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Optics is the branch of
physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force. "Physical scie ...

physics
that studies the behaviour and properties of
light Light or visible light is electromagnetic radiation within the portion of the electromagnetic spectrum that is visual perception, perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nan ...

light
, including its interactions with
matter In classical physics Classical physics is a group of physics theories that predate modern, more complete, or more widely applicable theories. If a currently accepted theory is considered to be modern, and its introduction represented a major ...
and the construction of
instruments Instrument may refer to: Science and technology * Flight instruments, the devices used to measure the speed, altitude, and pertinent flight angles of various kinds of aircraft * Laboratory equipment, the measuring tools used in a scientific labo ...
that use or detect it. Optics usually describes the behaviour of
visible Visibility is in meteorology, a measure of the distance at which an object or light can be seen. Visibility may also refer to: * Visual perception ** Naked-eye visibility * A measure of turbidity in water quality control * Interferometric visibili ...
,
ultraviolet Ultraviolet (UV) is a form of electromagnetic radiation In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, ...

ultraviolet
, and
infrared Infrared (IR), sometimes called infrared light, is electromagnetic radiation In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior ...

infrared
light. Because light is an
electromagnetic wave In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular s ...

electromagnetic wave
, other forms of
electromagnetic radiation In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force. ...

electromagnetic radiation
such as
X-ray An X-ray, or, much less commonly, X-radiation, is a penetrating form of high-energy electromagnetic radiation In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Moti ...

X-ray
s,
microwave Microwave is a form of electromagnetic radiation In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space a ...

microwave
s, and
radio wave Radio waves are a type of electromagnetic radiation In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space ...
s exhibit similar properties. Most optical phenomena can be accounted for by using the 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 Geometry (from the grc, γεωμετρία; ''wikt:γῆ, geo-'' "earth", ''wikt:μέτρον, -metron'' "measurement") is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space that are related ...
, treats light as a collection of rays that travel in straight lines and bend when they pass through or reflect from surfaces.
Physical optics In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force. "P ...
is a more comprehensive model of light, which includes
wave In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular su ...

wave
effects such as
diffraction Diffraction refers to various phenomena that occur when a wave In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which r ...

diffraction
and
interference Interference is the act of interfering, invading, or poaching. Interference may also refer to: Communications * Interference (communication), anything which alters, modifies, or disrupts a message * Adjacent-channel interference, caused by extran ...
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. Some phenomena depend on the fact that light has both . Explanation of these effects requires
quantum mechanics Quantum mechanics is a fundamental theory A theory is a reason, rational type of abstraction, abstract thinking about a phenomenon, or the results of such thinking. The process of contemplative and rational thinking is often associated with ...
. When considering light's particle-like properties, the light is modelled as a collection of particles called "
photon The photon ( el, φῶς, phōs, light) is a type of elementary particle In , an elementary particle or fundamental particle is a that is not composed of other particles. Particles currently thought to be elementary include the fundamental s ...

photon
s".
Quantum optics #REDIRECT Quantum optics#REDIRECT Quantum optics Quantum optics is a branch of atomic, molecular, and optical physics dealing with how individual quanta of light, known as photons, interact with atoms and molecules. It includes the study of the p ...
deals with the application of quantum mechanics to optical systems. Optical science is relevant to and studied in many related disciplines including
astronomy Astronomy (from el, ἀστρονομία, literally meaning the science that studies the laws of the stars) is a natural science that studies astronomical object, celestial objects and celestial event, phenomena. It uses mathematics, phys ...
, various
engineering Engineering is the use of scientific principles to design and build machines, structures, and other items, including bridges, tunnels, roads, vehicles, and buildings. The discipline of engineering encompasses a broad range of more speciali ...

engineering
fields,
photography Photography is the art Art is a diverse range of (products of) human activities Humans (''Homo sapiens'') are the most populous and widespread species of primates, characterized by bipedality, opposable thumbs, hairlessness, and int ...

photography
, and
medicine Medicine is the science Science () is a systematic enterprise that builds and organizes knowledge Knowledge is a familiarity, awareness, or understanding of someone or something, such as facts ( descriptive knowledge), skills (proced ...

medicine
(particularly
ophthalmology Ophthalmology () is a branch of medicine and surgery that deals with the diagnosis and treatment of disorders of the eye. An ophthalmologist is a physician who Specialty (medicine), specializes in ophthalmology. The credentials include a degree i ...
and
optometry Optometry is a specialized health care profession that involves examining the eyes and related structures for defects or abnormalities. This often involves prescribing corrective lenses and providing medical eye care. Optometrists (Doctors of Op ...
, in which it is called physiological optics). Practical applications of optics are found in a variety of technologies and everyday objects, including
mirror A mirror is an object that reflects an image An image (from la, imago) is an artifact that depicts visual perception Visual perception is the ability to interpret the surrounding environment Environment most often refers t ...

mirror
s,
lenses A lens is a transmissive optics, optical device that focuses or disperses a light beam by means of refraction. A simple lens consists of a single piece of transparent material, while a #Compound lenses, compound lens consists of several simple ...

lenses
,
telescopes A telescope is an optical instrument using lenses, curved mirrors, or a combination of both to observe distant objects, or various devices used to observe distant objects by their emission, absorption, or reflection of electromagnetic radiation. ...
,
microscope A microscope (from grc, μικρός ''mikrós'' 'small' and ''skopeîn'' 'to look (at); examine, inspect') is a laboratory instrument used to examine objects that are too small to be seen by the naked eye Naked eye, also called bare ...

microscope
s,
laser A laser is a device that emits light Light or visible light is electromagnetic radiation within the portion of the electromagnetic spectrum that is visual perception, perceived by the human eye. Visible light is usually defined as h ...

laser
s, and
fibre optics An optical fiber (or fibre in British English British English (BrE) is the standard dialect A standard language (also standard variety, standard dialect, and standard) is a language variety that has undergone substantial codificati ...
.


History

Optics began with the development of lenses by the
ancient Egypt Ancient Egypt was a civilization  A civilization (or civilisation) is a that is characterized by , , a form of government, and systems of communication (such as ). Civilizations are intimately associated with additional char ...

ancient Egypt
ians and
Mesopotamia Mesopotamia ( grc, Μεσοποταμία ''Mesopotamíā''; ar, بِلَاد ٱلرَّافِدَيْن ; syc, ܐܪܡ ܢܗܪ̈ܝܢ, or , ) is a historical region of Western Asia situated within the Tigris–Euphrates river system, in th ...

Mesopotamia
ns. The earliest known lenses, made from polished crystal, often
quartz Quartz is a hard, crystalline mineral composed of silica (silicon dioxide). The atoms are linked in a continuous framework of SiO4 silicon-oxygen Tetrahedral molecular geometry, tetrahedra, with each oxygen being shared between two tetrahedra, ...

quartz
, date from as early as 2000 BC from
Crete Crete ( el, Κρήτη, translit=, Modern Modern may refer to: History *Modern history Human history, also known as world history, is the description of humanity's past. It is informed by archaeology Archaeology or archeology ...

Crete
(Archaeological Museum of Heraclion, Greece). Lenses from
Rhodes Rhodes (; el, Ρόδος, translit=Ródos ) is the largest of the Dodecanese The Dodecanese (, ; el, Δωδεκάνησα, ''Dodekánisa'' , literally "twelve islands") are a group of 15 larger plus 150 smaller Greek#REDIRECT Greek Gre ...

Rhodes
date around 700 BC, as do
Assyria Assyria (), also called the Assyrian Empire, was a Mesopotamia Mesopotamia ( grc, Μεσοποταμία ''Mesopotamíā''; ar, بِلَاد ٱلرَّافِدَيْن ; syc, ܐܪܡ ܢܗܪ̈ܝܢ, or , ) is a historical region of We ...

Assyria
n lenses such as the
Nimrud lens The Nimrud lens, also called Layard lens, is a 3000-year-old piece of rock crystal, which was unearthed in 1850 by Austen Henry Layard at the Assyrian palace of Nimrud, in modern-day Iraq. It may have been used as a magnifying glass, or as a burning ...
. The
ancient Roman In historiography, ancient Rome is Roman people, Roman civilization from the founding of the Italian city of Rome in the 8th century BC to the collapse of the Western Roman Empire in the 5th century AD, encompassing the Roman Kingdom (753 BC ...
s and
Greeks The Greeks or Hellenes (; el, Έλληνες, ''Éllines'' ) are an ethnic group An ethnic group or ethnicity is a grouping of people A people is any plurality of person A person (plural people or persons) is a being that has cer ...
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#REDIRECT Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially the Hellenic Republic, is a country located in Southeast Europe. Its population is approximately 10.7 million as of ...
and
Indian Indian or Indians refers to people or things related to India, or to the indigenous people of the Americas, or Aboriginal Australians until the 19th century. People South Asia * Indian people, people of Indian nationality, or people who come ...
philosophers, and the development of
geometrical optics Geometrical optics, or ray optics, is a model of optics Optics is the branch of physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural sci ...
in the
Greco-Roman world The term "Greco-Roman world" (also "Greco-Roman culture" or ; spelled Graeco-Roman in the Commonwealth), as understood by modern scholars and writers, refers to geographical regions and countries that culturally—and so historically—were ...
. The word ''optics'' comes from the
ancient Greek Ancient Greek includes the forms of the Greek language Greek ( el, label=Modern Greek Modern Greek (, , or , ''Kiní Neoellinikí Glóssa''), generally referred to by speakers simply as Greek (, ), refers collectively to the diale ...
word (''optikē''), meaning "appearance, look". Greek philosophy on optics broke down into two opposing theories on how vision worked, the
intromission theory Visual perception is the ability to interpret the surrounding environment using light in the visible spectrum reflected by the objects in the environment. This is different from visual acuity, which refers to how clearly a person sees (for e ...
and the
emission theory Emission theory, also called emitter theory or ballistic theory of light, was a competing theory for the special theory of relativity, explaining the results of the Michelson–Morley experiment of 1887. Emission theories obey the principle of relat ...
. The intromission 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 Democritus (; el, Δημόκριτος, ''Dēmókritos'', meaning "chosen of the people"; – ) was an Ancient Greek Ancient Greek includes the forms of the Greek language used in ancient Greece and the classical antiquity, ancient w ...

Democritus
,
Epicurus Epicurus, ''Epíkouros'', "ally, comrade" (341–270 BC) was an ancient Greek philosopher and sage who founded Epicureanism Epicureanism is a system of founded around 307 BC based upon the teachings of the . Epicureanism was originally ...

Epicurus
,
Aristotle Aristotle (; grc-gre, Ἀριστοτέλης ''Aristotélēs'', ; 384–322 BC) was a Greek philosopher A philosopher is someone who practices philosophy Philosophy (from , ) is the study of general and fundamental questio ...

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.
Plato Plato ( ; grc-gre, Πλάτων ; 428/427 or 424/423 – 348/347 BC) was an Classical Athens, Athenian philosopher during the Classical Greece, Classical period in Ancient Greece, founder of the Platonist school of thought and the Platoni ...

Plato
first articulated the emission theory, the idea that
visual perception Visual perception is the ability to interpret the surrounding environment (biophysical), environment through photopic vision (daytime vision), color vision, scotopic vision (night vision), and mesopic vision (twilight vision), using light in ...
is accomplished by rays emitted by the eyes. He also commented on the parity reversal of mirrors in '' Timaeus''. Some hundred years later,
Euclid Euclid (; grc-gre, Εὐκλείδης Euclid (; grc, Εὐκλείδης – ''Eukleídēs'', ; fl. 300 BC), sometimes called Euclid of Alexandria to distinguish him from Euclid of Megara, was a Greek mathematician, often referre ...

Euclid
(4th–3rd century BC) wrote a treatise entitled ''
Optics Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of optical instruments, instruments that use or Photodetector, detect it. Optics usually describes t ...
'' where he linked vision to
geometry Geometry (from the grc, γεωμετρία; ' "earth", ' "measurement") is, with , one of the oldest branches of . It is concerned with properties of space that are related with distance, shape, size, and relative position of figures. A mat ...

geometry
, creating ''geometrical optics''. He based his work on Plato's emission theory wherein he described the mathematical rules of perspective and described the effects of
refraction In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular ...

refraction
qualitatively, although he questioned that a beam of light from the eye could instantaneously light up the stars every time someone blinked. Euclid stated the principle of shortest trajectory of light, and considered multiple reflections on flat and spherical mirrors.
Ptolemy Claudius Ptolemy (; grc-koi, Κλαύδιος Πτολεμαῖος, , ; la, Claudius Ptolemaeus; AD) was a mathematician A mathematician is someone who uses an extensive knowledge of mathematics Mathematics (from Greek: ) includes ...
, in his treatise ''
Optics Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of optical instruments, instruments that use or Photodetector, detect it. Optics usually describes t ...

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 summarized much of Euclid and went on to describe a way to measure the
angle of refraction of light at the interface between two media of different refractive indices, with n2 > n1. Since the velocity is lower in the second medium (v2 < v1), the angle of refraction θ2 is less than the angle of incidence θ1< ...
, though he failed to notice the empirical relationship between it and the angle of incidence.
Plutarch Plutarch (; grc-gre, Πλούταρχος, ''Ploútarchos''; ; AD 46 – after AD 119) was a Greek Middle Platonist Middle Platonism is the modern name given to a stage in the development of Platonic philosophy, lasting from about 90 BC&nbs ...

Plutarch
(1st–2nd century AD) described multiple reflections on spherical mirrors and discussed the creation of magnified and reduced images, both real and imaginary, including the case of
chirality Chirality is a property of asymmetry Asymmetry is the absence of, or a violation of, symmetry (the property of an object being invariant to a transformation, such as reflection). Symmetry is an important property of both physical and abstrac ...

chirality
of the images. During the
Middle Ages In the history of Europe The history of Europe concerns itself with the discovery and collection, the study, organization and presentation and the interpretation of past events and affairs of the people of Europe since the beginning of ...
, Greek ideas about optics were resurrected and extended by writers in the
Muslim world The terms Muslim world and Islamic world commonly refer to the Islamic Islam (; ar, اَلْإِسْلَامُ, al-’Islām, "submission o God Oh God may refer to: * An exclamation; similar to "oh no", "oh yes", "oh my", "aw goodne ...

Muslim world
. One of the earliest of these was
Al-Kindi Abu Yūsuf Yaʻqūb ibn ʼIsḥāq aṣ-Ṣabbāḥ al-Kindī (; ar, أبو يوسف يعقوب بن إسحاق الصبّاح الكندي; la, Alkindus; c. 801–873 AD) was an Arab The Arabs (singular Arab ; singular ar, عَرَب ...
(c. 801–873) who wrote on the merits of Aristotelian and Euclidean ideas of optics, favouring the emission theory since it could better quantify optical phenomena. In 984, the
Persia Iran ( fa, ایران ), also called Persia, and officially the Islamic Republic of Iran, is a country in Western Asia. It is bordered to the northwest by Armenia and Azerbaijan, to the north by the Caspian Sea, to the northeast by Tu ...

Persia
n mathematician Ibn Sahl wrote the treatise "On burning mirrors and lenses", correctly describing a law of refraction equivalent to Snell's law. He used this law to compute optimum shapes for lenses and
curved mirror A curved mirror is a mirror A mirror is an object that Reflection (physics), reflects an image. Light that bounces off a mirror will show an image of whatever is in front of it, when focused through the lens of the eye or a camera. Mirr ...
s. In the early 11th century, Alhazen (Ibn al-Haytham) wrote the ''
Book of Optics The ''Book of Optics'' ( ar, كتاب المناظر, Kitāb al-Manāẓir; la, De Aspectibus or ''Perspectiva''; it, Deli Aspecti) is a seven-volume treatise on optics Optics is the branch of physics Physics (from grc, φυσι ...
'' (''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. 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. 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 Vitello (or Witelo; fl. c. 1270–1285) was a Silesian friar A friar is a brother and a member of one of the mendicant orders founded in the twelfth or thirteenth century; the term distinguishes the mendicants' itinerant apostolic characte ...
making it a standard text on optics in Europe for the next 400 years. In the 13th century in medieval Europe, English bishop
Robert Grosseteste Robert Grosseteste, ', ', or ') or the gallicized Robert Grosstête ( ; la, Robertus Grossetesta or '). Also known as Robert of Lincoln ( la, Robertus Lincolniensis, ', &c.) or Rupert of Lincoln ( la, Rubertus Lincolniensis, &c.). ( ; la, Robe ...

Robert Grosseteste
wrote on a wide range of scientific topics, and discussed light from four different perspectives: an
epistemology Epistemology (; ) is the Outline of philosophy, branch of philosophy concerned with knowledge. Epistemologists study the nature, origin, and scope of knowledge, epistemic Justification (epistemology), justification, the Reason, rationality o ...

epistemology
of light, a
metaphysics Metaphysics is the branch of philosophy that studies the first principles of being, identity and change, space and time, causality, necessity and possibility. It includes questions about the nature of consciousness and the relationship between ...

metaphysics
or
cosmogony Cosmogony is any model concerning the origin of either the cosmos The cosmos (, ) is another name for the Universe The universe ( la, universus) is all of space and time and their contents, including planets, stars, galaxy, galaxies, and ...
of light, an
etiology Etiology (pronounced ; alternatively: aetiology or ætiology) is the study of causation or origination. The word is derived from the Greek#REDIRECT Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ε ...
or physics of light, and a
theology Theology is the systematic study of the nature of the divine Divinity or the divine are things that are either related to, devoted to, or proceeding from a deity A deity or god is a supernatural The supernatural encompasses supposed ...
of light, basing it on the works Aristotle and Platonism. Grosseteste's most famous disciple,
Roger Bacon Roger Bacon (; la, Rogerus or ', also '' Rogerus''; ), also known by the scholastic accolade It was customary in the European Middle Ages, more precisely in the period of scholasticism which extended into early modern times, to designate th ...
, wrote works citing a wide range of recently translated optical and philosophical works, including those of Alhazen, Aristotle,
Avicenna Ibn Sina ( fa, ابن سینا), also known as Abu Ali Sina (), Pur Sina (), and often known in the West as Avicenna (;  – June 1037), was a Persian Persian may refer to: * People and things from Iran, historically called ''Persia' ...

Avicenna
,
Averroes Ibn Rushd ( ar, ; full name Image:FML names-2.png, 300px, First/given, middle and last/family/surname with John Fitzgerald Kennedy as example. This shows a structure typical for the Anglosphere, among others. Other cultures use other struc ...

Averroes
, Euclid, al-Kindi, Ptolemy, Tideus, and
Constantine the African Constantine the African ( la, Constantinus Africanus; died before 1098/1099, Monte Cassino Monte Cassino (today usually spelled Montecassino) is a rocky hill about southeast of Rome , established_title = Founded , established_date ...
. Bacon was able to use parts of glass spheres as
magnifying glass A magnifying glass is a Lens (optics)#Types of simple lenses, convex lens that is used to produce a magnification, magnified image of an object. The lens (optics), lens is usually mounted in a frame with a handle. A magnifying glass can be used ...

magnifying glass
es to demonstrate that light reflects from objects rather than being released from them. The first wearable eyeglasses were invented in Italy around 1286. 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, and later in the spectacle making centres in both the Netherlands and Germany. 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). This practical development, mastery, and experimentation with lenses led directly to the invention of the compound
optical microscope The optical microscope, also referred to as a light microscope, is a type of microscope A microscope (from the grc, μικρός, ''mikrós'', "small" and , ''skopeîn'', "to look" or "see") is a laboratory instrument used to examine ob ...
around 1595, and the
refracting telescope A refracting telescope (also called a refractor) is a type of optical telescope that uses a lens (optics), lens as its objective (optics), objective to form an image (also referred to a dioptrics, dioptric telescope). The refracting telescope de ...
in 1608, both of which appeared in the spectacle making centres in the Netherlands. 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 A pinhole camera is a simple camera without a lens but with a tiny aperture In optics, an aperture is a hole or an opening through which light travels. More specifically, the aperture and focal length of an optical system determine the cone ...

pinhole camera
s, inverse-square law governing the intensity of light, and the optical explanations of astronomical phenomena such as
lunar Lunar most commonly means "of or relating to the Moon The Moon is Earth's only natural satellite. At about one-quarter the diameter of Earth (comparable to the width of Australia (continent), Australia), it is the largest natural satellite ...

lunar
and
solar eclipse A solar eclipse occurs when a portion of the Earth Earth is the third planet from the Sun and the only astronomical object known to harbour and support life. 29.2% of Earth's surface is land consisting of continents and islands. The r ...

solar eclipse
s and astronomical
parallax Parallax is a displacement or difference in the apparent positionThe apparent place of an object Object may refer to: General meanings * Object (philosophy), a thing, being, or concept ** Entity, something that is tangible and within the ...

parallax
. He was also able to correctly deduce the role of the
retina The retina (from la, rete "net") is the innermost, light-sensitive layer of tissue of the eye Eyes are organs of the visual system. They provide living organisms with vision, the ability to receive and process visual detail, as well ...

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. 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 A refracting telescope (also called a refractor) is a type of optical telescope An optical telescope is a telescope that gathers and Focus (optics), focuses light, mainly from the Visible spectrum, visible part of the electromagnetic spectrum, ...
'', using two convex lenses to produce higher magnification. Optical theory progressed in the mid-17th century with
treatises A treatise is a Formality, formal and systematic written discourse on some subject, generally longer and treating it in greater depth than an essay, and more concerned with investigating or exposing the principles of the subject and its conclusio ...
written by philosopher
René Descartes René Descartes ( or ; ; Latinized Latinisation or Latinization can refer to: * Latinisation of names, the practice of rendering a non-Latin name in a Latin style * Latinisation in the Soviet Union, the campaign in the USSR during the 1920s ...

René Descartes
, which explained a variety of optical phenomena including reflection and refraction by assuming that light was emitted by objects which produced it. This differed substantively from the ancient Greek emission theory. In the late 1660s and early 1670s,
Isaac Newton Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician A mathematician is someone who uses an extensive knowledge of mathematics Mathematics (from Greek: ) includes the study of such topics a ...

Isaac Newton
expanded Descartes' ideas into a corpuscle theory of light, famously determining that white light was a mix of colours that can be separated into its component parts with a
prism A prism An optical prism is a transparent optics, optical element with flat, polished surfaces that refraction, refract light. At least one surface must be angled—elements with two parallel surfaces are not prisms. The traditional geometrical ...

prism
. In 1690,
Christiaan Huygens Christiaan Huygens ( , also , ; la, Hugenius; 14 April 1629 – 8 July 1695), also spelled Huyghens, was a Dutch mathematician A mathematician is someone who uses an extensive knowledge of mathematics Mathematics (from Greek: ) i ...

Christiaan Huygens
proposed a
wave theory In historical linguistics Historical linguistics, also termed diachronic linguistics, is the scientific study of language change Language change is variation over time in a language A language is a structured system of communicatio ...
for light based on suggestions that had been made by
Robert Hooke Robert Hooke FRS FRS may also refer to: Government and politics * Facility Registry System, a centrally managed Environmental Protection Agency database that identifies places of environmental interest in the United States * Family Resources ...
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 ''Opticks: or, A Treatise of the Reflexions, Refractions, Inflexions and Colours of Light'' is a book by English natural philosopher Isaac Newton Sir Isaac Newton (25 December 1642 – 20 March Old Style and New Style dates, 1726/ ...

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. Newtonian optics was generally accepted until the early 19th century when and
Augustin-Jean Fresnel Augustin-Jean Fresnel ( or ; ; 10 May 1788 – 14 July 1827) was a French civil engineer A civil engineer is a person who practices civil engineering Civil engineering is a Regulation and licensure in engineering, professional engi ...
conducted experiments on the
interference Interference is the act of interfering, invading, or poaching. Interference may also refer to: Communications * Interference (communication), anything which alters, modifies, or disrupts a message * Adjacent-channel interference, caused by extran ...
of light that firmly established light's wave nature. Young's famous
double slit experiment In modern physics, the double-slit experiment is a demonstration that light and matter can display characteristics of both classically defined waves and particles; moreover, it displays the fundamentally probabilistic nature of quantum mechani ...
showed that light followed the
superposition principle The superposition principle, also known as superposition property, states that, for all linear system In systems theory Systems theory is the interdisciplinary study of systems, i.e. cohesive groups of interrelated, interdependent parts that ...
, 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. Wave optics was successfully unified with
electromagnetic theory Electromagnetism is a branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electric charge, electrically charged particles. The electromagnetic force is carried by electromagneti ...
by
James Clerk Maxwell James Clerk Maxwell (13 June 1831 – 5 November 1879) was a Scottish mathematician A mathematician is someone who uses an extensive knowledge of mathematics Mathematics (from Greek: ) includes the study of such topics as num ...

James Clerk Maxwell
in the 1860s. The next development in optical theory came in 1899 when
Max Planck Max Karl Ernst Ludwig Planck, (; ; 23 April 1858 – 4 October 1947) was a Germans, German theoretical physicist whose discovery of quantum mechanics, energy quanta won him the Nobel Prize in Physics in 1918. Planck made many substantial co ...

Max Planck
correctly modelled
blackbody radiation ) of black-body radiation scales inversely with the temperature of the black body; the locus of such colors, shown here in CIE 1931 ''x,y'' space, is known as the Planckian locus. Black-body radiation is the thermal radiation, thermal electrom ...

blackbody radiation
by assuming that the exchange of energy between light and matter only occurred in discrete amounts he called ''quanta''. In 1905,
Albert Einstein Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest physicists of all time. Einstein is known for developing the theory of relativity The theo ...

Albert Einstein
published the theory of the
photoelectric effect The photoelectric effect is the emission of electron The electron is a subatomic particle In physical sciences, subatomic particles are smaller than atom An atom is the smallest unit of ordinary matter In classical physics and ...

photoelectric effect
that firmly established the quantization of light itself. In 1913,
Niels Bohr Niels Henrik David Bohr (; 7 October 1885 – 18 November 1962) was a Danish Danish may refer to: * Something of, from, or related to the country of Denmark * A national or citizen of Denmark, also called a "Dane", see Demographics of D ...

Niels Bohr
showed that atoms could only emit discrete amounts of energy, thus explaining the discrete lines seen in emission and
absorption spectra Absorption may refer to: Chemistry and biology *Absorption (chemistry), diffusion of particles of gas or liquid into liquid or solid materials *Absorption (skin), a route by which substances enter the body through the skin *Absorption (pharmacolo ...
. The understanding of the interaction between light and matter that followed from these developments not only formed the basis of quantum optics but also was crucial for the
development Development or developing may refer to: Arts *Development hell, when a project is stuck in development *Filmmaking#Development, Filmmaking, development phase, including finance and budgeting *Development (music), the process thematic material i ...
of quantum mechanics as a whole. The ultimate culmination, the theory of
quantum electrodynamics In particle physics, quantum electrodynamics (QED) is the relativity theory, relativistic quantum field theory of electrodynamics. In essence, it describes how light and matter interact and is the first theory where full agreement between quantum m ...
, explains all optics and electromagnetic processes in general as the result of the exchange of real and virtual photons. Quantum optics gained practical importance with the inventions of the
maser (see description below) A maser (, an acronym for microwave amplification by stimulated emission of radiation) is a device that produces coherence (physics), coherent electromagnetic waves through amplification by stimulated emission. The firs ...

maser
in 1953 and of the laser in 1960. Following the work of
Paul Dirac Paul Adrien Maurice Dirac (; 8 August 1902 – 20 October 1984) was an English theoretical physicist who is regarded as one of the most significant physicists of the 20th century. Dirac made fundamental contributions to the early develop ...

Paul Dirac
in
quantum field theory In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and ...
,
George Sudarshan Ennackal Chandy George Sudarshan (also known as E. C. G. Sudarshan; 16 September 1931 – 14 May 2018) was an Indian-American theoretical physicist A physicist is a scientist A scientist is a person who conducts Scientific method, scien ...
, Roy J. Glauber, and
Leonard Mandel Leonard Mandel (May 9, 1927 – February 9, 2001) was the Lee DuBridge Professor Emeritus of Physics and Optics at the University of Rochester when he died at the age of 73 at his home in Pittsford (village), New York, Pittsford, New York. He contri ...
applied quantum theory to the electromagnetic field in the 1950s and 1960s to gain a more detailed understanding of photodetection and the
statistics Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data Data (; ) are individual facts, statistics, or items of information, often numeric. In a more technical sens ...
of light.


Classical optics

Classical optics is divided into two main branches: geometrical (or ray) optics and physical (or wave) optics. In geometrical optics, light is considered to travel in straight lines, while in physical optics, light is considered as an electromagnetic wave. Geometrical optics can be viewed as an approximation of physical optics that applies when the wavelength of the light used is much smaller than the size of the optical elements in the system being modelled.


Geometrical optics

''Geometrical optics'', or ''ray optics'', describes the 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. These laws were discovered empirically as far back as 984 AD and have been used in the design of optical components and instruments from then until the present day. They can be summarised as follows: When a ray of light hits the boundary between two transparent materials, it is divided into a reflected and a refracted ray. :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. :The law of refraction says that the refracted ray lies in the plane of incidence, and the sine of the angle of incidence divided by the sine of the angle of refraction is a constant: ::\frac = n, where is a constant for any two materials and a given colour of light. If the first material is air or vacuum, is the
refractive index In optics Optics is the branch of physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or ...

refractive index
of the second material. The laws of reflection and refraction can be derived from
Fermat's principle Fermat's principle, also known as the principle of least time, is the link between ray optics and wave optics. In its original "strong" form, Fermat's principle states that the path taken by a ray between two given points is the path ...
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.''


Approximations

Geometric optics is often simplified by making the
paraxial approximation In geometric optics, the paraxial approximation is a small-angle approximation used in Gaussian optics and Ray tracing (physics), ray tracing of light through an optical system (such as a lens (optics), lens). A paraxial ray is a Ray (optics), r ...
, 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 Gaussian optics is a technique in geometrical optics Geometrical optics, or ray optics, is a model of optics Optics is the branch of physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of na ...
and ''paraxial ray tracing'', which are used to find basic properties of optical systems, such as approximate
image An image (from la, imago) is an artifact that depicts visual perception Visual perception is the ability to interpret the surrounding environment (biophysical), environment through photopic vision (daytime vision), color vision, sco ...

image
and object positions and
magnification Magnification is the process of enlarging the apparent size, not physical size, of something. This enlargement is quantified by a calculated number also called "magnification". When this number is less than one, it refers to a reduction in size, ...
s.


Reflections

Reflections can be divided into two types:
specular reflection Reflections on still water are an example of specular reflection. Specular reflection, or regular reflection, is the mirror-like reflection of waves, such as light Light or visible light is electromagnetic radiation within the portion of ...
and
diffuse reflection Diffuse reflection is the reflectionReflection or reflexion may refer to: Philosophy * Self-reflection Science * Reflection (physics), a common wave phenomenon ** Specular reflection, reflection from a smooth surface *** Mirror image, a reflec ...

diffuse reflection
. Specular reflection describes the gloss of surfaces such as mirrors, which reflect light in a simple, predictable way. This allows for the production of reflected images that can be associated with an actual (
real Real may refer to: * Reality Reality is the sum or aggregate of all that is real or existent within a system, as opposed to that which is only Object of the mind, imaginary. The term is also used to refer to the ontological status of things, ind ...

real
) or extrapolated () location in space. Diffuse reflection describes non-glossy 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 In optics Optics is the branch of physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies matter, its Motion (physics ...
, which describes surfaces that have equal
luminance Luminance is a photometricPhotometry can refer to: * Photometry (optics), the science of measurement of visible light in terms of its perceived brightness to human vision * Photometry (astronomy), the measurement of the flux or intensity of an ...

luminance
when viewed from any angle. Glossy surfaces can give both specular and diffuse reflection. In specular reflection, the direction of the reflected ray is determined by the angle the incident ray makes with the
surface normal In geometry Geometry (from the grc, γεωμετρία; ' "earth", ' "measurement") is, with , one of the oldest branches of . It is concerned with properties of space that are related with distance, shape, size, and relative position ...

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. This is known as the
Law of Reflection Image:Tso Kiagar Lake Ladakh.jpg, Reflections on still water are an example of specular reflection. Specular reflection, or regular reflection, is the mirror-like reflection (physics), reflection of waves, such as light, from a surface. The la ...
. For , 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 A mirror image (in a plane mirror) is a reflected duplication of an object that appears almost identical, but is reversed in the direction perpendicular to the mirror surface. As an optical Optics is the branch of physics Physics is ...

mirror image
s are 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 A corner reflector is a retroreflector consisting of three mutually perpendicular, intersection (Euclidean geometry), intersecting flat surfaces, which reflects waves directly towards the source, but Translation (geometry), translated. The three ...

Corner reflector
s produce reflected rays that travel back in the direction from which the incident rays came. This is called retroreflection. Mirrors with curved surfaces can be modelled by ray tracing and using the law of reflection at each point on the surface. For mirrors with parabolic surfaces, parallel rays incident on the mirror produce reflected rays that converge at a common
focus Focus, FOCUS, or foci may refer to: Arts * Focus or Focus Festival, former name of the Adelaide Fringe The Adelaide Fringe, formerly Adelaide Fringe Festival, is the world's second-largest annual arts festival (after the Edinburgh Festival ...
. 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 Spherical aberration (SA) is a type of aberration found in optical systems that use elements with spherical surfaces. Lenses and curved mirrors are most often made with surfaces that are spherical, because this shape is easier to form than non ...

spherical aberration
. Curved mirrors can form images with a 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.


Refractions

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 Interface or interfacing may refer to: Academic journals * Interface (journal), ''Interface'' (journal), by the Electrochemical Society * ''Interface, Journal of Applied Linguistics'', now merged with ''ITL International Journal of Applied Lin ...
between a uniform medium with index of refraction n_1 and another medium with index of refraction n_2. In such situations,
Snell's Law of light at the interface between two media of different refractive index, refractive indices, with n2 > n1. Since the velocity is lower in the second medium (v2 < v1), the angle of refraction θ2 is less than the angle of in ...

Snell's Law
describes the resulting deflection of the light ray: :n_1\sin\theta_1 = n_2\sin\theta_2\ where \theta_1 and \theta_2 are the angles between the normal (to the interface) and the incident and refracted waves, respectively. The index of refraction of a medium is related to the speed, , of light in that medium by :n=c/v, where is the
speed of light in vacuum The speed of light in vacuum A vacuum is space devoid of matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched are ult ...
. 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. In most materials, the index of refraction varies with the frequency of the light. Taking this into account, Snell's Law can be used to predict how a prism will disperse light into a spectrum. The discovery of this phenomenon when passing light through a prism is famously attributed to Isaac Newton. Some media have an index of refraction which varies gradually with position and, therefore, light rays in the medium are curved. This effect is responsible for
mirage A mirage is a naturally-occurring in which light rays bend via to produce a displaced image of distant objects or the sky. The word comes to via the ''(se) mirer'', from the ''mirari'', meaning "to look at, to wonder at". Mirages can be c ...

mirage
s seen on hot days: a change in index of refraction air with height causes light rays to bend, creating the appearance of specular reflections in the distance (as if on the surface of a pool of water). Optical materials with varying indexes of refraction are called gradient-index (GRIN) materials. Such materials are used to make gradient-index optics. For light rays travelling from a material with a high index of refraction to a material with a low index of refraction, Snell's law predicts that there is no \theta_2 when \theta_1 is large. In this case, no transmission occurs; all the light is reflected. This phenomenon is called
total internal reflection Total internal reflection (TIR) is the optical phenomenon Optical phenomena are any observable events that result from the interaction of light Light or visible light is electromagnetic radiation within the portion of the electromagnetic s ...

total internal reflection
and allows for fibre optics technology. As light travels down an optical fibre, it undergoes total internal reflection allowing for essentially no light to be lost over the length of the cable.


=Lenses

= A device that produces converging or diverging light rays due to refraction is known as a ''lens''. Lenses are characterized by their
focal length The focal length of an optical Optics is the branch of physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space ...

focal length
: a converging lens has positive focal length, while a diverging lens has negative focal length. Smaller focal length indicates that the lens has a stronger converging or diverging effect. The focal length of a simple lens in air is given by the
lensmaker's equation A lens is a transmissive optics, optical device which focuses or disperses a light beam by means of refraction. A simple lens consists of a single piece of transparent material, while a #Compound lenses, compound lens consists of several simp ...
. Chapters 5 & 6. Ray tracing can be used to show how images are formed by a lens. For a
thin lens A lens may be considered a thin lens if its thickness is much less than the radii of curvature of its surfaces ( and )., 300px In optics, a thin lens is a lens (optics), lens with a thickness (distance along the optical axis between the two surfa ...
in air, the location of the image is given by the simple equation :\frac + \frac = \frac , where S_1 is the distance from the object to the lens, S_2 is the distance from the lens to the image, and f is the focal length of the lens. In the
sign conventionIn physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies matter, its Motion (physics), motion and behavior through Spac ...
used here, the object and image distances are positive if the object and image are on opposite sides of the lens. Incoming parallel rays are focused by a converging lens onto a spot one focal length from the lens, on the far side of the lens. This is called the rear focal point of the lens. Rays from an object at a 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 diverging lenses, incoming parallel rays diverge after going through the lens, in such a way that they seem to have originated at a spot one focal length in front of the lens. This is the lens's front focal point. Rays from an object at a finite distance are associated with a virtual image that is closer to the lens than the focal point, 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. As with mirrors, upright images produced by a single lens are virtual, while inverted images are real. Lenses suffer from aberrations that distort images. ''Monochromatic aberrations'' occur because the geometry of the lens does not perfectly direct rays from each object point to a single point on the image, while
chromatic aberration In optics Optics is the branch of that studies the behaviour and properties of , including its interactions with and the construction of that use or it. Optics usually describes the behaviour of , , and light. Because light is an , oth ...

chromatic aberration
occurs because the index of refraction of the lens varies with the wavelength of the light.


Physical optics

In physical optics, light is considered to propagate as a wave. This model predicts phenomena such as interference and diffraction, which are not explained by geometric optics. The
speed of light The speed of light in vacuum A vacuum is a space Space is the boundless three-dimensional Three-dimensional space (also: 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called paramet ...
waves in
air The atmosphere of Earth is the layer of gas Gas is one of the four fundamental states of matter In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (ph ...

air
is approximately 3.0×108 m/s (exactly 299,792,458 m/s in
vacuum A vacuum is a space Space is the boundless three-dimensional Three-dimensional space (also: 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called parameter A parameter (from the Ancient Gr ...

vacuum
). The
wavelength In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular su ...

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). 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. The existence of electromagnetic waves was predicted in 1865 by
Maxwell's equations Maxwell's equations are a set of coupled partial differential equation In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), ...
. 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. Light waves are now generally treated as electromagnetic waves except when quantum mechanical effects have to be considered.


Modelling and design of optical systems using physical optics

Many simplified approximations are available for analysing and designing optical systems. Most of these use a single
scalar Scalar may refer to: *Scalar (mathematics), an element of a field, which is used to define a vector space, usually the field of real numbers *Scalar (physics), a physical quantity that can be described by a single element of a number field such as ...
quantity to represent the electric field of the light wave, rather than using a
vector Vector may refer to: Biology *Vector (epidemiology) In epidemiology Epidemiology is the study and analysis of the distribution (who, when, and where), patterns and risk factor, determinants of health and disease conditions in defined pop ...
model with orthogonal electric and magnetic vectors.M. Born and E. Wolf (1999). ''Principle of Optics''. Cambridge: Cambridge University Press. . The Huygens–Fresnel equation is one such model. This was derived empirically by Fresnel in 1815, based on Huygens' hypothesis that each point on a wavefront generates a secondary spherical wavefront, which Fresnel combined with the principle of superposition of waves. The , 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 articles on diffraction and
Fraunhofer diffraction In optics, the Fraunhofer diffraction equation is used to model the diffraction of waves when the diffraction pattern is viewed at a long distance from the diffracting object (in the far-field region), and also when it is viewed at the focal plan ...
. More rigorous models, involving the modelling of both electric and magnetic fields of the light wave, are required when dealing with materials whose electric and magnetic properties affect the interaction of light with the material. 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. Numerical modeling techniques such as the
finite element method The finite element method (FEM) is a widely used method for numerically solving differential equations In mathematics, a differential equation is an equation In mathematics, an equation is a statement that asserts the equality (mathematics) ...
, the
boundary element method The boundary element method (BEM) is a numerical computational method of solving linear partial differential equations which have been formulated as integral equations (i.e. in ''boundary integral'' form), including fluid mechanics, acoustics, ele ...
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. All of the results from geometrical optics can be recovered using the techniques of
Fourier opticsFourier optics is the study of classical optics Optics is the branch of physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that ...
which apply many of the same mathematical and analytical techniques used in
acoustic engineering Acoustical engineering (also known as acoustic engineering) is the branch of engineering dealing with sound and oscillation, vibration. It includes the application of acoustics, the science of sound and vibration, in technology. Acoustical engineers ...
and
signal processing Signal processing is an electrical engineering Electrical engineering is an engineering discipline concerned with the study, design, and application of equipment, devices, and systems which use electricity, electronics, and electromagnetis ...

signal processing
. 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.


Superposition and interference

In the absence of
nonlinear In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). I ...
effects, the superposition principle can be used to predict the shape of interacting waveforms through the simple addition of the disturbances. 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 Phase or phases may refer to: Science * State of matter, or phase, one of the distinct forms in which matter can exist *Phase (matter) In the physical sciences, a phase is a region of space (a thermodynamic system A thermodynamic system is a ...
'', both the wave crests and wave troughs align. This results in
constructive interference In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies matter, its Motion (physics), motion and behavior throug ...

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 In physics, interference is a phenomenon in which two waves Superposition principle, superpose to form a resultant wave of greater, lower, or the same amplitude. Constructive and destructive interference result from the interaction of waves tha ...

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.Chapter 37 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.
Interferometry Interferometry is a technique which uses the ''interference Interference is the act of interfering, invading, or poaching. Interference may also refer to: Communications * Interference (communication), anything which alters, modifies, or dis ...
is the science of measuring these patterns, usually as a means of making precise determinations of distances or
angular resolution Angular resolution describes the ability of any image-forming device In optics, an image-forming optical system is a system capable of being used for Image, imaging. The diameter of the aperture of the main objective is a common criterion for c ...

angular resolution
s. The
Michelson interferometer 300px, Figure 1. A basic Michelson interferometer, not including the optical source and detector. The Michelson interferometer is a common configuration for optical interferometry and was invented by Albert Abraham Michelson. Using a beam splitter, ...

Michelson interferometer
was a famous instrument which used interference effects to accurately measure the speed of light. The appearance of thin films and coatings is directly affected by interference effects.
Antireflective coating An antireflective or anti-reflection (AR) coating is a type of optical coating applied to the surface of lens A lens is a transmissive optical device that focuses or disperses a light beam by means of refraction. A simple lens consists ...
s use destructive interference to reduce the reflectivity of the surfaces they coat, and can be used to minimise glare and unwanted reflections. The simplest case is a single layer with a thickness of one-fourth the wavelength of incident light. The reflected wave from the top of the film and the reflected wave from the film/material interface are then exactly 180° out of phase, causing destructive interference. The waves are only exactly out of phase for one wavelength, which would typically be chosen to be near the centre of the visible spectrum, around 550 nm. More complex designs using multiple layers can achieve low reflectivity over a broad band, or extremely low reflectivity at a single wavelength. Constructive interference in thin films can create a strong reflection of light in a range of wavelengths, which can be narrow or broad depending on the design of the coating. These films are used to make
dielectric mirror A dielectric mirror, also known as a Bragg mirror, is a type of mirror composed of multiple thin film, thin layers of dielectric material, typically deposited on a substrate of glass or some other optical material. By careful choice of the type a ...
s,
interference filter Band-pass interference filter for laser experiments An interference filter or dichroic filter is an optical filter that reflects one or more spectral bands or lines and transmits others, while maintaining a nearly zero coefficient of absorption (opt ...
s, heat reflectors, and filters for colour separation in
colour television Color (American English American English (AmE, AE, AmEng, USEng, en-US), sometimes called United States English or U.S. English, is the set of varieties of the English language native to the United States. Currently, American English ...
cameras. This interference effect is also what causes the colourful rainbow patterns seen in oil slicks.


Diffraction and optical resolution

Diffraction is the process by which light interference is most commonly observed. The effect was first described in 1665 by
Francesco Maria Grimaldi Francesco Maria Grimaldi (2 April 1618 – 28 December 1663) was an Italian Italian may refer to: * Anything of, from, or related to the country and nation of Italy ** Italians, an ethnic group or simply a citizen of the Italian Republic ** Itali ...

Francesco Maria Grimaldi
, who also coined the term from the Latin ''diffringere'', 'to break into pieces'. Later that century, Robert Hooke and Isaac Newton also described phenomena now known to be diffraction in Newton's rings while James Gregory recorded his observations of diffraction patterns from bird feathers. The first physical optics model of diffraction that relied on the Huygens–Fresnel principle was developed in 1803 by Thomas Young in 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. In 1815 and 1818, Augustin-Jean Fresnel firmly established the mathematics of how wave interference can account for diffraction. 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 :m \lambda = d \sin \theta where d is the separation between two wavefront sources (in the case of Young's experiments, it was two slits), \theta is the angular separation between the central fringe and the mth order fringe, where the central maximum is m = 0.Chapter 38 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 In optics, a diffraction grating is an optical component with a periodic structure that diffraction, diffracts light into several beams travelling in different directions (i.e., different diffraction angles). The emerging coloration is a form ...

diffraction grating
that contains a large number of slits at equal spacing. More complicated models of diffraction require working with the mathematics of
Fresnel Augustin-Jean Fresnel ( or ; ; 10 May 1788 – 14 July 1827) was a French civil engineer A civil engineer is a person who practices civil engineering Civil engineering is a Regulation and licensure in engineering, professional engi ...

Fresnel
or Fraunhofer diffraction.
X-ray diffraction X-ray crystallography (XRC) is the experimental science determining the atomic and molecular structure of a crystal A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a ...
makes use of the fact that atoms in a
crystal A crystal or crystalline solid is a solid Solid is one of the four fundamental states of matter (the others being liquid A liquid is a nearly incompressible fluid In physics, a fluid is a substance that continually Deformatio ...

crystal
have regular spacing at distances that are on the order of one
angstrom The angstromEntry "angstrom" in the Oxford online dictionary. Retrieved on 2019-03-02 from https://en.oxforddictionaries.com/definition/angstrom.Entry "angstrom" in the Merriam-Webster online dictionary. Retrieved on 2019-03-02 from https://www.m ...

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 In physics, Bragg's law, Wulff–Bragg's condition or Laue-Bragg interference, a special case of Laue diffraction, gives the angles for coherent scattering of waves from a crystal lattice. It encompasses the superposition of wave fronts scattered by ...
, with the associated bright spots occurring in unique patterns and d being twice the spacing between atoms. Diffraction effects limit the ability of an optical detector to optically resolve separate light sources. In general, light that is passing through an
aperture In optics, an aperture is a hole or an opening through which light travels. More specifically, the aperture and focal length of an optical system determine the cone angle of a bundle of ray (optics), rays that come to a focus (optics), focus ...

aperture
will experience diffraction and the best images that can be created (as described in diffraction-limited optics) appear as a central spot with surrounding bright rings, separated by dark nulls; this pattern is known as an
Airy pattern A computer-generated Airy disk from diffracted white light ( D65 spectrum). Note that the red component is diffracted more than the blue, so that the center appears slightly bluish. In optics Optics is the branch of physics Physics (f ...

Airy pattern
, and the central bright lobe as an
Airy disk A computer-generated Airy disk from diffracted white light ( D65 spectrum). Note that the red component is diffracted more than the blue, so that the center appears slightly bluish. In optics Optics is the branch of physics Physics (f ...
. The size of such a disk is given by : \sin \theta = 1.22 \frac where ''θ'' is the angular resolution, ''λ'' is the wavelength of the light, and ''D'' is the
diameter In geometry Geometry (from the grc, γεωμετρία; ' "earth", ' "measurement") is, with , one of the oldest branches of . It is concerned with properties of space that are related with distance, shape, size, and relative position ...

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. Rayleigh defined the somewhat arbitrary "
Rayleigh criterion Angular resolution describes the ability of any image-forming device such as an optical or radio telescope A radio telescope is a specialized antenna and radio receiver radio in the 1940s. During the golden age of radio, 1925–1955, fa ...
" 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.
Interferometry Interferometry is a technique which uses the ''interference Interference is the act of interfering, invading, or poaching. Interference may also refer to: Communications * Interference (communication), anything which alters, modifies, or dis ...
, with its ability to mimic extremely large baseline apertures, allows for the greatest angular resolution possible. For astronomical imaging, the atmosphere prevents optimal resolution from being achieved in the visible spectrum due to the atmospheric
scattering Scattering is a term used in physics to describe a wide range of physical processes where moving particles or radiation of some form, such as light Light or visible light is electromagnetic radiation within the portion of the electromagnetic ...

scattering
and dispersion which cause stars to
twinkle Twinkle may refer to: * Twinkling, the variation of brightness of distant objects People * Twinkle (singer) (1948–2015), born Lynn Annette Ripley, English singer-songwriter * Twinkle Khanna, Indian movie actress * Twinkle Bajpai, female conte ...
. Astronomers refer to this effect as the quality of
astronomical seeing Astronomy (from el, ἀστρονομία, literally meaning the science that studies the laws of the stars) is a natural science that studies astronomical object, celestial objects and celestial event, phenomena. It uses mathematics, physi ...
. Techniques known as
adaptive optics Adaptive optics (AO) is a technology used to improve the performance of optical systems by reducing the effect of incoming wavefront In physics, the wavefront of a time-varying field is the set (locus Locus (plural loci) is Latin for "place ...

adaptive optics
have been used to eliminate the atmospheric disruption of images and achieve results that approach the diffraction limit.


Dispersion and scattering

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 Thomson scattering is the elastic scattering of electromagnetic radiation In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural sc ...
which occurs when electromagnetic waves are deflected by single particles. In the limit of Thomson scattering, in which the wavelike nature of light is evident, light is dispersed independent of the frequency, in contrast to
Compton scattering Compton scattering, discovered by Arthur Holly Compton Arthur Holly Compton (September 10, 1892 – March 15, 1962) was an American physicist who won the Nobel Prize in Physics in 1927 for his 1923 discovery of the Compton effect, whic ...

Compton scattering
which is frequency-dependent and strictly a
quantum mechanical Quantum mechanics is a fundamental theory A theory is a rational Rationality is the quality or state of being rational – that is, being based on or agreeable to reason Reason is the capacity of consciously making sense of things, ...
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 Rayleigh scattering ( ), named after the nineteenth-century British physicist Lord Rayleigh (John William Strutt), is the predominantly elastic scattering of light or other electromagnetic radiation by particles much smaller than the wavelength o ...

Rayleigh scattering
while the similar process for scattering by particles that are similar or larger in wavelength is known as
Mie scattering The Mie solution to Maxwell's equations Maxwell's equations are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric cir ...

Mie scattering
with the being a commonly observed result. A small proportion of light scattering from atoms or molecules may undergo
Raman scattering#REDIRECT Raman scattering Raman scattering or the Raman effect () is the inelastic scattering of photon The photon (Greek: φῶς, phōs, light) is a type of elementary particle. It is the quantum of the electromagnetic field including ele ...

Raman scattering
, wherein the frequency changes due to excitation of the atoms and molecules.
Brillouin scatteringBrillouin scattering (also known as Brillouin light scattering or BLS), named after Léon Brillouin, refers to the interaction of light Light or visible light is electromagnetic radiation within the portion of the electromagnetic spectrum that ...

Brillouin scattering
occurs when the frequency of light changes due to local changes with time and movements of a dense material. Dispersion occurs when different frequencies of light have different
phase velocities in groups of gravity waves on the surface of deep water. The red square moves with the phase velocity, and the       green circles propagate with the group velocity. In this deep-water case, ''the phase velocity is twice th ...

phase velocities
, due either to material properties (''material dispersion'') or to the geometry of an
optical waveguide An optical waveguide is a physical structure that guides electromagnetic waves In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural ...
(''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 , in wavelength ranges where the material does not absorb light. In wavelength ranges where a medium has significant absorption, the index of refraction can increase with wavelength. This is called "anomalous dispersion". 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 A rainbow is a meteorological Meteorology is a branch of the atmospheric sciences which includes atmospheric chemistry and atmospheric physics, with a major focus on weather forecasting Weather forecasting is the application of sc ...

rainbow
pattern. Material dispersion is often characterised by the
Abbe number In optics and lens design, the Abbe number, also known as the V-number or constringence of a Transparency (optics), transparent material, is an approximate measure of the material's dispersion (optics), dispersion (change of refractive index versus ...
, 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 The propagation constant of a sinusoidal electromagnetic wave Electromagnetism is a branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electric charge, electrically charged pa ...
. 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: :D = \frac \frac where v_g is the group velocity. For a uniform medium, the group velocity is :v_g = c \left( n - \lambda \frac \right)^ where ''n'' is the index of refraction and ''c'' is the speed of light in a vacuum. This gives a simpler form for the dispersion delay parameter: :D = - \frac \, \frac. 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 A chirp is a signal In signal processing Signal processing is an electrical engineering subfield that focuses on analysing, modifying, and synthesizing signals such as audio signal processing, sound, image processing, images, and scie ...

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. 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 An optical fiber (or fibre in British English British English (BrE) is the standard dialect A standard language (also standard variety, standard dialect, and standard) is a language variety that has undergone substantial codificati ...

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.


Polarization

Polarization is a general property of waves that describes the orientation of their oscillations. For
transverse wave In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and forc ...

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 In electrodynamics, linear polarization or plane polarization of electromagnetic radiation is a confinement of the electric field vector or magnetic field A magnetic field is a vector field that describes the magnetic influence on movin ...
), or the oscillation direction may rotate as the wave travels (
circular Circular may refer to: * The shape of a circle * Circular (album), ''Circular'' (album), a 2006 album by Spanish singer Vega * Circular letter (disambiguation) ** Flyer (pamphlet), a form of advertisement * Circular reasoning, a type of logical fa ...
or
elliptical polarization In electrodynamics Electromagnetism is a branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electric charge, electrically charged particles. The electromagnetic force is carri ...
). 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
chirality Chirality is a property of asymmetry Asymmetry is the absence of, or a violation of, symmetry (the property of an object being invariant to a transformation, such as reflection). Symmetry is an important property of both physical and abstrac ...

chirality
.Chapter 34 The typical way to consider polarization is to keep track of the orientation of the electric field
vector Vector may refer to: Biology *Vector (epidemiology) In epidemiology Epidemiology is the study and analysis of the distribution (who, when, and where), patterns and risk factor, determinants of health and disease conditions in defined pop ...
as the electromagnetic wave propagates. The electric field vector of a plane wave may be arbitrarily divided into two perpendicular
components Component may refer to: In engineering, science, and technology Generic systems *System A system is a group of Interaction, interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounde ...

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''. 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.
''Linear''
''Circular''
''Elliptical polarization''
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. 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''. 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.


=Changing polarization

= Media that have different indexes of refraction for different polarization modes are called ''birefringence, birefringent''. Well known manifestations of this effect appear in optical wave plates/retarders (linear modes) and in Faraday rotation/optical rotation (circular modes). 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 microscopes. Additionally, many plastics that are not normally birefringent will become so when subject to mechanical stress, a phenomenon which is the basis of photoelasticity. Non-birefringent methods, to rotate the linear polarization of light beams, include the use of prismatic polarization rotators which use total internal reflection in a prism set designed for efficient collinear transmission. Media that reduce the amplitude of certain polarization modes are called ''dichroic'', with devices that block nearly all of the radiation in one mode known as ''polarizing filters'' or simply "polarisers". 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 : I = I_0 \cos^2 \theta_i \quad , where :''I''0 is the initial intensity, :and ''θi'' is the angle between the light's initial polarization direction and the axis of the polariser. 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 \cos^2 \theta is 1/2, the transmission coefficient becomes : \frac = \frac \quad 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. 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 the angle of incidence and the angle of refraction. In this way, physical optics recovers Brewster's angle. 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.


=Natural light

= 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. 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.


Modern optics

''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 photomultipliers and channeltrons, respond to individual photons. Electronic image sensors, such as Charge-coupled device, CCDs, exhibit shot noise corresponding to the statistics of individual photon events. Light-emitting diodes and photovoltaic cells, too, cannot be understood without quantum mechanics. In the study of these devices, quantum optics often overlaps with quantum electronics. Specialty areas of optics research include the study of how light interacts with specific materials as in crystal optics and metamaterials. 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 engineers have taken an interest in integrated optics, machine vision, and photonic computing as possible components of the "next generation" of computers. 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. A professional community of researchers in nonlinear optics has developed in the last several decades due to advances in laser technology.


Lasers

A laser is a device that emits light, a kind of electromagnetic radiation, through a process called ''stimulated emission''. The term ''laser'' is an acronym for ''Light Amplification by Stimulated Emission of Radiation''. 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 lenses. 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''. The first working laser was demonstrated on 16 May 1960 by Theodore Maiman at Hughes Research Laboratories. When first invented, they were called "a solution looking for a problem". Since then, lasers have become a multibillion-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. 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. 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 pointers. 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, bubblegrams, laser lighting display, laser light shows, and laser hair removal.


Kapitsa–Dirac effect

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).


Applications

Optics is part of everyday life. The ubiquity of visual systems 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 mirages are examples of optical phenomena. Optical communication provides the backbone for both the Internet and modern telephony.


Human eye

The human eye functions by focusing light onto a layer of photoreceptor cells 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. There are two types of photoreceptor cells, rods and cones, which are sensitive to different aspects of light. 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. 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. Ciliary muscles 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. Optometrists, ophthalmologists, and opticians usually consider an appropriate near point to be closer than normal reading distance—approximately 25 cm. 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 (eye), 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. All of these conditions can be corrected using corrective lenses. 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. The optical power of corrective lenses is measured in diopters, a value equal to the multiplicative inverse, reciprocal of the focal length measured in metres; 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.


Visual effects

Optical illusions (also called visual illusions) are characterized by 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 inferences. 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 illusions 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 images with artistic perspective. 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. 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''. 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 illusions. 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 patterns, while the superimposition of periodic transparent patterns comprising parallel opaque lines or curves produces line moiré patterns.


Optical instruments

Single lenses have a variety of applications including photographic lenses, corrective lenses, and magnifying glasses while single mirrors are used in parabolic reflectors and rear-view mirrors. 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 microscope and the telescope which were both invented by the Dutch in the late 16th century. 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. 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. The first telescopes, called refracting telescopes, 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 the 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. Since crafting large lenses is much more difficult than crafting large mirrors, most modern telescopes are ''reflecting telescopes'', 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.


Photography

The optics of photography involves both 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 :Exposure ∝ ApertureArea × ExposureTime × SceneLuminance 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. A camera's aperture is measured by a unitless number called the f-number or f-stop, #, often notated as N, and given by :f/\# = N = \frac fD \ where f is the focal length, and D is the diameter of the entrance pupil. By convention, "#" is treated as a single symbol, and specific values of # 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. 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: * Normal lens: angle of view of about 50° (called ''normal'' because this angle considered roughly equivalent to human vision) and a focal length approximately equal to the diagonal of the film or sensor. * Wide-angle lens: angle of view wider than 60° and focal length shorter than a normal lens. * 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. 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. Modern zoom lenses may have some or all of these attributes. 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). 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. 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.


Atmospheric optics

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, afterglows, Corona (meteorology), coronas, Crepuscular rays, rays of sunlight, and sun dogs. The variation in these kinds of phenomena is due to different particle sizes and geometries. Mirages 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". Rainbows 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.


See also

*Ion optics *List of publications in physics#Optics, Important publications in optics *List of optical topics


References

;Further reading * * * * * *


External links

;Relevant discussions * ;Textbooks and tutorials
Light and Matter
– an open-source textbook, containing a treatment of optics in ch. 28-32
Optics2001
– Optics library and community
Fundamental Optics
– Melles Griot Technical Guide
Physics of Light and Optics
– Brigham Young University Undergraduate Book
Optics for PV
– a step-by-step introduction to classical optics ;Wikibooks modules * b:Physics Study Guide/Optics, Physics Study Guide/Optics * b:Optics, Optics ;Further reading
Optics and photonics: Physics enhancing our lives
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;Societies * European Optical Society
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* The Optical Society (OSA)
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* SPIE
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* European Photonics Industry Consortium
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