Editing Electromagnetic radiation (section)

== Physics ==
[[File:VisibleEmrWavelengths.svg|thumb|The relative wavelengths of the electromagnetic waves of three different colours of [[Visible light|light]] (blue, green, and red) with a distance scale in micrometers along the x-axis]]

=== Properties ===

Electromagnetic radiation is produced by accelerating charged particles and can be naturally emitted,<ref name="Cloude">{{cite book |last1=Cloude |first1=Shane |url=https://books.google.com/books?id=8-NLj54dU2YC&q=%22electromagnetic+radiation%22+charges+accelerates&pg=PA28 |title=An Introduction to Electromagnetic Wave Propagation and Antennas |date=1995 |publisher=Springer Science and Business Media |isbn=978-0-387-91501-2 |pages=28–33}}</ref><ref name="Bettini">{{cite book |last1=Bettini |first1=Alessandro |url=https://books.google.com/books?id=Ip9xDQAAQBAJ&q=%22electromagnetic+waves%22+charges+accelerating&pg=PA95 |title=A Course in Classical Physics, Vol. 4 – Waves and Light |date=2016 |publisher=Springer |isbn=978-3-319-48329-0 |pages=95, 103}}</ref> as from the Sun and other celestial bodies, or artificially generated for various applications. The energy in electromagnetic waves is sometimes called [[radiant energy]].<ref>{{Cite news |title=What Is Electromagnetic Radiation? |url=https://www.livescience.com/38169-electromagnetism.html |url-status=live |archive-url=https://web.archive.org/web/20170904152301/https://www.livescience.com/38169-electromagnetism.html |archive-date=4 September 2017 |access-date=4 September 2017 |work=Live Science}}</ref><ref>{{Cite book |url={{google books |plainurl=y |id=AUriAAAAMAAJ|page=22}} |title=The Michigan Technic |date=1960 |publisher=UM Libraries |language=en}}</ref> The electromagnetic waves' energy does not need a propagating medium to travel through space; they move through a vacuum at the speed of light.<ref>{{Cite web |date=2016-08-10 |title=Anatomy of an Electromagnetic Wave |url=https://science.nasa.gov/ems/02_anatomy/ |access-date=2025-03-25 |website=NASA Science |language=en-US}}</ref>
[[File:Electromagneticwave3D.gif|thumb|Electromagnetic waves can be imagined as a self-propagating transverse oscillating wave of electric and magnetic fields. This 3D animation shows a plane linearly polarized wave propagating from left to right. The electric and magnetic fields in such a wave are in phase with each other, reaching minima and maxima together.]]

Electric and magnetic fields obey the properties of [[superposition principle|superposition]]. Thus, a field due to any particular particle or time-varying electric or magnetic field contributes to the fields present in the same space due to other causes. Further, as they are [[Vector (geometric)|vector]] fields, all magnetic and electric field vectors add together according to [[vector addition]].<ref>Purcell, p442: "Any number of electromagnetic waves can propagate through the same region without affecting one another. The field '''E''' at a space time point is the vector sum of the electric fields of the individual waves, and the same goes for '''B'''".</ref> For example, in optics two or more coherent light waves may interact and by constructive or destructive [[Interference (wave propagation)|interference]] yield a resultant irradiance deviating from the sum of the component irradiances of the individual light waves.<ref>{{Cite web|title=PV Performance Modeling Collaborative {{!}} Plane of Array (POA) Irradiance|url=https://pvpmc.sandia.gov/modeling-steps/1-weather-design-inputs/plane-of-array-poa-irradiance/|access-date=14 January 2022|language=en-US|archive-date=14 January 2022|archive-url=https://web.archive.org/web/20220114171617/https://pvpmc.sandia.gov/modeling-steps/1-weather-design-inputs/plane-of-array-poa-irradiance/|url-status=live}}</ref> The electromagnetic fields of light are not affected by traveling through static electric or magnetic fields in a linear medium such as a vacuum. However, in nonlinear media, such as some [[crystal]]s, interactions can occur between light and static electric and magnetic fields—these interactions include the [[Faraday effect]] and the [[Kerr effect]].<ref>{{cite journal|title=Experimental observation of relativistic nonlinear Thomson scattering|first1=Szu-yuan|last1=Chen|first2=Anatoly|last2=Maksimchuk|first3=Donald|last3=Umstadter|date=17 December 1998|journal=Nature|volume=396|issue=6712|pages=653–655|doi=10.1038/25303|arxiv=physics/9810036|bibcode=1998Natur.396..653C|s2cid=16080209}}</ref><ref name="crowther-1920">{{Cite book |last=Crowther |first=James Arnold |author-link=James Arnold Crowther |url={{google books|plainurl=y|id=iWe4AAAAIAAJ|page=5}} |title=The life and discoveries of Michael Faraday |date=1920 |publisher=Society for promoting Christian knowledge |pages=54–57 |access-date=15 June 2014}}</ref>

In [[refraction]], a wave crossing from one medium to another of different [[density]] alters its [[Velocity|speed and direction]] upon entering the new medium. The ratio of the refractive indices of the media determines the degree of refraction, and is summarized by [[Snell's law]]. Light of composite wavelengths (natural sunlight) disperses into a visible [[electromagnetic spectrum|spectrum]] passing through a prism, because of the wavelength-dependent [[refractive index]] of the [[Prism (optics)|prism]] material ([[Dispersion (optics)|dispersion]]); that is, each component wave within the composite light is bent a different amount.<ref>{{Cite journal|title=Prisms|url=https://www.spectroscopyonline.com/view/prisms|access-date=17 January 2021|journal=Spectroscopy|series=Spectroscopy-09-01-2008|date=September 2008|volume=23|issue=9|archive-date=22 January 2021|archive-url=https://web.archive.org/web/20210122044456/https://www.spectroscopyonline.com/view/prisms|url-status=live}}</ref>

EM radiation exhibits both wave properties and [[Subatomic particle|particle]] properties at the same time (known as [[wave–particle duality]]). Both wave and particle characteristics have been confirmed in many experiments. Wave characteristics are more apparent when EM radiation is measured over relatively large timescales and over large distances while particle characteristics are more evident when measuring small timescales and distances. For example, when electromagnetic radiation is absorbed by matter, particle-like properties will be more obvious when the average number of photons in the cube of the relevant wavelength is much smaller than 1. It is not so difficult to experimentally observe non-uniform deposition of energy when light is absorbed, however this alone is not evidence of "particulate" behavior. Rather, it reflects the quantum nature of ''matter''.<ref>{{cite web |url=http://www.qo.phy.auckland.ac.nz/talks/photoelectric.pdf|archive-url=https://web.archive.org/web/20070627171942/http://www.qo.phy.auckland.ac.nz/talks/photoelectric.pdf|url-status=dead|archive-date=27 June 2007|title=Einstein and the Photoelectric Effect |first=H. J. |last=Carmichael |publisher=Quantum Optics Theory Group, University of Auckland |access-date=22 December 2009}}</ref> A [[Quantum mechanics|quantum theory]] of the interaction between electromagnetic radiation and matter such as electrons is described by the theory of [[quantum electrodynamics]].

Electromagnetic waves can be [[Polarization (waves)|polarized]], reflected, refracted, or [[diffracted]], and can interfere with each other.<ref>{{Cite web |title=DATE |url=http://galileo.phys.virginia.edu/classes/usem/SciImg/home_files/introduction.htm |url-status=live |archive-url=https://web.archive.org/web/20150512060344/http://galileo.phys.virginia.edu/classes/usem/SciImg/home_files/introduction.htm |archive-date=12 May 2015 |access-date=4 September 2017 |website=galileo.phys.virginia.edu}}</ref><ref>{{Cite web |title=Physics – Waves |url=http://www-jcsu.jesus.cam.ac.uk/~rpc25/notes/physics/waves/waves.html |url-status=live |archive-url=https://web.archive.org/web/20170904153721/http://www-jcsu.jesus.cam.ac.uk/~rpc25/notes/physics/waves/waves.html |archive-date=4 September 2017 |access-date=4 September 2017 |website=www-jcsu.jesus.cam.ac.uk}}</ref><ref>{{Cite web |title=Wave Behaviors {{!}} Science Mission Directorate |url=https://science.nasa.gov/ems/03_behaviors |url-status=live |archive-url=https://web.archive.org/web/20170514053337/https://science.nasa.gov/ems/03_behaviors |archive-date=14 May 2017 |access-date=4 September 2017 |website=science.nasa.gov |date=10 August 2016 |language=en}}</ref> Some experiments display both the wave and particle natures of electromagnetic waves, such as the self-interference of a single [[photon]].<ref>{{cite journal|doi=10.1119/1.1737397|url=http://people.whitman.edu/~beckmk/QM/grangier/Thorn_ajp.pdf|title=Observing the quantum behavior of light in an undergraduate laboratory|year=2004|last1=Thorn|first1=J. J.|last2=Neel|first2=M. S.|last3=Donato|first3=V. W.|last4=Bergreen|first4=G. S.|last5=Davies|first5=R. E.|last6=Beck|first6=M.|journal=American Journal of Physics|volume=72|issue=9|pages=1210|bibcode=2004AmJPh..72.1210T|url-status=live|archive-url=https://web.archive.org/web/20160201214040/http://people.whitman.edu/~beckmk/QM/grangier/Thorn_ajp.pdf|archive-date=1 February 2016}}</ref> When a low intensity light is sent through an [[interferometer]] it will detected by a [[photomultiplier]] or other sensitive detector only along one arm of the device, consistent with particle properties, and yet the accumulated effect of many such detections will be interference consistent with wave properties.

=== Wave model ===

[[File:Circular.Polarization.Circularly.Polarized.Light Right.Handed.Animation.305x190.255Colors.gif|thumb|right|Representation of the electric field vector of a wave of circularly polarized electromagnetic radiation]] In homogeneous, isotropic media, electromagnetic radiation is a [[transverse wave]],<ref>{{cite book |title=Electromagnetic Theory |first=Julius Adams|last=Stratton|publisher=McGraw-Hill Book Company, New York, NY |year=1941 |chapter-url=https://books.google.com/books?id=zFeWdS2luE4C&q=%22electromagnetic+theory%22+stratton |chapter=Chapter V Plane waves in unbounded, isotropic media|isbn=978-0-470-13153-4}}</ref> meaning that its oscillations are perpendicular to the direction of energy transfer and travel. It comes from the [[Electromagnetic wave equation|following equations]]:<math display="block">\begin{align}
\nabla \cdot \mathbf{E}  &= 0\\
\nabla \cdot \mathbf{B}  &= 0
\end{align}</math>These equations predicate that any electromagnetic wave must be a transverse wave, where the electric field {{math|'''E'''}} and the magnetic field {{math|'''B'''}} are both perpendicular to the direction of wave propagation. The electric and magnetic parts of the field in an electromagnetic wave stand in a fixed ratio of strengths to satisfy the two [[Maxwell's equations]] that specify how one is produced from the other. In dissipation-less (lossless) media, these {{math|E}} and {{math|B}} fields are also in phase, with both reaching maxima and minima at the same points in space.

In the [[Near and far field|far-field]] EM radiation which is described by the two source-free Maxwell [[curl operator]] equations, a time-change in one type of field is proportional to the curl of the other. These derivatives require that the {{math|E}} and {{math|B}} fields in EMR are in phase.{{anchor|frequency}} An important aspect of light's nature is its [[frequency]]. The frequency of a wave is its rate of oscillation and is measured in [[hertz]], the [[SI]] unit of frequency, where one hertz is equal to one oscillation per second. Light usually has multiple frequencies that sum to form the resultant wave. Different frequencies undergo different angles of refraction, a phenomenon known as [[Dispersion relation|dispersion]].

A monochromatic wave (a wave of a single frequency) consists of successive troughs and crests, and the distance between two adjacent crests or troughs is called the [[wavelength]]. Waves of the electromagnetic spectrum vary in size, from very long radio waves longer than a continent to very short gamma rays smaller than atom nuclei. Frequency is inversely proportional to wavelength, according to the equation:<ref>{{Cite web|url=https://astronomy.swin.edu.au/cosmos/E/Electromagnetic+Radiation|title=Electromagnetic Radiation {{!}} COSMOS|website=astronomy.swin.edu.au|access-date=29 March 2020|archive-date=19 March 2020|archive-url=https://web.archive.org/web/20200319090846/https://www.astronomy.swin.edu.au/cosmos/E/Electromagnetic+Radiation|url-status=live}}</ref>
: <math>\displaystyle v=f\lambda</math>
where ''v'' is the speed of the wave ([[speed of light|''c'']] in a vacuum or less in other media), ''f'' is the frequency, and ''λ'' is the wavelength. As waves cross boundaries between different media, their speeds change but their frequencies remain constant.

Electromagnetic waves in free space must be solutions of Maxwell's [[electromagnetic wave equation]]. Two main classes of solutions are known, namely plane waves and spherical waves. The plane waves may be viewed as the limiting case of spherical waves at a very large (ideally infinite) distance from the source. Both types of waves can have a waveform which is an arbitrary time function (so long as it is sufficiently differentiable to conform to the wave equation). As with any time function, this can be decomposed by means of [[Fourier analysis]] into its [[frequency spectrum]], or individual sinusoidal components, each of which contains a single frequency, amplitude, and phase. Such a component wave is said to be ''monochromatic''.

Interference is the superposition of two or more waves resulting in a new wave pattern. If the fields have components in the same direction, they constructively interfere, while opposite directions cause destructive interference. Additionally, multiple polarization signals can be combined (i.e. interfered) to form new states of polarization, which is known as parallel polarization state generation.<ref>{{cite journal |last1=She |first1=Alan |last2=Capasso |first2=Federico |date=17 May 2016 |title=Parallel Polarization State Generation |journal=Scientific Reports |volume=6 |pages=26019 |arxiv=1602.04463 |bibcode=2016NatSR...626019S |doi=10.1038/srep26019 |pmc=4869035 |pmid=27184813}}</ref>

=== Maxwell's equations ===
{{Main|Maxwell's equations}}
[[James Clerk Maxwell]] derived a [[Electromagnetic wave equation|wave form of the electric and magnetic equations]], thus uncovering the wave-like nature of [[Electric Field|electric]] and [[magnetic fields]] and their [[Symmetry (physics)|symmetry]]. Because the speed of EM waves predicted by the wave equation coincided with the measured [[speed of light]], Maxwell concluded that light itself is an EM wave.<ref>{{Cite web|url=https://physics.info/em-waves/|title=Electromagnetic Waves|website=The Physics Hypertextbook|last=Elert|first=Glenn|access-date=4 June 2018|archive-date=2 April 2019|archive-url=https://web.archive.org/web/20190402081830/https://physics.info/em-waves/|url-status=live}}</ref><ref>{{Cite web|url=http://www.clerkmaxwellfoundation.org/html/maxwell-s_impact_.html|title=The Impact of James Clerk Maxwell's Work|website=clerkmaxwellfoundation.org|access-date=4 September 2017|url-status=live|archive-url=https://web.archive.org/web/20170917213509/http://www.clerkmaxwellfoundation.org/html/maxwell-s_impact_.html|archive-date=17 September 2017}}</ref> Maxwell's equations were confirmed by [[Heinrich Hertz]] through experiments with radio waves.<ref>{{Cite web|date=18 December 2015|title=Maxwell's equations and the secrets of nature|url=https://plus.maths.org/content/maxwells-equation-and-power-unification|access-date=2 May 2021|website=plus.maths.org|language=en|archive-date=2 May 2021|archive-url=https://web.archive.org/web/20210502084738/https://plus.maths.org/content/maxwells-equation-and-power-unification|url-status=live}}</ref> Out of the four equations, two of the equations that Maxwell refine were [[Electromagnetic induction|Faraday's Law of Induction]] and [[Ampère's circuital law]], which he extended by adding the [[displacement current]] term to the equations himself. Maxwell thought that the displacement current, which he viewed as the motion of bound charges, gave rise to the magnetic field.<ref>{{Cite journal |last=Suárez |first=Álvaro |last2=Martí |first2=Arturo C. |last3=Zuza |first3=Kristina |last4=Guisasola |first4=Jenaro |date=2023-08-17 |title=Electromagnetic field presented in introductory physics textbooks and consequences for its teaching |url=https://link.aps.org/doi/10.1103/PhysRevPhysEducRes.19.020113 |journal=Physical Review Physics Education Research |language=en |volume=19 |issue=2 |doi=10.1103/PhysRevPhysEducRes.19.020113 |issn=2469-9896|hdl=10810/63511 |hdl-access=free }}</ref> The other two equations are [[Gauss's law]] and [[Gauss's law for magnetism]].

=== Near and far fields ===
{{Main|Near and far field|Liénard–Wiechert potential}}
[[File:FarNearFields-USP-4998112-1.svg|thumb|upright=1.35|In electromagnetic radiation (such as microwaves from an antenna, shown here) the term ''radiation'' applies only to the parts of the [[electromagnetic field]] that radiate into infinite space and decrease in intensity by an [[inverse-square law]] of power, such that the total energy that crosses through an imaginary sphere surrounding the source is the same regardless of the size of the sphere. Electromagnetic radiation thus reaches the ''[[near and far field|far]]'' part of the electromagnetic field around a transmitter. A part of the ''near'' field (close to the transmitter) includes the changing ''[[electromagnetic field]]'', but that is not electromagnetic ''radiation''.]]
Maxwell's equations established that some charges and currents (''sources'') produce local [[electromagnetic field]]s near them that do not radiate. Currents directly produce magnetic fields, but such fields of a [[magnetic dipole|magnetic-dipole]]–type that dies out with distance from the current. In a similar manner, moving charges pushed apart in a conductor by a changing electrical potential (such as in an antenna) produce an [[electric dipole|electric-dipole]]–type electrical field, but this also declines with distance. These fields make up the ''[[near and far field|near]]'' field. Neither of these behaviours is responsible for EM radiation. Instead, they only efficiently transfer energy to a receiver very close to the source, such as inside a [[transformer]]. The near field has strong effects on its source, with any energy withdrawn by a receiver causing increased ''load'' (decreased [[electrical reactance]]) on the source. The near field does not propagate freely into space, carrying energy away without a distance limit, but rather oscillates, returning its energy to the transmitter if it is not absorbed by a receiver.<ref>{{Cite web |date=2023-09-15 |title=Electromagnetic radiation {{!}} Spectrum, Examples, & Types {{!}} Britannica |url=https://www.britannica.com/science/electromagnetic-radiation |access-date=2023-10-16 |website=www.britannica.com |language=en |archive-date=2 May 2015 |archive-url=https://web.archive.org/web/20150502222537/http://www.britannica.com/EBchecked/topic/183228/electromagnetic-radiation/59182/Microwaves |url-status=live }}</ref>

By contrast, the ''[[Near and far field|far]]'' field is composed of ''radiation'' that is free of the transmitter, in the sense that the transmitter requires the same power to send changes in the field out regardless of whether anything absorbs the signal, e.g. a radio station does not need to increase its power when more receivers use the signal. This far part of the electromagnetic field ''is'' electromagnetic radiation. The far fields propagate (radiate) without allowing the transmitter to affect them. This causes them to be independent in the sense that their existence and their energy, after they have left the transmitter, is completely independent of both transmitter and receiver. Due to [[conservation of energy]], the amount of power passing through any closed surface drawn around the source is the same. The [[power density]] of EM radiation from an [[isotropic]] source decreases with the inverse square of the distance from the source; this is called the [[inverse-square law]]. Field intensity due to dipole parts of the near field varies according to an inverse-cube law,<ref>{{Cite journal |last=Capps |first=Charles |date=August 16, 2001 |title=Near field or far field? |url=https://people.eecs.ku.edu/~callen58/501/Capps2001EDNpp95.pdf |journal=designfeature |pages=96}}</ref> and thus fades with distance.

In the [[Liénard–Wiechert potential]] formulation of the electric and magnetic fields due to motion of a single particle (according to Maxwell's equations), the terms associated with acceleration of the particle are those that are responsible for the part of the field that is regarded as electromagnetic radiation. By contrast, the term associated with the changing static electric field of the particle and the magnetic term that results from the particle's uniform velocity are both associated with the near field, and do not comprise electromagnetic radiation.<ref>{{Cite web |date=2021-12-09 |title=10.1: Liénard-Wiechert Potentials |url=https://phys.libretexts.org/Bookshelves/Electricity_and_Magnetism/Essential_Graduate_Physics_-_Classical_Electrodynamics_(Likharev)/10%3A_Radiation_by_Relativistic_Charges/10.01%3A_Lienard-Wiechert_Potentials |access-date=2024-07-26 |website=Physics LibreTexts |language=en |archive-date=26 July 2024 |archive-url=https://web.archive.org/web/20240726225813/https://phys.libretexts.org/Bookshelves/Electricity_and_Magnetism/Essential_Graduate_Physics_-_Classical_Electrodynamics_(Likharev)/10%3A_Radiation_by_Relativistic_Charges/10.01%3A_Lienard-Wiechert_Potentials |url-status=live }}</ref>

=== Particle model and quantum theory ===
{{See also|Quantization (physics)|Quantum optics}}

An anomaly arose in the late 19th century involving a contradiction between the wave theory of light and measurements of the electromagnetic spectra that were being emitted by thermal radiators known as [[black bodies]]. Physicists struggled with this problem unsuccessfully for many years, and it later became known as the [[ultraviolet catastrophe]]. In 1900, [[Max Planck]] developed a new theory of [[Planck's law of black-body radiation|black-body radiation]] that explained the observed spectrum. Planck's theory was based on the idea that black bodies emit light (and other electromagnetic radiation) only as discrete bundles or packets of energy. These packets were called [[quantum|quanta]]. In 1905, [[Albert Einstein]] proposed that light quanta be regarded as real particles. Later the particle of light was given the name [[photon]], to correspond with other particles being described around this time, such as the [[electron]] and [[proton]]. A photon has an energy, ''E'', proportional to its frequency, ''f'', by
: <math>E = hf = \frac{hc}{\lambda} \,\!</math>
where ''h'' is the [[Planck constant]], <math>\lambda</math> is the wavelength and ''c'' is the [[speed of light]]. This is sometimes known as the [[Planck–Einstein equation]].<ref>{{cite book
 | title = Physical Chemistry
 | author = Paul M. S. Monk
 | publisher = John Wiley and Sons
 | year = 2004
 | isbn = 978-0-471-49180-4
 | page = [https://archive.org/details/physicalchemistr00monk_857/page/n460 435]
 | url =https://archive.org/details/physicalchemistr00monk_857
 | url-access = limited
 }}</ref> In quantum theory (see [[first quantization]]) the energy of the photons is thus directly proportional to the frequency of the EMR wave.<ref>{{cite book
 |last=Weinberg
 |first=S.
 |author-link=Steven Weinberg
 |title=The Quantum Theory of Fields
 |volume=1
 |publisher=[[Cambridge University Press]]
 |year=1995
 |isbn=978-0-521-55001-7
 |pages=[https://archive.org/details/quantumtheoryoff00stev/page/15 15–17]
 |url=https://archive.org/details/quantumtheoryoff00stev/page/15
 }}</ref> Likewise, the momentum ''p'' of a photon is also proportional to its frequency and inversely proportional to its wavelength:
: <math>p = { E \over c } = { hf \over c } = { h \over \lambda }. </math>

The source of Einstein's proposal that light was composed of particles (or could act as particles in some circumstances) was an experimental anomaly not explained by the wave theory: the [[photoelectric effect]], in which light striking a metal surface ejected electrons from the surface, causing an [[electric current]] to flow across an applied [[voltage]]. Experimental measurements demonstrated that the energy of individual ejected electrons was proportional to the ''[[frequency]]'', rather than the ''[[intensity (physics)|intensity]]'', of the light. Furthermore, below a certain minimum frequency, which depended on the particular metal, no current would flow regardless of the intensity. These observations appeared to contradict the wave theory, and for years physicists tried to find an explanation. In 1905, Einstein explained this phenomenon by resurrecting the particle theory of light. Because of the preponderance of evidence in favor of the wave theory, however, Einstein's ideas were met initially with great skepticism among established physicists. Eventually Einstein's explanation was accepted as new particle-like behavior of light was observed, such as the [[Compton effect]].<ref name="Commins QM">{{cite book |last1=Commins |first1=Eugene |title=Quantum Mechanics; An Experimentalist's Approach |date=2014 |publisher=Cambridge University Press |isbn=978-1-107-06399-0}}</ref><ref>{{Cite book|last1=Ling|first1=Samuel J.|title=University physics. Volume 3|last2=Sanny|first2=Jeff|last3=Moebs|first3=William|publisher=OpenStax|year=2016|isbn=978-1-947172-22-7|chapter=The Compton Effect}}</ref>

As a photon is absorbed by an [[atom]], it [[excites]] the atom, elevating an electron to a higher [[energy level]] (one that is on average farther from the nucleus). When an electron in an excited molecule or atom descends to a lower energy level, it emits a photon of light at a frequency corresponding to the energy difference. Since the energy levels of electrons in atoms are discrete, each element and each molecule emits and absorbs its own characteristic frequencies. Immediate photon emission is called [[fluorescence]], a type of [[photoluminescence]]. An example is visible light emitted from fluorescent paints, in response to ultraviolet ([[blacklight]]). Many other fluorescent emissions are known in spectral bands other than visible light. Delayed emission is called [[phosphorescence]].<ref>{{Cite web|url=http://www.majordifferences.com/2016/11/7-differences-between-fluorescence-and-Phosphorescence.html|title=7 Differences between Fluorescence and Phosphorescence|last=Haneef|first=Deena T. Kochunni, Jazir|access-date=4 September 2017|url-status=live|archive-url=https://web.archive.org/web/20170904152324/http://www.majordifferences.com/2016/11/7-differences-between-fluorescence-and-Phosphorescence.html|archive-date=4 September 2017}}</ref><ref>{{Cite book|url={{google books |plainurl=y |id=kAn4AgAAQBAJ|page=93}}|title=Fundamental Physics of Radiology|last1=Meredith|first1=W. J.|last2=Massey|first2=J. B.|date=22 October 2013|publisher=Butterworth-Heinemann|isbn=978-1-4832-8435-4|language=en}}</ref>

Quantum mechanics also governs [[Emission (electromagnetic radiation)|emission]], which is seen when an emitting gas glows due to excitation of the atoms from any mechanism, including heat. As electrons descend to lower energy levels, a spectrum is emitted that represents the jumps between the energy levels of the electrons, but lines are seen because again emission happens only at particular energies after excitation.<ref>Browne, p 376: "Radiation is emitted or absorbed only when the electron jumps from one orbit to the other, and the frequency of radiation depends only upon on the energies of the electron in the initial and final orbits.</ref> An example is the emission spectrum of [[nebula]]e.<ref>{{cite book |last1=Hunter |first1=Tim B. |title=The Barnard Objects: Then and Now |last2=Dobek |first2=Gerald O. |date=19 July 2023 |publisher=Springer Cham |isbn=978-3-031-31485-8 |chapter=Nebulae: An Overview |bibcode=2023botn.book.....H |doi=10.1007/978-3-031-31485-8}}</ref> Rapidly moving electrons are most sharply accelerated when they encounter a region of force, so they are responsible for producing much of the highest frequency electromagnetic radiation observed in nature. These phenomena can be used to detect the composition of gases lit from behind ([[Absorption spectroscopy|absorption spectra]]) and for glowing gases ([[Emission spectrum|emission spectra]]). [[Spectroscopy]] (for example) determines what [[chemical element]]s comprise a particular star. Shifts in the frequency of the spectral lines for an element, called a [[redshift]], can be used to determine the star's [[Comoving and proper distances|cosmological distance]].<ref>{{Cite book |last=Longair |first=Malcolm S. |url=https://link.springer.com/10.1007/978-3-662-65891-8 |title=Galaxy Formation |date=2023 |publisher=Springer Berlin Heidelberg |isbn=978-3-662-65890-1 |series=Astronomy and Astrophysics Library |location=Berlin, Heidelberg |language=en |bibcode=2023gafo.book.....L |doi=10.1007/978-3-662-65891-8}}</ref>{{rp|181}}

=== Wave–particle duality ===
{{Main|Wave–particle duality}}

The modern theory that explains the nature of light includes the notion of wave–particle duality. The theory is based on the concept that every quantum entity can show wave-like or particle-like behaviors, depending on observation. The observation led to the collapse of the entity's [[wave function]]. If it is based on the [[Copenhagen interpretation]], the observation does really collapse the wave function; for the [[many-worlds interpretation]], all possible outcomes of the collapse happened in [[Multiverse|parallel universes]]; for the [[pilot wave theory]], the particle behaviour is simply determined by waves. The duality nature of a real photon has been observed in the [[double-slit experiment]].

Together, wave and particle effects fully explain the emission and absorption spectra of EM radiation. The matter-composition of the medium through which the light travels determines the nature of the absorption and emission spectrum. These bands correspond to the allowed energy levels in the atoms. Dark bands in the [[absorption spectroscopy|absorption spectrum]] are due to the atoms in an intervening medium between source and observer. The atoms absorb certain frequencies of the light between emitter and detector/eye, then emit them in all directions. A dark band appears to the detector, due to the radiation scattered out of the [[light beam]]. For instance, dark bands in the light emitted by a distant [[star]] are due to the atoms in the star's atmosphere.

=== Propagation speed ===
{{Main|Speed of light}}

In empty space (vacuum), electromagnetic radiation travels at the [[speed of light]], <math>c</math>, 299,792,458 meters per second (approximately 186,000 miles per second). In a medium other than vacuum it travels at a lower velocity <math>v</math>, given by a dimensionless parameter between 0 and 1 characteristic of the medium called the [[velocity factor]] <math>\mathit{VF}</math> or its reciprocal, the [[refractive index]] <math>n</math>:  
:<math>v = \mathit{VF} \cdot c = {c \over n}</math>.
The reason for this is that in matter the electric and magnetic fields of the wave are slowed because they polarize the charged particles in the medium they pass through.<ref name="Griffiths">{{cite book| last = Griffiths| first = David J. | title = Introduction to Electrodynamics, Vol. 2| publisher = Cambridge Univ. Press| date = 2017| url = https://books.google.com/books?id=ndAoDwAAQBAJ| isbn = 9781108420419| mr = | zbl = | jfm =}}</ref>{{rp|401}} The oscillating electric field causes nearby positive and negative charges in atoms to move slightly apart and together, inducing an oscillating [[polarization density|polarization]], creating an electric polarization field. The oscillating magnetic field moves nearby [[magnetic dipoles]], inducing an oscillating [[magnetization]], creating an induced oscillating magnetic field. These induced fields, [[superposition|superposed]] on the original wave fields, slow the wave ([[Ewald–Oseen extinction theorem]]). The amount of slowing depends on the electromagnetic properties of the medium, the [[permittivity|electric permittivity]] and [[magnetic permeability]]. In the [[Systeme International|SI]] system of units, empty space has a [[Permittivity of Free Space|vacuum permittivity]] of <math>\epsilon_\text{0} =</math> 8.854×10<sup>−12</sup> F/m ([[farad]]s per meter) and a [[vacuum permeability]] of <math>\mu_\text{0} =</math> 1.257×10<sup>−6</sup> H/m ([[Henry (unit)|henries]] per meter). These universal constants determine the speed of light in a vacuum:
:<math>c = {1 \over \sqrt{\epsilon_\text{0}\mu_\text{0}}}</math>
In a medium that is isotropic and linear, which means the electric polarization is proportional to the electric field <math>\mathbf{D} = \epsilon\mathbf{E}</math> and the magnetization is proportional to the magnetic field <math>\mathbf{H} = {1 \over \mu}\mathbf{B}</math>. The speed of the waves, the <math>\mathit{VF}</math>, and the refractive index are determined by only two parameters: the [[permittivity|electric permittivity]] <math>\epsilon</math> of the medium in farads per meter, and the [[magnetic permeability]] of the medium <math>\mu</math> in henrys per meter<ref name="Griffiths" />{{rp|401}}
:<math>v = {1 \over \sqrt{\epsilon\mu}}</math>
:<math>n = {1 \over \mathit{VF}} = c\sqrt{\epsilon\mu} = \sqrt{{\epsilon\mu \over \epsilon_\text{0}\mu_\text{0}}}</math>
If the permittivity and permeability of the medium is constant for different frequency EM waves, this is called a ''[[dispersion (optics)|non-dispersive]]'' medium.<ref name="Griffiths" />{{rp|417-418}} In this case all EM wave frequencies would travel at the same velocity, and the waveshape stays constant as it travels. However in real matter <math>\epsilon</math> and <math>\mu</math> typically vary with frequency, this is called a ''[[dispersion (optics)|dispersive]]'' medium. In dispersive media different spectral bands have different propagation characteristics, and an arbitrary wave changes shape as it travels through the medium.