of human pitch perception,<ref>{{Cite book|title=This is Your Brain on Music: The Science of a Human Obsession|last=Levitin|first=Daniel J.|publisher=Dutton|year=2006|isbn= 978- | With [[Musical tuning|tuning]] instruments that can produce sustained tones, beats can be readily recognized. Tuning two tones to a [[unison]] will present a peculiar effect: when the two tones are close in pitch but not identical, the difference in frequency generates the beating. The volume varies like in a [[tremolo]] as the sounds alternately interfere constructively and destructively. As the two tones gradually approach unison, the beating slows down and may become so slow as to be imperceptible. As the two tones get further apart, their beat frequency starts to approach the range of human pitch perception,<ref>{{Cite book|title=This is Your Brain on Music: The Science of a Human Obsession|last=Levitin|first=Daniel J.|publisher=Dutton|year=2006|isbn= 978-0-525-94969-5 |page=22}}</ref> the beating starts to sound like a note, and a [[combination tone]] is produced. This combination tone can also be referred to as a [[missing fundamental]], as the beat frequency of any two tones is equivalent to the frequency of their implied fundamental frequency. | ||
=== Interferometry === | === Interferometry === | ||
{{Main|Interferometry}} | {{Main|Interferometry}} | ||
Interferometry | Interferometry is an experimental technique for measuring or using interference. It can be used with many types of waves. All interferometers require a source of [[Coherence (physics)|coherent]] waves. | ||
==== Optical interferometry ==== | ==== Optical interferometry ==== | ||
{{Main|Optical interferometry}} | {{Main|Optical interferometry}} | ||
The simplest interferometer has a pinhole to create a coherent source followed by a mask with two holes and a screen to observe the interference. This gives the [[double-slit experiment]]. Modern versions replace the initial pinhole with the coherent light of a laser.{{rp|385}} Other wave-front splitting interferometers use mirror or prisms to split and recombine waves; amplitude splitting devices use thin dielectric films. Multiple beam interferometers can include lenses.<ref name=Hecht-3th>{{Cite book |last=Hecht |first=Eugene |title=Optics |date=1998 |publisher=Addison-Wesley |isbn=978-0-201-83887-9 |edition=3 |location=Reading, Mass. Harlow}}</ref> | |||
The results of the [[Michelson–Morley experiment]] are generally considered to be the first strong evidence against the theory of a [[luminiferous aether]] and in favor of [[special relativity]]. | The results of the [[Michelson–Morley experiment]] are generally considered to be the first strong evidence against the theory of a [[luminiferous aether]] and in favor of [[special relativity]]. | ||
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==== Acoustic interferometry ==== | ==== Acoustic interferometry ==== | ||
An [[acoustic interferometer]] is an instrument for measuring the physical characteristics of sound waves in a [[gas]] or liquid, such [[velocity]], wavelength, [[absorption (acoustics)|absorption]], or [[ | An [[acoustic interferometer]] is an instrument for measuring the physical characteristics of sound waves in a [[gas]] or liquid, such as [[velocity]], wavelength, [[absorption (acoustics)|absorption]], or [[Acoustic impedance|impedance]]. A vibrating [[crystal]] creates ultrasonic waves that are radiated into the medium. The waves strike a reflector placed parallel to the crystal, reflected back to the source and measured. | ||
== See also == | == See also == | ||
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{{Wiktionary|interference}} | {{Wiktionary|interference}} | ||
{{Commons}} | {{Commons}} | ||
* [ | * [https://iwant2study.org/lookangejss/04waves_11superposition/ejss_model_wave1d01/wave1d01_Simulation.xhtml Easy JavaScript Simulation Model of One Dimensional Wave Interference] | ||
* {{usurped|1=[https://web.archive.org/web/20020211001109/http://www.citycollegiate.com/interference1.htm Expressions of position and fringe spacing]}} | * {{usurped|1=[https://web.archive.org/web/20020211001109/http://www.citycollegiate.com/interference1.htm Expressions of position and fringe spacing]}} | ||
* [http://www.phy.hk/wiki/englishhtm/Interference.htm Java simulation of interference of water waves 1] | * [http://www.phy.hk/wiki/englishhtm/Interference.htm Java simulation of interference of water waves 1] | ||