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| {{About|the branch of physics|the book by Sir Isaac Newton|Opticks|the musical artist|Optical (artist)|other uses|Optic (disambiguation)}}
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| [[File:Light dispersion of a mercury-vapor lamp with a flint glass prism IPNr°0125.jpg|thumb|right|Optics includes study of [[Dispersion (optics)|dispersion]] of light.]]
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| '''Optics''' is the branch of [[physics]] which involves the behaviour and properties of [[light]], including its interactions with [[matter]] and the construction of [[optical instruments|instruments]] that use or [[Photodetector|detect]] it.<ref name=McGrawHill>{{cite book|title=McGraw-Hill Encyclopedia of Science and Technology|edition=5th|publisher=McGraw-Hill|year=1993}}</ref> Optics usually describes the behaviour of [[visible light|visible]], [[ultraviolet]], and [[infrared]] light. Because light is an [[electromagnetic wave]], other forms of [[electromagnetic radiation]] such as [[X-ray]]s, [[microwave]]s, and [[radio wave]]s exhibit similar properties.<ref name=McGrawHill />
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| Most optical phenomena can be accounted for using the [[Classical electromagnetism|classical electromagnetic]] description of light. Complete electromagnetic descriptions of light are, however, often difficult to apply in practice. Practical optics is usually done using simplified models. The most common of these, [[geometric optics]], treats light as a collection of [[Ray (optics)|ray]]s that travel in straight lines and bend when they pass through or reflect from surfaces. [[Physical optics]] is a more comprehensive model of light, which includes [[wave]] effects such as [[diffraction]] and [[Interference (optics)|interference]] that cannot be accounted for in geometric optics. Historically, the ray-based model of light was developed first, followed by the wave model of light. Progress in electromagnetic theory in the 19th century led to the discovery that light waves were in fact electromagnetic radiation.
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| Some phenomena depend on the fact that light has both [[wave-particle duality|wave-like and particle-like properties]]. Explanation of these effects requires [[quantum mechanics]]. When considering light's particle-like properties, the light is modelled as a collection of particles called "[[photon]]s". [[Quantum optics]] deals with the application of quantum mechanics to optical systems.
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| Optical science is relevant to and studied in many related disciplines including [[astronomy]], various [[engineering]] fields, [[photography]], and [[medicine]] (particularly [[ophthalmology]] and [[optometry]]). Practical applications of optics are found in a variety of technologies and everyday objects, including [[mirror]]s, lenses, [[optical telescope|telescopes]], [[microscope]]s, lasers, and [[fibre optics]].
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| ==History==
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| {{Main|History of optics}}
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| {{See also|Timeline of electromagnetism and classical optics}}
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| [[File:Nimrud lens British Museum.jpg|thumb|right|The Nimrud lens]]
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| Optics began with the development of lenses by the [[ancient Egypt]]ians and [[Mesopotamia]]ns. The earliest known lenses, made from polished crystal, often [[quartz]], date from as early as 700 BC for [[Assyria]]n lenses such as the Layard/[[Nimrud lens]].<ref>{{cite news |url=http://news.bbc.co.uk/1/hi/sci/tech/380186.stm |title=World's oldest telescope? |publisher=BBC News |date=July 1, 1999 |accessdate=Jan 3, 2010}}</ref> The [[ancient Roman]]s and [[Ancient Greece|Greeks]] filled glass spheres with water to make lenses. These practical developments were followed by the development of theories of light and vision by ancient [[Greek philosophy|Greek]] and [[Indian philosophy|Indian]] philosophers, and the development of [[geometrical optics]] in the [[Greco-Roman world]]. The word ''optics'' comes from the [[ancient Greek]] word {{lang|grc|ὀπτική}}, meaning "appearance, look".<ref>{{cite book|title=The Concise Oxford Dictionary of English Etymology|year=1996|author=T. F. Hoad|isbn=0-19-283098-8}}</ref>
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| Greek philosophy on optics broke down into two opposing theories on how vision worked, the "intro-mission theory" and the [[emission theory (vision)|"emission theory"]].<ref>[http://www.stanford.edu/class/history13/earlysciencelab/body/eyespages/eye.html A History Of The Eye]. stanford.edu. Retrieved on 2012-06-10.</ref> The intro-mission approach saw vision as coming from objects casting off copies of themselves (called eidola) that were captured by the eye. With many propagators including [[Democritus]], [[Epicurus]], [[Aristotle]] and their followers, this theory seems to have some contact with modern theories of what vision really is, but it remained only speculation lacking any experimental foundation.
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| [[Plato]] first articulated the emission theory, the idea that [[visual perception]] is accomplished by rays emitted by the eyes. He also commented on the [[parity (physics)|parity]] reversal of mirrors in ''[[Timaeus (dialogue)|Timaeus]]''.<ref>{{cite book|title=A manual of greek mathematics|author=T. L. Heath|publisher=Courier Dover Publications|isbn=0-486-43231-9|pages=181–182|year=2003}}</ref> Some hundred years later, [[Euclid]] wrote a treatise entitled ''[[Euclid#Other works|Optics]]'' where he linked vision to [[geometry]], creating ''geometrical optics''.<ref>{{cite book|author=William R. Uttal |title=Visual Form Detection in 3-Dimensional Space |url=http://books.google.com/books?id=rhVOVKp0-5wC&pg=PA25 |year=1983 |publisher=Psychology Press |isbn=978-0-89859-289-4 |pages=25–}}</ref> He based his work on Plato's emission theory wherein he described the mathematical rules of [[perspective (graphical)|perspective]] and described the effects of [[refraction]] qualitatively, although he questioned that a beam of light from the eye could instantaneously light up the stars every time someone blinked.<ref>{{cite book|author=Euclid|title=The Arabic version of Euclid's optics = Kitāb Uqlīdis fī ikhtilāf al-manāẓir|editor=Elaheh Kheirandish|publisher=New York: Springer|year=1999|isbn=0-387-98523-9}}</ref> [[Ptolemy]], in his treatise ''[[Ptolemy#Optics|Optics]]'', held an extramission-intromission theory of vision: the rays (or flux) from the eye formed a cone, the vertex being within the eye, and the base defining the visual field. The rays were sensitive, and conveyed information back to the observer’s intellect about the distance and orientation of surfaces. He summarised much of Euclid and went on to describe a way to measure the [[angle of refraction]], though he failed to notice the empirical relationship between it and the angle of incidence.<ref name=Ptolemy>{{cite book|title=Ptolemy's theory of visual perception: an English translation of the Optics with introduction and commentary|author=Ptolemy|editor=A. Mark Smith|publisher=DIANE Publishing|year=1996|isbn=0-87169-862-5}}</ref>
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| [[File:Ibn Sahl manuscript.jpg|thumb|right|upright|Reproduction of a page of [[Ibn Sahl]]'s manuscript showing his knowledge of the law of refraction, now known as [[Snell's law]]]]
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| During the [[Middle Ages]], Greek ideas about optics were resurrected and extended by writers in the [[Muslim world]]. One of the earliest of these was [[Al-Kindi]] (c. 801–73) who wrote on the merits of Aristotelian and Euclidean ideas of optics, favouring the emission theory since it could better quantify optical phenomenon.<ref>Adamson, Peter (2006). "Al-Kindi¯ and the reception of Greek philosophy". In Adamson, Peter; Taylor, R.. The Cambridge companion to Arabic philosophy. Cambridge University Press. p. 45. ISBN 978-0-521-52069-0.</ref> In 984, the [[Persia]]n mathematician [[Ibn Sahl]] wrote the treatise "On burning mirrors and lenses", correctly describing a law of refraction equivalent to [[Snell's law]].<ref name=j1>{{cite journal |doi=10.1086/355456 |last=Rashed |first=Roshdi |title=A pioneer in anaclastics: Ibn Sahl on burning mirrors and lenses |journal=Isis |volume=81 |issue = 3 |year=1990 |pages=464–491 |jstor=233423}}</ref> He used this law to compute optimum shapes for lenses and [[curved mirror]]s. In the early 11th century, [[Alhazen]] (Ibn al-Haytham) wrote the ''[[Book of Optics]]'' (''Kitab al-manazir'') in which he explored reflection and refraction and proposed a new system for explaining vision and light based on observation and experiment.<ref>{{cite book|author=A. I. Sabra and J. P. Hogendijk|year=2003|title=The Enterprise of Science in Islam: New Perspectives |pages=85–118 |publisher=MIT Press |isbn=0-262-19482-1 |oclc=237875424 50252039}}</ref><ref>{{cite book |author=G. Hatfield |contribution=Was the Scientific Revolution Really a Revolution in Science?|url=http://books.google.com/books?id=Kl1COWj9ubAC&pg=PA489|isbn=9004101195 |editor =F. J. Ragep, P. Sally, S. J. Livesey |year=1996 |title=Tradition, Transmission, Transformation: Proceedings of Two Conferences on Pre-modern Science held at the University of Oklahoma |page=500|publisher=Brill Publishers}}</ref><ref>{{cite journal|author=Nader El-Bizri|title=A Philosophical Perspective on Alhazen's Optics|journal= Arabic Sciences and Philosophy |volume=15 |year=2005|pages=189–218|doi=10.1017/S0957423905000172}}</ref><ref>{{cite journal|author=Nader El-Bizri|title=In Defence of the Sovereignty of Philosophy: al-Baghdadi's Critique of Ibn al-Haytham's Geometrisation of Place|doi=10.1017/S0957423907000367|journal=Arabic Sciences and Philosophy |volume=17 |year=2007|pages=57–80}}</ref><ref>{{cite journal|journal=The Medieval History Journal|volume=9|page=89|year=2006|doi=10.1177/097194580500900105|title=The Gaze in Ibn al-Haytham|author=G. Simon}}</ref> He rejected the "emission theory" of Ptolemaic optics with its rays being emitted by the eye, and instead put forward the idea that light reflected in all directions in straight lines from all points of the objects being viewed and then entered the eye, although he was unable to correctly explain how the eye captured the rays.<ref>{{cite book|author1=Ian P. Howard |author2=Brian J. Rogers |title=Binocular Vision and Stereopsis |url=http://books.google.com/books?id=I8vqITdETe0C&pg=PA7 |year=1995 |publisher=Oxford University Press |isbn=978-0-19-508476-4 |page=7}}</ref> Alhazen's work was largely ignored in the Arabic world but it was anonymously translated into Latin around 1200 A.D. and further summarised and expanded on by the Polish monk [[Witelo]]<ref>{{cite book|author1=Elena Agazzi |author2=Enrico Giannetto |author3=Franco Giudice |title=Representing Light Across Arts and Sciences: Theories and Practices |url=http://books.google.com/books?id=ipyT7askd8EC&pg=PA42 |year=2010 |publisher=V&R unipress GmbH |isbn=978-3-89971-735-8 |page=42}}</ref> making it a standard text on optics in Europe for the next 400 years.
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| In the 13th century medieval Europe the English bishop [[Robert Grosseteste]] wrote on a wide range of scientific topics discussing light from four different perspectives: an [[epistemology]] of light, a [[metaphysics]] or [[cosmogony]] of light, an [[etiology]] or [[physics]] of light, and a [[theology]] of light,<ref>D. C. Lindberg, ''Theories of Vision from al-Kindi to Kepler'', (Chicago: Univ. of Chicago Pr., 1976), pp. 94–99.</ref> basing it on the works Aristotle and Platonism. Grosseteste's most famous disciple, [[Roger Bacon]], wrote works citing a wide range of recently translated optical and philosophical works, including those of [[Alhazen]], Aristotle, [[Avicenna]], [[Averroes]], Euclid, al-Kindi, Ptolemy, Tideus, and [[Constantine the African]]. Bacon was able to use parts of glass spheres as [[magnifying glass]]es to demonstrate that light reflects from objects rather than being released from them.
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| In Italy, around 1284, [[Salvino D'Armate]] invented the first wearable eyeglasses.<ref>{{cite web|author=M. Bellis|title=The History of Eye Glasses or Spectacles |work=About.com:Inventors |url=http://inventors.about.com/od/gstartinventions/a/glass_3.htm |accessdate=Sep 1, 2007}}</ref>
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| This was the start of the optical industry of grinding and polishing lenses for these "spectacles", first in Venice and Florence in the thirteenth century,<ref>[http://galileo.rice.edu/sci/instruments/telescope.html '''The Galileo Project > Science > The Telescope''' by Al Van Helden '']. Galileo.rice.edu. Retrieved on 2012-06-10.</ref> and later in the spectacle making centres in both the [[Netherlands]] and Germany.<ref>{{cite book|author=Henry C. King |title=The History of the Telescope |url=http://books.google.com/books?id=KAWwzHlDVksC&pg=PR1 |year=2003 |publisher=Courier Dover Publications |isbn=978-0-486-43265-6 |page=27}}</ref> Spectacle makers created improved types of lenses for the correction of vision based more on empirical knowledge gained from observing the effects of the lenses rather than using the rudimentary optical theory of the day (theory which for the most part could not even adequately explain how spectacles worked).<ref>{{cite book|author1=Paul S. Agutter |author2=Denys N. Wheatley |title=Thinking about Life: The History and Philosophy of Biology and Other Sciences |url=http://books.google.com/books?id=Gm4bqeBMR8cC&pg=PA17 |year=2008 |publisher=Springer |isbn=978-1-4020-8865-0 |page=17}}</ref><ref>{{cite book|author=Vincent Ilardi|title=Renaissance Vision from Spectacles to Telescopes|url=http://books.google.com/books?id=peIL7hVQUmwC&pg=PA210|accessdate=11 June 2012|year=2007|publisher=American Philosophical Society|isbn=978-0-87169-259-7|page=210}}</ref> This practical development, mastery, and experimentation with lenses led directly to the invention of the compound [[optical microscope]] around 1595, and the [[refracting telescope]] in 1608, both of which appeared in the spectacle making centres in the [[Netherlands]].<ref>[http://nobelprize.org/educational_games/physics/microscopes/timeline/index.html Microscopes: Time Line], Nobel Foundation, retrieved April 3, 2009</ref><ref name="LZZginzib4C page 55">{{cite book|author=Fred Watson |title=Stargazer: The Life and Times of the Telescope |url=http://books.google.com/books?id=2LZZginzib4C&pg=PA55 |year=2007 |publisher=Allen & Unwin |isbn=978-1-74175-383-7 |page=55}}</ref>
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| In the early 17th century [[Johannes Kepler]] expanded on geometric optics in his writings, covering lenses, reflection by flat and curved mirrors, the principles of [[pinhole camera]]s, inverse-square law governing the intensity of light, and the optical explanations of astronomical phenomena such as lunar and [[solar eclipse]]s and astronomical [[parallax]]. He was also able to correctly deduce the role of the [[retina]] as the actual organ that recorded images, finally being able to scientifically quantify the effects of different types of lenses that spectacle makers had been observing over the previous 300 years.<ref>{{cite book|author=Vincent Ilardi |title=Renaissance Vision from Spectacles to Telescopes |url=http://books.google.com/books?id=peIL7hVQUmwC&pg=PA244 |year=2007 |publisher=American Philosophical Society |isbn=978-0-87169-259-7 |page=244}}</ref> After the invention of the telescope Kepler set out the theoretical basis on how they worked and described an improved version, known as the ''[[Keplerian telescope]]'', using two convex lenses to produce higher magnification.<ref>Caspar, ''Kepler'', [http://books.google.com/books?id=0r68pggBSbgC&pg=PA198 pp. 198–202], Courier Dover Publications, 1993, ISBN 0486676056.</ref>
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| [[File:Opticks.jpg|thumb|right|upright|Cover of the first edition of Newton's ''Opticks'']]
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| Optical theory progressed in the mid-17th century with [[The World (Descartes)#Descartes' Theory on Light|treatises]] written by philosopher [[René Descartes]], which explained a variety of optical phenomena including reflection and refraction by assuming that light was emitted by objects which produced it.<ref name=Sabra>{{cite book|title=Theories of light, from Descartes to Newton|author=A. I. Sabra|publisher=CUP Archive|year=1981|isbn=0-521-28436-8}}</ref> This differed substantively from the ancient Greek emission theory. In the late 1660s and early 1670s, Newton expanded Descartes' ideas into a [[corpuscle theory of light]], famously determining that white light was a mix of colours which can be separated into its component parts with a [[prism (optics)|prism]]. In 1690, [[Christiaan Huygens]] proposed a [[wave theory]] for light based on suggestions that had been made by [[Robert Hooke]] in 1664. Hooke himself publicly criticised Newton's theories of light and the feud between the two lasted until Hooke's death. In 1704, Newton published ''[[Opticks]]'' and, at the time, partly because of his success in other areas of [[physics]], he was generally considered to be the victor in the debate over the nature of light.<ref name=Sabra />
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| Newtonian optics was generally accepted until the early 19th century when [[Thomas Young (scientist)|Thomas Young]] and [[Augustin-Jean Fresnel]] conducted experiments on the [[Interference (wave propagation)|interference]] of light that firmly established light's wave nature. Young's famous [[Young's interference experiment|double slit experiment]] showed that light followed the [[law of superposition]], which is a wave-like property not predicted by Newton's corpuscle theory. This work led to a theory of diffraction for light and opened an entire area of study in physical optics.<ref>{{cite book|author=W. F. Magie|title=A Source Book in Physics|publisher=Harvard University Press|year=1935|page=309}}</ref> Wave optics was successfully unified with [[electromagnetic theory]] by [[James Clerk Maxwell]] in the 1860s.<ref>{{cite journal|author=J. C. Maxwell|title=[[A Dynamical Theory of the Electromagnetic Field]]|journal=Philosophical Transactions of the Royal Society of London|volume=155|page=459|year=1865|bibcode = 1865RSPT..155..459C|doi=10.1098/rstl.1865.0008}}</ref>
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| The next development in optical theory came in 1899 when [[Max Planck]] correctly modelled [[blackbody radiation]] by assuming that the exchange of energy between light and matter only occurred in discrete amounts he called ''quanta''.<ref>For a solid approach to the complexity of Planck's intellectual motivations for the quantum, for his reluctant acceptance of its implications, see H. Kragh, [http://physicsworld.com/cws/article/print/373 Max Planck: the reluctant revolutionary], ''Physics World''. December 2000.</ref> In 1905 [[Albert Einstein]] published the theory of the [[photoelectric effect]] that firmly established the quantization of light itself.<ref>{{cite book |last1=Einstein |first1=A. |authorlink1=Albert Einstein |editor1-first=D. |editor1-last=Ter Haar |title=The Old Quantum Theory |url=http://wien.cs.jhu.edu/AnnusMirabilis/AeReserveArticles/eins_lq.pdf |accessdate=March 18, 2010 |year=1967 |publisher=Pergamon |pages=91–107 |chapter=On a heuristic viewpoint concerning the production and transformation of light}} The chapter is an English translation of Einstein's 1905 paper on the photoelectric effect.</ref><ref name=AnnPhysik322132>{{Cite journal |first=A. |last=Einstein |year=1905 |title=Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt |language=German |trans_title=On a heuristic viewpoint concerning the production and transformation of light |journal=Annalen der Physik |volume=322 |issue=6 |pages=132–148 |doi=10.1002/andp.19053220607|bibcode = 1905AnP...322..132E}}</ref> In 1913 [[Niels Bohr]] showed that atoms could only emit discrete amounts of energy, thus explaining the discrete lines seen in [[emission spectrum|emission]] and [[absorption spectrum|absorption spectra]].<ref>{{cite journal
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| |url= http://web.archive.org/web/20070704225134/http://dbhs.wvusd.k12.ca.us/webdocs/Chem-History/Bohr/Bohr-1913a.html |year=1913 |title=On the Constitution of Atoms and Molecules |journal=Philosophical Magazine |volume=26, Series 6 |pages=1–25}}. The landmark paper laying the [[Bohr model of the atom]] and [[molecular bond]]ing.</ref> The understanding of the interaction between light and matter which followed from these developments not only formed the basis of quantum optics but also was crucial for the [[history of quantum mechanics|development]] of [[quantum mechanics]] as a whole. The ultimate culmination, the theory of [[quantum electrodynamics]], explains all optics and electromagnetic processes in general as the result of the exchange of real and [[virtual particles|virtual]] [[photon]]s.<ref>{{cite book|author=R. Feynman|authorlink=Richard Feynman|year=1985|title=QED: The Strange Theory of Light and Matter|chapter=Chapter 1|page=6|publisher=Princeton University Press|isbn=0-691-08388-6}}</ref>
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| Quantum optics gained practical importance with the inventions of the [[maser]] in 1953 and of the laser in 1960.<ref>{{cite book|author=N. Taylor|title=LASER: The inventor, the Nobel laureate, and the thirty-year patent war|year=2000|publisher=Simon & Schuster|location=New York|isbn=0-684-83515-0}}</ref> Following the work of [[Paul Dirac]] in [[quantum field theory]], [[George Sudarshan]], [[Roy J. Glauber]], and [[Leonard Mandel]] applied quantum theory to the electromagnetic field in the 1950s and 1960s to gain a more detailed understanding of photodetection and the [[statistical mechanics|statistics]] of light.
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| ==Classical optics==
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| Classical optics is divided into two main branches: geometrical optics and physical optics. In geometrical, or ray optics, light is considered to travel in straight lines, and in physical, or wave optics, light is considered to be an electromagnetic wave.
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| Geometrical optics can be viewed as an approximation of physical optics which can be applied when the wavelength of the light used is much smaller than the size of the optical elements or system being modelled.
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| ===Geometrical optics===
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| {{Main|Geometrical optics}}
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| [[File:Reflection and refraction.svg|thumb|250px|right|Geometry of reflection and refraction of light rays]]''Geometrical optics'', or ''ray optics'', describes the [[Wave propagation|propagation]] of light in terms of "rays" which travel in straight lines, and whose paths are governed by the laws of reflection and refraction at interfaces between different media.<ref>{{cite book|author1=Ariel Lipson|author2=Stephen G. Lipson|author3=Henry Lipson|title=Optical Physics|url=http://books.google.com/books?id=aow3o0dhyjYC&pg=PA48|accessdate=12 July 2012|date=28 October 2010|publisher=Cambridge University Press|isbn=978-0-521-49345-1|page=48}}</ref> These laws were discovered empirically as far back as 984 AD<ref name=j1/> and have been used in the design of optical components and instruments from then until the present day. They can be summarised as follows:
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| When a ray of light hits the boundary between two transparent materials, it is divided into a reflected and a refracted ray.
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| :The law of reflection says that the reflected ray lies in the plane of incidence, and the angle of reflection equals the angle of incidence.
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| :The law of refraction says that the refracted ray lies in the plane of incidence, and the sine of the angle of refraction divided by the sine of the angle of incidence is a constant.
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| ::<math>\frac {\sin {\theta_1}}{\sin {\theta_2}} = n</math>
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| where {{math|''n''}} is a constant for any two materials and a given colour of light. It is known as the [[refractive index]].
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| The laws of reflection and refraction can be derived from [[Fermat's principle]] which states that ''the path taken between two points by a ray of light is the path that can be traversed in the least time.''<ref>{{cite book|author=Sir Arthur Schuster|title=An Introduction to the Theory of Optics|url=http://books.google.com/books?id=X0AcBd-bcCwC&pg=PA41|year=1904|publisher=E. Arnold|page=41}}</ref>
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| ====Approximations====
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| Geometric optics is often simplified by making the [[paraxial approximation]], or "small angle approximation." The mathematical behaviour then becomes linear, allowing optical components and systems to be described by simple matrices. This leads to the techniques of [[Gaussian optics]] and ''paraxial [[ray tracing (physics)|ray tracing]]'', which are used to find basic properties of optical systems, such as approximate [[image]] and object positions and [[magnification]]s.<ref>{{cite book|author=J. E. Greivenkamp|year=2004|title=Field Guide to Geometrical Optics. SPIE Field Guides vol. '''FG01'''|publisher=SPIE|isbn=0-8194-5294-7|pages=19–20}}</ref>
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| ====Reflections====
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| {{Main|Reflection (physics)}}
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| [[File:Reflection angles.svg|frame|Diagram of specular reflection]]
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| Reflections can be divided into two types: [[specular reflection]] and [[diffuse reflection]]. Specular reflection describes the gloss of surfaces such as mirrors, which reflect light in a simple, predictable way. This allows for production of reflected images that can be associated with an actual ([[real image|real]]) or extrapolated ([[virtual image|virtual]]) location in space. Diffuse reflection describes opaque, non limpid materials, such as paper or rock. The reflections from these surfaces can only be described statistically, with the exact distribution of the reflected light depending on the microscopic structure of the material. Many diffuse reflectors are described or can be approximated by [[Lambert's cosine law]], which describes surfaces that have equal [[luminance]] when viewed from any angle. Glossy surfaces can give both specular and diffuse reflection.
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| In specular reflection, the direction of the reflected ray is determined by the angle the incident ray makes with the [[surface normal]], a line perpendicular to the surface at the point where the ray hits. The incident and reflected rays and the normal lie in a single plane, and the angle between the reflected ray and the surface normal is the same as that between the incident ray and the normal.<ref name=Geoptics>{{cite book|title=University Physics 8e|author=H. D. Young|publisher=Addison-Wesley|year=1992|isbn=0-201-52981-5|chapter =35}}</ref> This is known as the [[Law of Reflection]].
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| For [[Plane mirror|flat mirrors]], the law of reflection implies that images of objects are upright and the same distance behind the mirror as the objects are in front of the mirror. The image size is the same as the object size. The law also implies that [[mirror image]]s are [[Parity (physics)|parity inverted]], which we perceive as a left-right inversion. Images formed from reflection in two (or any even number of) mirrors are not parity inverted. [[Corner reflector]]s<ref name=Geoptics /> [[retroreflector|retroreflect]] light, producing reflected rays that travel back in the direction from which the incident rays came.
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| [[curved mirror|Mirrors with curved surfaces]] can be modelled by [[Ray tracing (physics)|ray-tracing]] and using the law of reflection at each point on the surface. For [[Parabolic reflector|mirrors with parabolic surfaces]], parallel rays incident on the mirror produce reflected rays that converge at a common [[focus (optics)|focus]]. Other curved surfaces may also focus light, but with aberrations due to the diverging shape causing the focus to be smeared out in space. In particular, spherical mirrors exhibit [[spherical aberration]]. Curved mirrors can form images with magnification greater than or less than one, and the magnification can be negative, indicating that the image is inverted. An upright image formed by reflection in a mirror is always virtual, while an inverted image is real and can be projected onto a screen.<ref name=Geoptics />
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| ====Refractions====
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| {{Main|Refraction}}
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| [[File:Snells law.svg|thumb|300px|Illustration of Snell's Law for the case n<sub>1</sub> < n<sub>2</sub>, such as air/water interface]]
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| Refraction occurs when light travels through an area of space that has a changing index of refraction; this principle allows for lenses and the focusing of light. The simplest case of refraction occurs when there is an [[Interface (chemistry)|interface]] between a uniform medium with index of refraction <math>n_1</math> and another medium with index of refraction <math>n_2</math>. In such situations, [[Snell's Law]] describes the resulting deflection of the light ray:
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| :<math>n_1\sin\theta_1 = n_2\sin\theta_2\ </math>
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| where <math>\theta_1</math> and <math>\theta_2</math> are the angles between the normal (to the interface) and the incident and refracted waves, respectively. This phenomenon is also associated with a changing speed of light as seen from the definition of index of refraction provided above which implies:
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| :<math>v_1\sin\theta_2\ = v_2\sin\theta_1</math>
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| where <math>v_1</math> and <math>v_2</math> are the wave velocities through the respective media.<ref name=Geoptics />
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| Various consequences of Snell's Law include the fact that for light rays travelling from a material with a high index of refraction to a material with a low index of refraction, it is possible for the interaction with the interface to result in zero transmission. This phenomenon is called [[total internal reflection]] and allows for [[fibre optics]] technology. As light signals travel down a fibre optic cable, it undergoes total internal reflection allowing for essentially no light lost over the length of the cable. It is also possible to produce [[plane polarization|polarised light rays]] using a combination of reflection and refraction: When a refracted ray and the reflected ray form a [[right angle]], the reflected ray has the property of "plane polarization". The angle of incidence required for such a scenario is known as Brewster's angle.<ref name=Geoptics />
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| Snell's Law can be used to predict the deflection of light rays as they pass through "linear media" as long as the indexes of refraction and the geometry of the media are known. For example, the propagation of light through a prism results in the light ray being deflected depending on the shape and orientation of the prism. Additionally, since different frequencies of light have slightly different indexes of refraction in most materials, refraction can be used to produce dispersion spectra that appear as rainbows. The discovery of this phenomenon when passing light through a prism is famously attributed to Isaac Newton.<ref name=Geoptics />
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| Some media have an index of refraction which varies gradually with position and, thus, light rays curve through the medium rather than travel in straight lines. This effect is what is responsible for [[mirage]]s seen on hot days where the changing index of refraction of the air causes the light rays to bend creating the appearance of specular reflections in the distance (as if on the surface of a pool of water). Material that has a varying index of refraction is called a gradient-index (GRIN) material and has many useful properties used in modern optical scanning technologies including [[photocopiers]] and [[scanners]]. The phenomenon is studied in the field of [[gradient-index optics]].<ref>E. W. Marchand, Gradient Index Optics, New York, NY, Academic Press, 1978.</ref>
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| [[File:lens3b.svg|360px|thumb|A ray tracing diagram for a converging lens.]]
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| A device which produces converging or diverging light rays due to refraction is known as a lens. Thin lenses produce focal points on either side that can be modelled using the [[lensmaker's equation]].<ref name=hecht>{{cite book|author=E. Hecht|year=1987|title=Optics|edition=2nd|publisher=Addison Wesley|isbn=0-201-11609-X}} Chapters 5 & 6.</ref> In general, two types of lenses exist: [[convex lens]]es, which cause parallel light rays to converge, and [[concave lens]]es, which cause parallel light rays to diverge. The detailed prediction of how images are produced by these lenses can be made using ray-tracing similar to curved mirrors. Similarly to curved mirrors, thin lenses follow a simple equation that determines the location of the images given a particular focal length (<math>f</math>) and object distance (<math>S_1</math>):
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| :<math>\frac{1}{S_1} + \frac{1}{S_2} = \frac{1}{f} </math>
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| where <math>S_2</math> is the distance associated with the image and is considered by convention to be negative if on the same side of the lens as the object and positive if on the opposite side of the lens.<ref name=hecht /> The focal length f is considered negative for concave lenses.
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| [[File:Lens1.svg|360px|thumb]]
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| Incoming parallel rays are focused by a convex lens into an inverted real image one focal length from the lens, on the far side of the lens. Rays from an object at finite distance are focused further from the lens than the focal distance; the closer the object is to the lens, the further the image is from the lens. With concave lenses, incoming parallel rays diverge after going through the lens, in such a way that they seem to have originated at an upright virtual image one focal length from the lens, on the same side of the lens that the parallel rays are approaching on. Rays from an object at finite distance are associated with a virtual image that is closer to the lens than the focal length, and on the same side of the lens as the object. The closer the object is to the lens, the closer the virtual image is to the lens.
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| Likewise, the magnification of a lens is given by
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| :<math> M = - \frac{S_2}{S_1} = \frac{f}{f - S_1} </math>
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| where the negative sign is given, by convention, to indicate an upright object for positive values and an inverted object for negative values. Similar to mirrors, upright images produced by single lenses are virtual while inverted images are real.<ref name=Geoptics />
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| Lenses suffer from [[optical aberration|aberrations]] that distort images and focal points. These are due to both to geometrical imperfections and due to the changing index of refraction for different wavelengths of light ([[chromatic aberration]]).<ref name=Geoptics />
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| [[File:Thin lens images.svg|thumb|none|500px|Images of black letters in a thin convex lens of focal length ''f'' are shown in red. Selected rays are shown for letters '''E''', '''I''' and '''K''' in blue, green and orange, respectively. Note that '''E''' (at 2''f'') has an equal-size, real and inverted image; '''I''' (at ''f'') has its image at infinity; and '''K''' (at ''f''/2) has a double-size, virtual and upright image.]]
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| ===Physical optics===
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| {{Main|Physical optics}}
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| In physical optics, light is considered to propagate as a [[wave]]. This model predicts phenomena such as [[Interference (wave propagation)|interference]] and [[diffraction]], which are not explained by geometric optics. The [[speed of light]] waves in [[air]] is approximately 3.0×10<sup>8</sup> m/s (exactly 299,792,458 m/s in [[vacuum]]). The [[wavelength]] of visible light waves varies between 400 and 700 nm, but the term "light" is also often applied to [[infrared]] (0.7–300 μm) and [[ultraviolet]] radiation (10–400 nm).
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| The wave model can be used to make predictions about how an optical system will behave without requiring an explanation of what is "waving" in what medium. Until the middle of the 19th century, most physicists believed in an "ethereal" medium in which the light disturbance propagated.<ref>MV Klein & TE Furtak, 1986, Optics, John Wiley & Sons, New York ISBN 0471872970.</ref> The existence of electromagnetic waves was predicted in 1865 by [[Electromagnetic waves#derivation|Maxwell's equations]]. These waves propagate at the [[speed of light]] and have varying electric and magnetic fields which are orthogonal to one another, and also to the direction of propagation of the waves.<ref>{{cite journal |last=Maxwell |first=James Clerk |authorlink=James Clerk Maxwell |title=A dynamical theory of the electromagnetic field|url=http://upload.wikimedia.org/wikipedia/commons/1/19/A_Dynamical_Theory_of_the_Electromagnetic_Field.pdf|doi = 10.1098/rstl.1865.0008 |format=PDF |journal=Philosophical Transactions of the Royal Society of London |volume=155 |page=499 |year=1865}} This article accompanied a December 8, 1864 presentation by Maxwell to the Royal Society. See also [[A dynamical theory of the electromagnetic field]].</ref> Light waves are now generally treated as electromagnetic waves except when [[Optics#Modern optics|quantum mechanical effects]] have to be considered.
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| ====Modelling and design of optical systems using physical optics====
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| Many simplified approximations are available for analysing and designing optical systems. Most of these use a single [[Scalar (physics)|scalar]] quantity to represent the electric field of the light wave, rather than using a [[Euclidean vector|vector]] model with orthogonal electric and magnetic vectors.<ref name = "Born and Wolf">M. Born and E. Wolf (1999). Principle of Optics. Cambridge: Cambridge University Press. ISBN 0-521-64222-1.</ref>
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| The [[Huygens–Fresnel principle|Huygens–Fresnel]] equation is one such model. This was derived empirically by Fresnel in 1815, based on Huygen's hypothesis that each point on a wavefront generates a secondary spherical wavefront, which Fresnel combined with the principle of [[Superposition principle|superposition]] of waves. The [[Kirchhoff's diffraction formula|Kirchhoff diffraction equation]], which is derived using Maxwell's equations, puts the Huygens-Fresnel equation on a firmer physical foundation. Examples of the application of Huygens–Fresnel principle can be found in the sections on [[diffraction]] and [[Fraunhofer diffraction (mathematics)|Fraunhofer diffraction]].
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| More rigorous models, involving the modelling of both electric and magnetic fields of the light wave, are required when dealing with the detailed interaction of light with materials where the interaction depends on their electric and magnetic properties. For instance, the behaviour of a light wave interacting with a metal surface is quite different from what happens when it interacts with a dielectric material. A vector model must also be used to model polarised light.
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| [[Computer simulation|Numerical modeling]] techniques such as the [[finite element method]], the [[boundary element method]] and the [[transmission-line matrix method]] can be used to model the propagation of light in systems which cannot be solved analytically. Such models are computationally demanding and are normally only used to solve small-scale problems that require accuracy beyond that which can be achieved with analytical solutions.<ref>{{cite book|author=J. Goodman|year=2005|title=Introduction to Fourier Optics|edition=3rd ed,|publisher=Roberts & Co Publishers|isbn=0-9747077-2-4|url= http://books.google.com/?id=ow5xs_Rtt9AC&printsec=frontcover}}</ref>
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| All of the results from geometrical optics can be recovered using the techniques of [[Fourier optics]] which apply many of the same mathematical and analytical techniques used in [[acoustic engineering]] and [[signal processing]].
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| [[Gaussian beam|Gaussian beam propagation]] is a simple paraxial physical optics model for the propagation of coherent radiation such as laser beams. This technique partially accounts for diffraction, allowing accurate calculations of the rate at which a laser beam expands with distance, and the minimum size to which the beam can be focused. Gaussian beam propagation thus bridges the gap between geometric and physical optics.<ref>{{cite book|author=A. E. Siegman|year=1986|title=Lasers|publisher=University Science Books|isbn=0-935702-11-3}} Chapter 16.</ref>
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| ====Superposition and interference====
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| {{Main|Superposition principle|Interference (optics)}}
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| 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.<ref name=interference /> 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.<ref name=interference>{{cite book|title=University Physics 8e|author=H. D. Young|publisher=Addison-Wesley|year=1992|isbn=0-201-52981-5}}Chapter 37</ref>
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| {|
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| |'''combined<br> waveform'''
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| |colspan="2" rowspan="3"|[[File:Interference of two waves.svg]]
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| |-
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| |'''wave 1'''
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| |-
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| |'''wave 2'''
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| |-
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| |<br>
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| |'''Two waves in phase'''
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| |'''Two waves 180° out <br>of phase'''
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| |}
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| [[File:Dieselrainbow.jpg|thumb|right|300px|When oil or fuel is spilled, colourful patterns are formed by thin-film interference.]]
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| 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.<ref name=interference /> [[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, USA|year=2003|url=http://www.astro.lsa.umich.edu/~monnier/Publications/ROP2003_final.pdf|isbn=0-12-325220-2}}</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>
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| 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 thickness 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 nm. More complex designs using multiple layers can achieve low reflectivity over a broad band, or extremely low reflectivity at a single wavelength.
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| Constructive interference in thin films can create 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.<ref name=interference />
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| ====Diffraction and optical resolution====
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| {{Main|Diffraction|Optical resolution}}
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| [[File:Double slit diffraction.svg|300px|right|thumb|Diffraction on two slits separated by distance <math>d</math>. The bright fringes occur along lines where black lines intersect with black lines and white lines intersect with white lines. These fringes are separated by angle <math>\theta</math> and are numbered as order <math>n</math>.]]
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| Diffraction is the process by which light interference is most commonly observed. The effect was first described in 1665 by [[Francesco Maria Grimaldi]], who also coined the term from the Latin ''diffringere'', 'to break into pieces'.<ref>{{cite book|title=Memoires pour l'histoire des sciences et des beaux arts|author=J. L. Aubert|publisher=Impr. de S. A. S.; Chez E. Ganeau|place=Paris|year=1760|page=149|url=http://books.google.com/?id=3OgDAAAAMAAJ&pg=PP151}}</ref><ref>{{cite book|title=A Treatise on Optics|author=D. Brewster|year=1831|publisher=Longman, Rees, Orme, Brown & Green and John Taylor|place=London|page = 95|url = http://books.google.com/?id=opYAAAAAMAAJ&pg=RA1-PA95}}</ref> Later that century, Robert Hooke and Isaac Newton also described phenomena now known to be diffraction in [[Newton's rings]]<ref>{{cite book|author=R. Hooke|title=Micrographia: or, Some physiological descriptions of minute bodies made by magnifying glasses|place=London|publisher=J. Martyn and J. Allestry|year=1665|isbn=0-486-49564-7}}</ref> while [[James Gregory (astronomer and mathematician)|James Gregory]] recorded his observations of diffraction patterns from bird feathers.<ref>{{cite journal|author=H. W. Turnbull|title=Early Scottish Relations with the Royal Society: I. James Gregory, F.R.S. (1638–1675)|journal = Notes and Records of the Royal Society of London|year=1940–1941|volume=3|page=22|doi=10.1098/rsnr.1940.0003|jstor = 531136}}</ref>
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| The first physical optics model of diffraction that relied on the [[Huygens–Fresnel principle]] was developed in 1803 by [[Thomas Young (scientist)|Thomas Young]] in [[Young's interference experiment|his interference experiments]] with the interference patterns of two closely spaced slits. Young showed that his results could only be explained if the two slits acted as two unique sources of waves rather than corpuscles.<ref>{{cite book|author=T. Rothman|authorlink =Tony Rothman|title=Everything's Relative and Other Fables in Science and Technology|publisher=Wiley|place=New Jersey|year=2003|isbn=0-471-20257-6}}</ref> In 1815 and 1818, Augustin-Jean Fresnel firmly established the mathematics of how wave interference can account for diffraction.<ref name=hecht />
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| The simplest physical models of diffraction use equations that describe the angular separation of light and dark fringes due to light of a particular wavelength (λ). In general, the equation takes the form
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| :<math>m \lambda = d \sin \theta</math>
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| where <math>d</math> is the separation between two wavefront sources (in the case of Young's experiments, it was [[Double-slit experiment|two slits]]), <math>\theta</math> is the angular separation between the central fringe and the <math>m</math>th order fringe, where the central maximum is <math>m = 0</math>.<ref name=diffraction>{{cite book|title=University Physics 8e|author=H. D. Young|publisher=Addison-Wesley|year=1992|isbn=0-201-52981-5}}Chapter 38</ref>
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| This equation is modified slightly to take into account a variety of situations such as diffraction through a single gap, diffraction through multiple slits, or diffraction through a [[diffraction grating]] that contains a large number of slits at equal spacing.<ref name=diffraction /> More complicated models of diffraction require working with the mathematics of [[Fresnel diffraction|Fresnel]] or [[Fraunhofer diffraction]].<ref name=phyoptics>{{cite book|author=R. S. Longhurst|title=Geometrical and Physical Optics, 2nd Edition|year=1968|publisher=Longmans|location=London}}</ref>
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| [[X-ray diffraction]] makes use of the fact that atoms in a [[crystal]] have regular spacing at distances that are on the order of one [[angstrom]]. To see diffraction patterns, x-rays with similar wavelengths to that spacing are passed through the crystal. Since crystals are three-dimensional objects rather than two-dimensional gratings, the associated diffraction pattern varies in two directions according to [[Bragg reflection]], with the associated bright spots occurring in [[Diffraction topography|unique patterns]] and <math>d</math> being twice the spacing between atoms.<ref name=diffraction />
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| Diffraction effects limit the ability for an optical detector to [[optical resolution|optically resolve]] separate light sources. In general, light that is passing through an [[aperture]] will experience diffraction and the best images that can be created (as described in [[Diffraction-limited system|diffraction-limited optics]]) appear as a central spot with surrounding bright rings, separated by dark nulls; this pattern is known as an [[Airy pattern]], and the central bright lobe as an [[Airy disk]].<ref name=hecht /> The size of such a disk is given by
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| :<math> \sin \theta = 1.22 \frac{\lambda}{D}</math>
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| where ''θ'' is the angular resolution, ''λ'' is the [[wavelength]] of the light, and ''D'' is the [[diameter]] of the lens aperture. If the angular separation of the two points is significantly less than the Airy disk angular radius, then the two points cannot be resolved in the image, but if their angular separation is much greater than this, distinct images of the two points are formed and they can therefore be resolved. [[John Strutt, 3rd Baron Rayleigh|Rayleigh]] defined the somewhat arbitrary "[[Rayleigh criterion]]" that two points whose angular separation is equal to the Airy disk radius (measured to first null, that is, to the first place where no light is seen) can be considered to be resolved. It can be seen that the greater the diameter of the lens or its aperture, the finer the resolution.<ref name=diffraction /> [[Astronomical interferometer|Interferometry]], with its ability to mimic extremely large baseline apertures, allows for the greatest angular resolution possible.<ref name=interferometry />
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| For astronomical imaging, the atmosphere prevents optimal resolution from being achieved in the visible spectrum due to the atmospheric [[scattering]] and dispersion which cause stars to [[Scintillation (astronomy)|twinkle]]. Astronomers refer to this effect as the quality of [[astronomical seeing]]. Techniques known as [[adaptive optics]] have been used to eliminate the atmospheric disruption of images and achieve results that approach the diffraction limit.<ref>[http://www.mrao.cam.ac.uk/telescopes/coast/theses/rnt/ Lucky Exposures: Diffraction limited astronomical imaging through the atmosphere]'' by Robert Nigel Tubbs</ref>
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| ====Dispersion and scattering====
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| {{Main|Dispersion (optics)|Scattering}}
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| [[File:Light dispersion conceptual waves.gif|thumb|right|Conceptual animation of light dispersion through a prism. High frequency (blue) light is deflected the most, and low frequency (red) the least.]]
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| Refractive processes take place in the physical optics limit, where the wavelength of light is similar to other distances, as a kind of scattering. The simplest type of scattering is [[Thomson scattering]] which occurs when electromagnetic waves are deflected by single particles. In the limit of Thompson scattering, in which the wavelike nature of light is evident, light is dispersed independent of the frequency, in contrast to [[Compton scattering]] which is frequency-dependent and strictly a [[quantum mechanical]] process, involving the nature of light as particles. In a statistical sense, elastic scattering of light by numerous particles much smaller than the wavelength of the light is a process known as [[Rayleigh scattering]] while the similar process for scattering by particles that are similar or larger in wavelength is known as [[Mie scattering]] with the [[Tyndall effect]] being a commonly observed result. A small proportion of light scattering from atoms or molecules may undergo [[Raman scattering]], wherein the frequency changes due to excitation of the atoms and molecules. [[Brillouin scattering]] occurs when the frequency of light changes due to local changes with time and movements of a dense material.<ref>{{cite book|author=C. F. Bohren and D. R. Huffman|title=Absorption and Scattering of Light by Small Particles|publisher=Wiley|year=1983|isbn=0-471-29340-7}}</ref>
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| Dispersion occurs when different frequencies of light have different [[phase velocity|phase velocities]], due either to material properties (''material dispersion'') or to the geometry of an [[optical waveguide]] (''waveguide dispersion''). The most familiar form of dispersion is a decrease in index of refraction with increasing wavelength, which is seen in most transparent materials. This is called "normal dispersion". It occurs in all [[dielectric|dielectric materials]], in wavelength ranges where the material does not absorb light.<ref name=J286>{{cite book|author=J. D. Jackson|title=Classical Electrodynamics|edition=2nd|publisher=Wiley|year=1975|isbn=0-471-43132-X|page=286}}</ref> In wavelength ranges where a medium has significant absorption, the index of refraction can increase with wavelength. This is called "anomalous dispersion".<ref name=Geoptics/><ref name=J286/>
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| The separation of colours by a prism is an example of normal dispersion. At the surfaces of the prism, Snell's law predicts that light incident at an angle θ to the normal will be refracted at an angle arcsin(sin (θ) / ''n''). Thus, blue light, with its higher refractive index, is bent more strongly than red light, resulting in the well-known [[rainbow]] pattern.<ref name=Geoptics />
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| [[File:Wave group.gif|frame|Dispersion: two sinusoids propagating at different speeds make a moving interference pattern. The red dot moves with the [[phase velocity]], and the green dots propagate with the [[group velocity]]. In this case, the phase velocity is twice the group velocity. The red dot overtakes two green dots, when moving from the left to the right of the figure. In effect, the individual waves (which travel with the phase velocity) escape from the wave packet (which travels with the group velocity).]]
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| Material dispersion is often characterised by the [[Abbe number]], which gives a simple measure of dispersion based on the index of refraction at three specific wavelengths. Waveguide dispersion is dependent on the [[propagation constant]].<ref name=hecht /> Both kinds of dispersion cause changes in the group characteristics of the wave, the features of the wave packet that change with the same frequency as the amplitude of the electromagnetic wave. "Group velocity dispersion" manifests as a spreading-out of the signal "envelope" of the radiation and can be quantified with a group dispersion delay parameter:
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| :<math>D = \frac{1}{v_g^2} \frac{dv_g}{d\lambda}</math>
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| where <math>v_g</math> is the group velocity.<ref name=optnet>{{cite book|author=R. Ramaswami and K. N. Sivarajan|title=Optical Networks: A Practical Perspective|url=http://books.google.com/books?id=WpByp4Ip0z8C&printsec=frontcover|isbn=0123740924|publisher=Academic Press|location=London|year=1998}}</ref> For a uniform medium, the group velocity is
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| :<math>v_g = c \left( n - \lambda \frac{dn}{d\lambda} \right)^{-1}</math>
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| where ''n'' is the index of refraction and ''c'' is the speed of light in a vacuum.<ref>Brillouin, Léon. ''Wave Propagation and Group Velocity''. Academic Press Inc., New York (1960)</ref> This gives a simpler form for the dispersion delay parameter:
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| :<math>D = - \frac{\lambda}{c} \, \frac{d^2 n}{d \lambda^2}.</math>
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| If ''D'' is less than zero, the medium is said to have ''positive dispersion'' or normal dispersion. If ''D'' is greater than zero, the medium has ''negative dispersion''. If a light pulse is propagated through a normally dispersive medium, the result is the higher frequency components slow down more than the lower frequency components. The pulse therefore becomes ''positively [[chirp]]ed'', or ''up-chirped'', increasing in frequency with time. This causes the spectrum coming out of a prism to appear with red light the least refracted and blue/violet light the most refracted. Conversely, if a pulse travels through an anomalously (negatively) dispersive medium, high frequency components travel faster than the lower ones, and the pulse becomes ''negatively chirped'', or ''down-chirped'', decreasing in frequency with time.<ref>{{cite book|author=M. Born and E. Wolf|authorlink = Max Born|title=Principle of Optics|publisher=Cambridge University Press|year=1999|location=Cambridge|pages=14–24|isbn=0-521-64222-1}}</ref>
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| The result of group velocity dispersion, whether negative or positive, is ultimately temporal spreading of the pulse. This makes dispersion management extremely important in optical communications systems based on [[optical fibre]]s, since if dispersion is too high, a group of pulses representing information will each spread in time and merge, making it impossible to extract the signal.<ref name=optnet />
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| ====Polarization====
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| {{Main|Polarization (waves)}}
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| Polarization is a general property of waves that describes the orientation of their oscillations. For [[transverse wave]]s such as many electromagnetic waves, it describes the orientation of the oscillations in the plane perpendicular to the wave's direction of travel. The oscillations may be oriented in a single direction ([[linear polarization]]), or the oscillation direction may rotate as the wave travels ([[circular polarization|circular]] or [[elliptical polarization]]). Circularly polarised waves can rotate rightward or leftward in the direction of travel, and which of those two rotations is present in a wave is called the wave's [[polarimetry|chirality]].<ref name=light>{{cite book|title=University Physics 8e|author=H. D. Young|publisher=Addison-Wesley|year=1992|isbn=0-201-52981-5}}Chapter 34</ref>
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| The typical way to consider polarization is to keep track of the orientation of the electric field [[vector (geometry)|vector]] as the electromagnetic wave propagates. The electric field vector of a plane wave may be arbitrarily divided into two perpendicular [[vector components|components]] labeled ''x'' and ''y'' (with '''z''' indicating the direction of travel). The shape traced out in the x-y plane by the electric field vector is a [[Lissajous curve|Lissajous figure]] that describes the ''polarization state''.<ref name=hecht /> The following figures show some examples of the evolution of the electric field vector (blue), with time (the vertical axes), at a particular point in space, along with its ''x'' and ''y'' components (red/left and green/right), and the path traced by the vector in the plane (purple): The same evolution would occur when looking at the electric field at a particular time while evolving the point in space, along the direction opposite to propagation.
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| <div style="float:left;width:170px">
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| [[File:Polarisation (Linear).svg|center|Linear polarization diagram]]
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| <center>''Linear''</center>
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| </div>
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| <div style="float:left;width:170px">
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| [[File:Polarisation (Circular).svg|center|Circular polarization diagram]]
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| <center>''Circular''</center>
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| </div>
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| <div style="float:left;width:170px">
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| [[File:Polarisation (Elliptical).svg|center|Elliptical polarization diagram]]
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| <center>''Elliptical polarization''</center>
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| </div>
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| {{-}}
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| In the leftmost figure above, the x and y components of the light wave are in phase. In this case, the ratio of their strengths is constant, so the direction of the electric vector (the vector sum of these two components) is constant. Since the tip of the vector traces out a single line in the plane, this special case is called [[linear polarization]]. The direction of this line depends on the relative amplitudes of the two components.<ref name=light />
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| In the middle figure, the two orthogonal components have the same amplitudes and are 90° out of phase. In this case, one component is zero when the other component is at maximum or minimum amplitude. There are two possible phase relationships that satisfy this requirement: the ''x'' component can be 90° ahead of the ''y'' component or it can be 90° behind the ''y'' component. In this special case, the electric vector traces out a circle in the plane, so this polarization is called circular polarization. The rotation direction in the circle depends on which of the two phase relationships exists and corresponds to ''right-hand circular polarization'' and ''left-hand circular polarization''.<ref name=hecht />
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| In all other cases, where the two components either do not have the same amplitudes and/or their phase difference is neither zero nor a multiple of 90°, the polarization is called [[elliptical polarization]] because the electric vector traces out an [[ellipse]] in the plane (the ''polarization ellipse''). This is shown in the above figure on the right. Detailed mathematics of polarization is done using [[Jones calculus]] and is characterised by the [[Stokes parameters]].<ref name=hecht />
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| =====Changing polarization=====
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| Media that have different indexes of refraction for different polarization modes are called ''[[birefringence|birefringent]]''.<ref name=light /> Well known manifestations of this effect appear in optical [[wave plate]]s/retarders (linear modes) and in [[Faraday rotation]]/[[optical rotation]] (circular modes).<ref name=hecht /> If the path length in the birefringent medium is sufficient, plane waves will exit the material with a significantly different propagation direction, due to [[refraction]]. For example, this is the case with macroscopic crystals of [[calcite]], which present the viewer with two offset, orthogonally polarised images of whatever is viewed through them. It was this effect that provided the first discovery of polarization, by [[Erasmus Bartholinus]] in 1669. In addition, the phase shift, and thus the change in polarization state, is usually frequency dependent, which, in combination with [[dichroism]], often gives rise to bright colours and rainbow-like effects. In [[mineralogy]], such properties, known as [[pleochroism]], are frequently exploited for the purpose of identifying minerals using polarization [[microscope]]s. Additionally, many plastics that are not normally birefringent will become so when subject to [[mechanical stress]], a phenomenon which is the basis of [[photoelasticity]].<ref name=light /> Non-birefringent methods, to rotate the linear polarization of light beams, include the use of prismatic [[polarization rotator]]s which use [[total internal reflection]] in a prism set designed for efficient collinear transmission.<ref>{{cite book|author=F. J. Duarte|authorlink = F. J. Duarte|title=Tunable Laser Optics|publisher=Elsevier-Academic|year=2003|location=New York|pages=87–90|isbn=0-12-222696-8}}</ref>
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| [[File:Malus law.svg|right|thumb|350px|A polariser changing the orientation of linearly polarised light. <br>In this picture, ''θ''<sub>1</sub> – ''θ<sub>0</sub>'' = ''θ<sub>i</sub>''.]]
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| Media that reduce the amplitude of certain polarization modes are called ''[[dichroism|dichroic]]''. with devices that block nearly all of the radiation in one mode known as ''polarizing filters'' or simply "[[polariser]]s". Malus' law, which is named after [[Étienne-Louis Malus]], says that when a perfect polariser is placed in a linear polarised beam of light, the intensity, ''I'', of the light that passes through is given by
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| :<math> I = I_0 \cos^2 \theta_i \quad ,</math>
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| where
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| :''I''<sub>0</sub> is the initial intensity,
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| :and ''θ<sub>i</sub>'' is the angle between the light's initial polarization direction and the axis of the polariser.<ref name=light />
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| A beam of unpolarised light can be thought of as containing a uniform mixture of linear polarizations at all possible angles. Since the average value of <math>\cos^2 \theta</math> is 1/2, the transmission coefficient becomes
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| :<math> \frac {I}{I_0} = \frac {1}{2}\quad</math>
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| In practice, some light is lost in the polariser and the actual transmission of unpolarised light will be somewhat lower than this, around 38% for Polaroid-type polarisers but considerably higher (>49.9%) for some birefringent prism types.<ref name=hecht />
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| In addition to birefringence and dichroism in extended media, polarization effects can also occur at the (reflective) interface between two materials of different refractive index. These effects are treated by the [[Fresnel equations]]. Part of the wave is transmitted and part is reflected, with the ratio depending on angle of incidence and the angle of refraction. In this way, physical optics recovers [[Brewster's angle]].<ref name=hecht /> When light reflects from a [[Thin-film optics|thin film]] on a surface, interference between the reflections from the film's surfaces can produce polarization in the reflected and transmitted light.
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| =====Natural light=====
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| [[File:CircularPolarizer.jpg|right|thumb|400px|The effects of a [[photographic filter#Polarizer|polarising filter]] on the sky in a photograph. Left picture is taken without polariser. For the right picture, filter was adjusted to eliminate certain polarizations of the scattered blue light from the sky.]]
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| Most sources of [[electromagnetic radiation]] contain a large number of atoms or molecules that emit light. The orientation of the electric fields produced by these emitters may not be [[statistical correlation|correlated]], in which case the light is said to be ''unpolarised''. If there is partial correlation between the emitters, the light is ''partially polarised''. If the polarization is consistent across the spectrum of the source, partially polarised light can be described as a superposition of a completely unpolarised component, and a completely polarised one. One may then describe the light in terms of the [[degree of polarization]], and the parameters of the polarization ellipse.<ref name=hecht />
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| Light reflected by shiny transparent materials is partly or fully polarised, except when the light is normal (perpendicular) to the surface. It was this effect that allowed the mathematician [[Étienne-Louis Malus]] to make the measurements that allowed for his development of the first mathematical models for polarised light. Polarization occurs when light is scattered in the [[earth's atmosphere|atmosphere]]. The scattered light produces the brightness and colour in clear [[sky|skies]]. This partial polarization of scattered light can be taken advantage of using polarizing filters to darken the sky in [[science of photography|photographs]]. Optical polarization is principally of importance in [[chemistry]] due to [[circular dichroism]] and [[optical rotation]] ("''circular birefringence''") exhibited by [[optical activity|optically active]] ([[chirality (chemistry)|chiral]]) [[molecules]].<ref name=hecht />
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| ==Modern optics==
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| {{Main|Optical physics|Optical engineering}}
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| ''Modern optics'' encompasses the areas of optical science and engineering that became popular in the 20th century. These areas of optical science typically relate to the electromagnetic or quantum properties of light but do include other topics. A major subfield of modern optics, [[quantum optics]], deals with specifically quantum mechanical properties of light. Quantum optics is not just theoretical; some modern devices, such as lasers, have principles of operation that depend on quantum mechanics. Light detectors, such as [[photomultiplier]]s and [[channeltron]]s, respond to individual photons. Electronic [[image sensor]]s, such as [[Charge-coupled device|CCDs]], exhibit [[shot noise]] corresponding to the statistics of individual photon events. [[Light-emitting diode]]s and [[photovoltaic cell]]s, too, cannot be understood without quantum mechanics. In the study of these devices, quantum optics often overlaps with [[quantum electronics]].<ref>[[Daniel Frank Walls|D. F. Walls]] and G. J. Milburn ''Quantum Optics'' (Springer 1994)</ref>
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| Specialty areas of optics research include the study of how light interacts with specific materials as in [[crystal optics]] and [[metamaterial]]s. Other research focuses on the phenomenology of electromagnetic waves as in [[optical vortex|singular optics]], [[non-imaging optics]], [[non-linear optics]], [[statistical optics]], and [[radiometry]]. Additionally, [[computer engineer]]s have taken an interest in [[integrated optics]], [[machine vision]], and [[photonic computing]] as possible components of the "next generation" of computers.<ref>{{cite book|author=Alastair D. McAulay|title=Optical computer architectures: the application of optical concepts to next generation computers|url=http://books.google.com/books?id=RuRRAAAAMAAJ|accessdate=12 July 2012|date=16 January 1991|publisher=Wiley|isbn=978-0-471-63242-9}}</ref>
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| Today, the pure science of optics is called optical science or [[optical physics]] to distinguish it from applied optical sciences, which are referred to as [[optical engineering]]. Prominent subfields of optical engineering include [[lighting|illumination engineering]], [[photonics]], and [[optoelectronics]] with practical applications like [[Optical lens design|lens design]], [[Fabrication and testing (optical components)|fabrication and testing of optical components]], and [[image processing]]. Some of these fields overlap, with nebulous boundaries between the subjects terms that mean slightly different things in different parts of the world and in different areas of industry.<ref>{{cite web|title=SPIE society|url=http://spie.org/}}</ref> A professional community of researchers in nonlinear optics has developed in the last several decades due to advances in [[laser|laser technology]].<ref>{{cite book|title=The principles of nonlinear optics|author=Y. R. Shen|publisher=New York, Wiley-Interscience|year=1984|isbn=0-471-88998-9}}
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| </ref>
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| ===Lasers===
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| [[File:Military laser experiment.jpg|thumb|300px|Experiments such as this one with high-power [[laser]]s are part of the modern optics research.]]
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| {{Main|Laser}}
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| A laser is a device that emits light (electromagnetic radiation) through a process called ''[[stimulated emission]]''. The term ''laser'' is an [[acronym]] for ''Light Amplification by Stimulated Emission of Radiation''.<ref>{{cite web|accessdate=2008-05-15|url=http://dictionary.reference.com/browse/laser|title=laser|publisher=[[Reference.com]]}}</ref> Laser light is usually spatially [[coherence (physics)|coherent]], which means that the light either is emitted in a narrow, [[Beam divergence|low-divergence beam]], or can be converted into one with the help of optical components such as [[lens (optics)|lens]]es. Because the [[microwave]] equivalent of the laser, the ''maser'', was developed first, devices that emit microwave and [[Radio frequency|radio]] frequencies are usually called ''masers''.<ref>[http://nobelprize.org/physics/laureates/1964/townes-lecture.pdf Charles H. Townes – Nobel Lecture]. nobelprize.org</ref>
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| The first working laser was demonstrated on 16 May 1960 by [[Theodore Maiman]] at [[Hughes Research Laboratories]].<ref>{{cite web|accessdate=2008-05-15|url=http://www.press.uchicago.edu/Misc/Chicago/284158_townes.html|title=The first laser|publisher=University of Chicago|author=C. H. Townes}}</ref> When first invented, they were called "a solution looking for a problem".<ref>{{cite book|title=A Century of Nature: Twenty-One Discoveries that Changed Science and the World|author=C. H. Townes|authorlink=Charles Hard Townes|chapter=The first laser|chapterurl=http://www.press.uchicago.edu/Misc/Chicago/284158_townes.html|editor= Laura Garwin and Tim Lincoln|publisher=University of Chicago Press|year=2003|pages=107–12|isbn=0-226-28413-1|accessdate=2008-02-02}}</ref> Since then, lasers have become a multi-billion dollar industry, finding utility in thousands of highly varied applications. The first application of lasers visible in the daily lives of the general population was the supermarket [[barcode]] scanner, introduced in 1974.<ref>[http://www.denso-wave.com/en/adcd/fundamental/barcode/index.html What is a bar code?] denso-wave.com</ref> The [[laserdisc]] player, introduced in 1978, was the first successful consumer product to include a laser, but the [[compact disc]] player was the first laser-equipped device to become truly common in consumers' homes, beginning in 1982.<ref name=BBC6950933>{{cite news|url=http://news.bbc.co.uk/2/hi/technology/6950933.stm|title=How the CD was developed
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| |publisher=BBC News|date=2007-08-17|accessdate=2007-08-17}}</ref> These [[optical storage]] devices use a [[semiconductor laser]] less than a millimetre wide to scan the surface of the disc for data retrieval. [[Fibre-optic communication]] relies on lasers to transmit large amounts of information at the speed of light. Other common applications of lasers include [[laser printers]] and [[laser pointer]]s. Lasers are used in medicine in areas such as [[bloodless surgery]], [[laser eye surgery]], and [[laser capture microdissection]] and in military applications such as [[Airborne Laser|missile defence systems]], [[DIRCM|electro-optical countermeasures (EOCM)]], and [[LIDAR]]. Lasers are also used in [[holograms]], [[bubblegram]]s, [[laser lighting display|laser light shows]], and [[laser hair removal]].<ref>{{cite book|author=J. Wilson and J.F.B. Hawkes|year=1987|title=Lasers: Principles and Applications, Prentice Hall International Series in Optoelectronics|publisher=Prentice Hall|isbn=0-13-523697-5}}</ref>
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| ===Kapitsa–Dirac effect===
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| The [[Kapitsa–Dirac effect]] causes beams of particles to diffract as the result of meeting a standing wave of light. Light can be used to position matter using various phenomena (see [[optical tweezers]]).
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| ==Applications==
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| Optics is part of everyday life. The ubiquity of [[visual system]]s in biology indicates the central role optics plays as the science of one of the [[sense|five senses]]. Many people benefit from [[eyeglasses]] or [[contact lenses]], and optics are integral to the functioning of many consumer goods including [[cameras]]. Rainbows and [[mirage]]s are examples of optical phenomena. [[Optical communication]] provides the backbone for both the [[Internet]] and modern [[telephony]].
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| ===Human eye===
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| [[File:Eye-diagram no circles border.svg|300px|thumb|right|Model of a human eye. Features mentioned in this article are 3. [[ciliary muscle]], 6. [[pupil]], 8. [[cornea]], 10. [[lens cortex]], 22. [[optic nerve]], 26. [[fovea]], 30. [[retina]]]]
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| {{Main|Human eye|Photometry (optics)}}
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| The human eye functions by focusing light onto a layer of [[photoreceptor cell]]s called the [[retina]], which forms the inner lining of the back of the eye. The focusing is accomplished by a series of transparent media. Light entering the eye passes first through the [[cornea]], which provides much of the eye's optical power. The light then continues through the fluid just behind the cornea—the [[anterior chamber]], then passes through the [[pupil]]. The light then passes through the [[lens (anatomy)|lens]], which focuses the light further and allows adjustment of focus. The light then passes through the main body of fluid in the eye—the [[vitreous humour]], and reaches the retina. The cells in the retina line the back of the eye, except for where the [[optic nerve]] exits; this results in a [[Blind spot (vision)|blind spot]].
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| There are two types of photoreceptor cells, rods and cones, which are sensitive to different aspects of light.<ref name=eyeoptics>{{cite book|author=D. Atchison and G. Smith|title=Optics of the Human Eye|year=2000|isbn=0-7506-3775-7|publisher=Elsevier}}</ref> Rod cells are sensitive to the intensity of light over a wide frequency range, thus are responsible for [[scotopic vision|black-and-white vision]]. Rod cells are not present on the [[fovea]], the area of the retina responsible for central vision, and are not as responsive as cone cells to spatial and temporal changes in light. There are, however, twenty times more rod cells than cone cells in the retina because the rod cells are present across a wider area. Because of their wider distribution, rods are responsible for [[peripheral vision]].<ref name="Kandel">{{cite book|author=E. R. Kandel, J. H. Schwartz, T. M. Jessell|title=Principles of Neural Science|edition= 4th|year=2000|publisher=McGraw-Hill|place=New York|isbn=0-8385-7701-6| pages=507–513}}</ref>
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| In contrast, cone cells are less sensitive to the overall intensity of light, but come in three varieties that are sensitive to different frequency-ranges and thus are used in the perception of [[colour]] and [[photopic vision]]. Cone cells are highly concentrated in the fovea and have a high visual acuity meaning that they are better at spatial resolution than rod cells. Since cone cells are not as sensitive to dim light as rod cells, most [[night vision]] is limited to rod cells. Likewise, since cone cells are in the fovea, central vision (including the vision needed to do most reading, fine detail work such as sewing, or careful examination of objects) is done by cone cells.<ref name="Kandel" />
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| [[Ciliary muscle]]s around the lens allow the eye's focus to be adjusted. This process is known as [[Accommodation (eye)|accommodation]]. The [[near point]] and [[far point]] define the nearest and farthest distances from the eye at which an object can be brought into sharp focus. For a person with normal vision, the far point is located at infinity. The near point's location depends on how much the muscles can increase the curvature of the lens, and how inflexible the lens has become with age. [[Optometrist]]s, [[ophthalmologist]]s, and [[optician]]s usually consider an appropriate near point to be closer than normal reading distance—approximately 25 cm.<ref name=eyeoptics />
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| Defects in vision can be explained using optical principles. As people age, the lens becomes less flexible and the near point recedes from the eye, a condition known as [[presbyopia]]. Similarly, people suffering from [[hyperopia]] cannot decrease the focal length of their lens enough to allow for nearby objects to be imaged on their retina. Conversely, people who cannot increase the focal length of their lens enough to allow for distant objects to be imaged on the retina suffer from [[myopia]] and have a far point that is considerably closer than infinity. A condition known as [[astigmatism]] results when the cornea is not spherical but instead is more curved in one direction. This causes horizontally extended objects to be focused on different parts of the retina than vertically extended objects, and results in distorted images.<ref name=eyeoptics />
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| All of these conditions can be corrected using [[corrective lens]]es. For presbyopia and hyperopia, a [[converging lens]] provides the extra curvature necessary to bring the near point closer to the eye while for myopia a [[diverging lens]] provides the curvature necessary to send the far point to infinity. Astigmatism is corrected with a [[cylinder (geometry)|cylindrical surface]] lens that curves more strongly in one direction than in another, compensating for the non-uniformity of the cornea.<ref name=lensdesign>{{cite web|url=http://www.opticampus.com/cecourse.php?url=lens_design/&OPTICAMP=f1e4252df70c63961503c46d0c8d8b60|title=Ophthalmic Lens Design|author=D. Meister|work=OptiCampus.com|accessdate=November 12, 2008}}</ref>
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| The optical power of corrective lenses is measured in [[diopter]]s, a value equal to the [[multiplicative inverse|reciprocal]] of the focal length measured in meters; with a positive focal length corresponding to a converging lens and a negative focal length corresponding to a diverging lens. For lenses that correct for astigmatism as well, three numbers are given: one for the spherical power, one for the cylindrical power, and one for the angle of orientation of the astigmatism.<ref name=lensdesign />
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| ====Visual effects====
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| {{Main|Optical illusions|Perspective (graphical)}}
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| {{for|the visual effects used in film, video, and computer graphics|visual effects}}
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| [[File:Ponzo illusion.gif|right|thumb|The Ponzo Illusion relies on the fact that parallel lines appear to converge as they approach infinity.]]
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| Optical illusions (also called visual illusions) are characterized by [[visual perception|visually perceived]] images that differ from objective reality. The information gathered by the eye is processed in the brain to give a [[percept]] that differs from the object being imaged. Optical illusions can be the result of a variety of phenomena including physical effects that create images that are different from the objects that make them, the physiological effects on the eyes and brain of excessive stimulation (e.g. brightness, tilt, colour, movement), and cognitive illusions where the eye and brain make [[unconscious inference]]s.<ref>{{cite web|url=http://www.livescience.com/strangenews/080602-foresee-future.html|title=Key to All Optical Illusions Discovered|author=J. Bryner|publisher=LiveScience.com|date=2008-06-02}}</ref>
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| Cognitive illusions include some which result from the unconscious misapplication of certain optical principles. For example, the [[Ames room]], [[Hering illusion|Hering]], [[Müller-Lyer illusion|Müller-Lyer]], [[Orbison's illusion|Orbison]], [[Ponzo illusion|Ponzo]], [[Sander illusion|Sander]], and [[Wundt illusion]]s all rely on the suggestion of the appearance of distance by using converging and diverging lines, in the same way that parallel light rays (or indeed any set of parallel lines) appear to converge at a [[vanishing point]] at infinity in two-dimensionally rendered [[perspective (graphical)|images with artistic perspective]].<ref>[http://mathdl.maa.org/convergence/1/?pa=content&sa=viewDocument&nodeId=477&bodyId=598 Geometry of the Vanishing Point] at [http://mathdl.maa.org/convergence/1/ Convergence]</ref> This suggestion is also responsible for the famous [[moon illusion]] where the moon, despite having essentially the same angular size, appears much larger near the [[horizon]] than it does at [[zenith]].<ref>[http://facstaff.uww.edu/mccreadd/ "The Moon Illusion Explained"], Don McCready, University of Wisconsin-Whitewater</ref> This illusion so confounded [[Ptolemy of Alexandria|Ptolemy]] that he incorrectly attributed it to atmospheric refraction when he described it in his treatise, ''[[Optics (Ptolemy)|Optics]]''.<ref name=Ptolemy />
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| Another type of optical illusion exploits broken patterns to trick the mind into perceiving symmetries or asymmetries that are not present. Examples include the [[Café wall illusion|café wall]], [[Ehrenstein illusion|Ehrenstein]], [[Fraser spiral illusion|Fraser spiral]], [[Poggendorff illusion|Poggendorff]], and [[Zöllner illusion]]s. Related, but not strictly illusions, are patterns that occur due to the superimposition of periodic structures. For example [[Transparency (optics)|transparent]] tissues with a grid structure produce shapes known as [[moiré pattern]]s, while the superimposition of periodic transparent patterns comprising parallel opaque lines or curves produces [[line moiré]] patterns.<ref>{{cite book|title=Energy Minimization Methods in Computer Vision and Pattern Recognition|author=A. K. Jain, M. Figueiredo, J. Zerubia|publisher=Springer
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| |year=2001|url = http://books.google.com/?id=yb8otde21fcC&pg=RA1-PA198|isbn=978-3-540-42523-6}}</ref>
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| ====Optical instruments====
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| [[File:Table of Opticks, Cyclopaedia, Volume 2.jpg|thumb|right|300px|Illustrations of various optical instruments from the 1728 ''[[Cyclopaedia, or an Universal Dictionary of Arts and Sciences|Cyclopaedia]]'']]
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| {{Main|Optical instruments}}
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| Single lenses have a variety of applications including [[photographic lens]]es, corrective lenses, and [[magnifying glass]]es while single mirrors are used in [[parabolic reflector]]s and [[rear-view mirror]]s. Combining a number of mirrors, prisms, and lenses produces compound optical instruments which have practical uses. For example, a [[periscope]] is simply two plane mirrors aligned to allow for viewing around obstructions. The most famous compound optical instruments in science are the [[optical microscope|microscope]] and the [[optical telescope|telescope]] which were both invented by the Dutch in the late 16th century.<ref name=instrument>{{cite book|title=University Physics 8e|author=H. D. Young|publisher=Addison-Wesley|year=1992|isbn=0-201-52981-5|chapter =36|publisher=Cornell University}}</ref>
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| Microscopes were first developed with just two lenses: an [[objective lens]] and an [[eyepiece]]. The objective lens is essentially a magnifying glass and was designed with a very small [[focal length]] while the eyepiece generally has a longer focal length. This has the effect of producing magnified images of close objects. Generally, an additional source of illumination is used since magnified images are dimmer due to the [[conservation of energy]] and the spreading of light rays over a larger surface area. Modern microscopes, known as ''compound microscopes'' have many lenses in them (typically four) to optimize the functionality and enhance image stability.<ref name=instrument /> A slightly different variety of microscope, the [[comparison microscope]], looks at side-by-side images to produce a [[Stereoscopy|stereoscopic]] [[binocular vision|binocular]] view that appears three dimensional when used by humans.<ref>{{cite web|url=http://www.microscopyu.com/articles/stereomicroscopy/stereointro.html|title=Introduction to Stereomicroscopy|author=P. E. Nothnagle, W. Chambers, M. W. Davidson|publisher=Nikon MicroscopyU}}</ref>
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| The first telescopes, called ''[[refracting telescope]]s'' were also developed with a single objective and eyepiece lens. In contrast to the microscope, the objective lens of the telescope was designed with a large focal length to avoid optical aberrations. The objective focuses an image of a distant object at its focal point which is adjusted to be at the focal point of an eyepiece of a much smaller focal length. The main goal of a telescope is not necessarily magnification, but rather collection of light which is determined by the physical size of the objective lens. Thus, telescopes are normally indicated by the diameters of their objectives rather than by the magnification which can be changed by switching eyepieces. Because the magnification of a telescope is equal to the focal length of the objective divided by the focal length of the eyepiece, smaller focal-length eyepieces cause greater magnification.<ref name=instrument />
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| Since crafting large lenses is much more difficult than crafting large mirrors, most modern telescopes are ''[[reflecting telescope]]s'', that is, telescopes that use a primary mirror rather than an objective lens. The same general optical considerations apply to reflecting telescopes that applied to refracting telescopes, namely, the larger the primary mirror, the more light collected, and the magnification is still equal to the focal length of the primary mirror divided by the focal length of the eyepiece. Professional telescopes generally do not have eyepieces and instead place an instrument (often a charge-coupled device) at the focal point instead.<ref name=instrument />
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| ===Photography===
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| {{Main|Science of photography}}
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| [[File:Jonquil flowers at f32.jpg|thumb|right|300px|Photograph taken with aperture {{f/}}32]]
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| [[File:Jonquil flowers at f5.jpg|thumb|right|300px|Photograph taken with aperture {{f/}}5]]
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| The optics of [[photography]] involves both [[photographic lens|lenses]] and the medium in which the electromagnetic radiation is recorded, whether it be a [[photographic plates|plate]], [[photographic film|film]], or [[charge-coupled device]]. Photographers must consider the [[Reciprocity (photography)|reciprocity]] of the camera and the shot which is summarized by the relation
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| :Exposure ∝ ApertureArea × ExposureTime × SceneLuminance<ref>
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| {{cite book
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| |title=Investigations on the Theory of the Photographic Process
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| |author=Samuel Edward Sheppard and Charles Edward Kenneth Mees
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| |publisher=Longmans, Green and Co
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| |year=1907
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| |page = 214
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| |url = http://books.google.com/?id=luNIAAAAIAAJ&pg=PA214
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| }}</ref>
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| In other words, the smaller the aperture (giving greater depth of focus), the less light coming in, so the length of time has to be increased (leading to possible blurriness if motion occurs). An example of the use of the law of reciprocity is the [[Sunny 16 rule]] which gives a rough estimate for the settings needed to estimate the proper [[exposure (photography)|exposure]] in daylight.<ref>{{cite book|title=Mastering Black-and-White Photography|author=B. J. Suess|publisher=Allworth Communications|year=2003|isbn=1-58115-306-6|url=http://books.google.com/?id=7LaRPNINH_YC&pg=PT112}}</ref>
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| A camera's aperture is measured by a unitless number called the [[f-number]] or f-stop, {{f/}}#, often notated as <math>N</math>, and given by
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| :<math>f/\# = N = \frac fD \ </math>
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| where <math>f</math> is the [[focal length]], and <math>D</math> is the diameter of the entrance pupil. By convention, "{{f/}}#" is treated as a single symbol, and specific values of {{f/}}# are written by replacing the [[number sign]] with the value. The two ways to increase the f-stop are to either decrease the diameter of the entrance pupil or change to a longer focal length (in the case of a [[zoom lens]], this can be done by simply adjusting the lens). Higher f-numbers also have a larger [[depth of field]] due to the lens approaching the limit of a [[pinhole camera]] which is able to focus all images perfectly, regardless of distance, but requires very long exposure times.<ref>{{cite book|title=Basic Photography|author=M. J. Langford|isbn=0-240-51592-7|year=2000|publisher=Focal Press}}</ref>
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| The field of view that the lens will provide changes with the focal length of the lens. There are three basic classifications based on the relationship to the diagonal size of the film or sensor size of the camera to the focal length of the lens:<ref name="Bruce Warren, Photography, page 71">{{cite book|author=Bruce Warren |title=Photography |url=http://books.google.com/books?id=sbdGeFem1zwC&pg=PA71 |year=2001 |publisher=Cengage Learning |isbn=978-0-7668-1777-7 |page=71}}</ref>
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| *[[Normal lens]]: angle of view of about 50° (called ''normal'' because this angle considered roughly equivalent to human vision<ref name="Bruce Warren, Photography, page 71"/>) and a focal length approximately equal to the diagonal of the film or sensor.<ref>{{cite book|title=View Camera Technique|author=Leslie D. Stroebel|publisher=Focal Press|year=1999|isbn=0-240-80345-0|url=http://books.google.com/?id=71zxDuunAvMC&pg=PA136}}</ref> <!-- It's generally accepted that 50mm is a bit longer than "normal" for 35mm film; I've based this on 75mm with 6×4cm. Maybe the angle of width, rather than diagonal, is better? -->
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| *[[Wide-angle lens]]: angle of view wider than 60° and focal length shorter than a normal lens.<ref>{{cite book|title=Using the View Camera|author=S. Simmons|publisher=Amphoto Books|year=1992|isbn=0-8174-6353-4|page=35}}</ref>
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| *[[Long focus lens]]: angle of view narrower than a normal lens. This is any lens with a focal length longer than the diagonal measure of the film or sensor.<ref>{{cite book|author=Sidney F. Ray |title=Applied Photographic Optics: Lenses and Optical Systems for Photography, Film, Video, Electronic and Digital Imaging |url=http://books.google.com/books?id=cuzYl4hx-B8C&pg=PA294 |year=2002 |publisher=Focal Press |isbn=978-0-240-51540-3 |page=294}}</ref> The most common type of long focus lens is the [[telephoto lens]], a design that uses a special ''telephoto group'' to be physically shorter than its focal length.<ref>{{cite book|url = http://books.google.com/?id=zqkdNwRxSooC&pg=PA109 |title=The New York Times Guide to Essential Knowledge|author=New York Times Staff|isbn=978-0-312-31367-8|year=2004|publisher=Macmillan}}</ref>
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| Modern [[zoom lens]]es may have some or all of these attributes.
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| The absolute value for the exposure time required depends on how [[sensitometry|sensitive]] to light the medium being used is (measured by the [[film speed]], or, for digital media, by the [[quantum efficiency]]).<ref>{{cite book|title=Principles of Radiographic Imaging: An Art and a Science|author=R. R. Carlton, A. McKenna Adler|publisher=Thomson Delmar Learning|year=2000|isbn=0-7668-1300-2|url = http://books.google.com/?id=oA-eBHsapX8C&pg=PA318}}</ref> Early photography used media that had very low light sensitivity, and so exposure times had to be long even for very bright shots. As technology has improved, so has the sensitivity through film cameras and digital cameras.<ref>{{cite book|author=W. Crawford|title=The Keepers of Light: A History and Working Guide to Early Photographic Processes|year=1979|publisher=Morgan & Morgan|location=Dobbs Ferry, New York|isbn=0-87100-158-6|page=20}}</ref>
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| Other results from physical and geometrical optics apply to camera optics. For example, the maximum resolution capability of a particular camera set-up is determined by the [[diffraction limit]] associated with the pupil size and given, roughly, by the Rayleigh criterion.<ref>{{cite book|author=J. M. Cowley|year=1975|title=Diffraction physics|location=Amsterdam|publisher=North-Holland|isbn=0-444-10791-6}}</ref>
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| ===Atmospheric optics===
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| {{main|Atmospheric optics}}
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| [[File:Firesunset2edit.jpg|thumb|right|300px|A colourful sky is often due to scattering of light off particulates and pollution, as in this photograph of a sunset during the [[October 2007 California wildfires]].]]
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| The unique optical properties of the atmosphere cause a wide range of spectacular optical phenomena. The blue colour of the sky is a direct result of [[Rayleigh scattering]] which redirects higher frequency (blue) sunlight back into the field of view of the observer. Because blue light is scattered more easily than red light, the sun takes on a reddish hue when it is observed through a thick atmosphere, as during a [[sunrise]] or [[sunset]]. Additional particulate matter in the sky can scatter different colours at different angles creating colourful glowing skies at dusk and dawn. Scattering off of ice crystals and other particles in the atmosphere are responsible for [[halo (optical phenomenon)|halos]], [[afterglow]]s, [[Corona (meteorology)|coronas]], [[Crepuscular rays|rays of sunlight]], and [[sun dog]]s. The variation in these kinds of phenomena is due to different particle sizes and geometries.<ref name="autogenerated1">{{cite book|author=C. D. Ahrens|year=1994|title=Meteorology Today: an introduction to weather, climate, and the environment|edition = 5th|pages=88–89|publisher=West Publishing Company|isbn=0-314-02779-3}}</ref>
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| [[Mirage]]s are optical phenomena in which light rays are bent due to thermal variations in the refraction index of air, producing displaced or heavily distorted images of distant objects. Other dramatic optical phenomena associated with this include the [[Novaya Zemlya effect]] where the sun appears to rise earlier than predicted with a distorted shape. A spectacular form of refraction occurs with a [[inversion (meteorology)|temperature inversion]] called the [[Fata Morgana (mirage)|Fata Morgana]] where objects on the horizon or even beyond the horizon, such as islands, cliffs, ships or icebergs, appear elongated and elevated, like "fairy tale castles".<ref>{{cite web|url=http://mintaka.sdsu.edu/GF/mirages/mirintro.html|title=An Introduction to Mirages|author=A. Young}}</ref>
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| [[Rainbow]]s are the result of a combination of internal reflection and dispersive refraction of light in raindrops. A single reflection off the backs of an array of raindrops produces a rainbow with an angular size on the sky that ranges from 40° to 42° with red on the outside. Double rainbows are produced by two internal reflections with angular size of 50.5° to 54° with violet on the outside. Because rainbows are seen with the sun 180° away from the centre of the rainbow, rainbows are more prominent the closer the sun is to the horizon.<ref name=light />
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| ==See also==
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| {{portal|Physics}}
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| *[[List of publications in physics#Optics|Important publications in optics]]
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| *[[List of optical topics]]
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| ==References==
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| {{reflist|colwidth=30em}}
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| ;Further reading
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| *{{cite isbn|1139643401}}
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| *{{cite isbn|0805385665}}
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| *{{cite isbn|0534408427}}
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| *{{cite isbn|0716708108}}
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| *{{cite isbn|0521436311}}
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| *{{cite isbn|0486659577}}
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| ==External links==
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| {{Commons category|Optics}}
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| ;Relevant discussions
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| *{{In Our Time|Optics|b00774t5|Optics}}
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| ;Textbooks and tutorials
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| *[http://www.lightandmatter.com/area1book5.html Optics] – an open-source optics textbook
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| *[http://www.optics2001.com Optics2001] – Optics library and community
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| *[http://www.cvimellesgriot.com/products/Documents/TechnicalGuide/fundamental-Optics.pdf Fundamental Optics] – CVI Melles Griot Technical Guide
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| *[http://optics.byu.edu/textbook.aspx Physics of Light and Optics] – [[Brigham Young University]] Undergraduate Book
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| ;Wikibooks modules
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| {{Col-begin}}
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| {{Col-break|width=50%}}
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| *[[wikibooks:Physics Study Guide/Optics|Physics Study Guide/Optics]]
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| {{Col-break|width=50%}}
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| *[[wikibooks:Optics|Optics]]
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| {{Col-end}}
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| ;Further reading
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| *[http://www.iop.org/publications/iop/2009/page_38205.html Optics and photonics: Physics enhancing our lives] by [http://www.iop.org/publications/iop/index.html Institute of Physics publications]
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| ;Societies
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| {{Col-begin}}
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| {{Col-break|width=50%}}
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| *[[SPIE]] – [http://www.spie.org link]
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| *[[Optical Society of America]] – [http://www.osa.org link]
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| *[[European Optical Society]] – [http://www.myeos.org link]
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| {{Col-break|width=50%}}
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| *[[European Photonics Industry Consortium]] – [http://www.epic-assoc.com link]
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| *[[Optical Society of India]] – [http://www.osiindia.org link]
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| {{Col-end}}
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| {{physics-footer}}
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| {{Glass science}}
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| [[Category:Optics| ]]
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| [[Category:Electromagnetic radiation]]
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| [[Category:Applied and interdisciplinary physics]]
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| [[Category:Natural philosophy]]
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| {{Link GA|tt}}
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