TheInfoList

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 succession of eve ...

, electromagnetic radiation (EMR) consists of waves of the electromagnetic (EM) field, propagating through space, carrying electromagnetic
radiant energy 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. "Ph ...
. It includes
radio wave Radio waves are a type of electromagnetic radiation In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies ma ...
s,
microwave Microwave is a form of electromagnetic radiation In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies mat ...

s,
infrared Infrared (IR), sometimes called infrared light, is electromagnetic radiation (EMR) with wavelengths longer than those of Light, visible light. It is therefore invisible to the human eye. IR is generally understood to encompass wavelengths from ...

, ,
ultraviolet Ultraviolet (UV) is a form of electromagnetic radiation In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that stud ...

,
X-ray An X-ray, or, much less commonly, X-radiation, is a penetrating form of high-energy electromagnetic radiation. Most X-rays have a wavelength ranging from 10 Picometre, picometers to 10 Nanometre, nanometers, corresponding to frequency ...

s, and
gamma ray A gamma ray, also known as gamma radiation (symbol γ or \gamma), is a penetrating form of electromagnetic radiation In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, it ...
s. All of these waves form part of the
electromagnetic spectrum The electromagnetic spectrum is the range of frequencies Frequency is the number of occurrences of a repeating event per unit of time A unit of time is any particular time Time is the indefinite continued sequence, progress of existe ...

. Classically, electromagnetic radiation consists of electromagnetic waves, which are synchronized
oscillation Oscillation is the repetitive variation, typically in time Time is the indefinite continued sequence, progress of existence and event (philosophy), events that occur in an apparently irreversible process, irreversible succession from the pas ...

s of
electric Electricity is the set of physics, physical Phenomenon, phenomena associated with the presence and motion of matter that has a property of electric charge. Electricity is related to magnetism, both being part of the phenomenon of electromagnet ...

and
magnetic field A magnetic field is a vector field In vector calculus and physics, a vector field is an assignment of a vector to each point in a subset of space. For instance, a vector field in the plane can be visualised as a collection of arrows with ...

s. Electromagnetic radiation or electromagnetic waves are created due to periodic change of electric or magnetic field. Depending on how this periodic change occurs and the power generated, different wavelengths of electromagnetic spectrum are produced. In a vacuum, electromagnetic waves travel at the
speed of light The speed of light in vacuum A vacuum is a space devoid of matter. The word is derived from the Latin adjective ''vacuus'' for "vacant" or "Void (astronomy), void". An approximation to such vacuum is a region with a gaseous pressure m ...
, commonly denoted ''c''. In homogeneous, isotropic media, the oscillations of the two fields are perpendicular to each other and perpendicular to the direction of energy and wave propagation, forming a . The
wavefront In physics, the wavefront of a time-varying field is the set () of all where the wave has the same of the sinusoid. The term is generally meaningful only for fields that, at each point, vary in time with a single temporal frequency (otherwise ...

of electromagnetic waves emitted from a
point source A point source is a single identifiable ''localised'' source of something. A point source has negligible extent, distinguishing it from other source geometries. Sources are called point sources because in mathematical modeling, these sources can us ...
(such as a light bulb) is a
sphere A sphere (from Greek language, Greek —, "globe, ball") is a Geometry, geometrical object that is a solid geometry, three-dimensional analogue to a circle in two-dimensional space. A sphere is the Locus (mathematics), set of points that are ...

. The position of an electromagnetic wave within the
electromagnetic spectrum The electromagnetic spectrum is the range of frequencies Frequency is the number of occurrences of a repeating event per unit of time A unit of time is any particular time Time is the indefinite continued sequence, progress of existe ...

can be characterized by either its
frequency Frequency is the number of occurrences of a repeating event per unit of time A unit of time is any particular time Time is the indefinite continued sequence, progress of existence and event (philosophy), events that occur in an apparen ...

of oscillation or its
wavelength In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is the distance between consecutive corresponding points of the same phase (waves), phase on the wave, such as two adja ...

. Electromagnetic waves of different frequency are called by different names since they have different sources and effects on matter. In order of increasing frequency and decreasing wavelength these are: radio waves, microwaves, infrared radiation, visible light, ultraviolet radiation, X-rays and gamma rays. Electromagnetic waves are emitted by electrically
charged particle 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 through Spa ...
s undergoing acceleration, and these waves can subsequently interact with other charged particles, exerting force on them. EM waves carry energy,
momentum In Newtonian mechanics, linear momentum, translational momentum, or simply momentum is the product of the mass Mass is both a property Property (''latin: Res Privata'') in the Abstract and concrete, abstract is what belongs to or w ...

and
angular momentum In , angular momentum (rarely, moment of momentum or rotational momentum) is the rotational equivalent of . It is an important quantity in physics because it is a —the total angular momentum of a closed system remains constant. In three , the ...

away from their source particle and can impart those quantities to
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 ultimately composed of atoms, which are made up of interacting subatomic particl ...
with which they interact. Electromagnetic radiation is associated with those EM waves that are free to propagate themselves ("radiate") without the continuing influence of the moving charges that produced them, because they have achieved sufficient distance from those charges. Thus, EMR is sometimes referred to as the
far field and Fresnel diffraction 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 engi ...
. In this language, the near field refers to EM fields near the charges and current that directly produced them, specifically
electromagnetic induction Electromagnetic or magnetic induction is the production of an electromotive force In electromagnetism and electronics, electromotive force (emf, denoted \mathcal and measured in volts) is the electrical action produced by a non-electrical sour ...

and
electrostatic induction Electrostatic induction, also known as "electrostatic influence" or simply "influence" in Europe and Latin America, is a redistribution of electric charge Electric charge is the physical property of matter that causes it to experience a force w ...

phenomena. In
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 ...
, an alternate way of viewing EMR is that it consists of
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 ...

s, uncharged
elementary particle In particle physics, an elementary particle or fundamental particle is a subatomic particle that is not composed of other particles. Particles currently thought to be elementary include the fundamental fermions (quarks, leptons, antiquarks, and a ...
s with zero
rest mass The invariant mass, rest mass, intrinsic mass, proper mass, or in the case of bound systems simply mass, is the portion of the total mass of an object Object may refer to: General meanings * Object (philosophy), a thing, being, or concept ** ...
which are the of the
electromagnetic field An electromagnetic field (also EM field or EMF) is a classical (i.e. non-quantum) field Field may refer to: Expanses of open ground * Field (agriculture), an area of land used for agricultural purposes * Airfield, an aerodrome that lacks the in ...
, responsible for all electromagnetic interactions.
Quantum electrodynamics In particle physics Particle physics (also known as high energy physics) is a branch of that studies the nature of the particles that constitute and . Although the word ' can refer to various types of very small objects (e.g. , gas particles ...
is the theory of how EMR interacts with matter on an atomic level. Quantum effects provide additional sources of EMR, such as the transition of electrons to lower
energy level A quantum mechanical 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 ...
s in an atom and
black-body radiation Black-body radiation is the within or surrounding a body in with its environment, emitted by a (an idealized opaque, non-reflective body). It has a specific spectrum of wavelengths, inversely related to intensity that depend only on the bod ...
. The energy of an individual photon is quantized and is greater for photons of higher frequency. This relationship is given by Planck's equation ''E'' = ''hf'', where ''E'' is the energy per photon, ''f'' is the frequency of the photon, and ''h'' is . A single gamma ray photon, for example, might carry ~100,000 times the energy of a single photon of visible light. The effects of EMR upon chemical compounds and biological organisms depend both upon the radiation's
power Power typically refers to: * Power (physics) In physics, power is the amount of energy transferred or converted per unit time. In the International System of Units, the unit of power is the watt, equal to one joule per second. In older works, p ...
and its frequency. EMR of visible or lower frequencies (i.e., visible light, infrared, microwaves, and radio waves) is called ''
non-ionizing radiation Non-ionizing (or non-ionising) radiation refers to any type of electromagnetic radiation In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion an ...
'', because its photons do not individually have enough energy to
ionize Ionization or ionisation is the process by which an atom An atom is the smallest unit of ordinary matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday ...
atoms or molecules or break
chemical bond A chemical bond is a lasting attraction between atom An atom is the smallest unit of ordinary matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday ...
s. The effects of these radiations on chemical systems and living tissue are caused primarily by heating effects from the combined energy transfer of many photons. In contrast, high frequency ultraviolet, X-rays and gamma rays are called ''
ionizing radiation Ionizing radiation (or ionising radiation), including nuclear radiation, consists of s or s that have sufficient to s or s by detaching s from them. The particles generally travel at a speed that is greater than 1% of , and the electromagnetic w ...
'', since individual photons of such high frequency have enough energy to
ionize Ionization or ionisation is the process by which an atom An atom is the smallest unit of ordinary matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday ...
molecules or break
chemical bond A chemical bond is a lasting attraction between atom An atom is the smallest unit of ordinary matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday ...
s. These radiations have the ability to cause
chemical reaction A chemical reaction is a process that leads to the chemical transformation of one set of chemical substance A chemical substance is a form of matter In classical physics and general chemistry, matter is any substance that has mass and t ...

s and damage living cells beyond that resulting from simple heating, and can be a health hazard.

# Physics

## Theory

### Maxwell's equations

James Clerk Maxwell James Clerk Maxwell (13 June 1831 – 5 November 1879) was a Scottish scientist A scientist is a person who conducts Scientific method, scientific research to advance knowledge in an Branches of science, area of interest. In classica ...

derived a wave form of the electric and magnetic equations, thus uncovering the wave-like nature of
electric Electricity is the set of physics, physical Phenomenon, phenomena associated with the presence and motion of matter that has a property of electric charge. Electricity is related to magnetism, both being part of the phenomenon of electromagnet ...

and
magnetic fields A magnetic field is a vector field that describes the magnetic influence on moving electric charge Electric charge is the physical property of matter that causes it to experience a force when placed in an electromagnetic field. There are two ...
and their
symmetry Symmetry (from 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 appro ...
. Because the speed of EM waves predicted by the wave equation coincided with the measured
speed of light The speed of light in vacuum A vacuum is a space devoid of matter. The word is derived from the Latin adjective ''vacuus'' for "vacant" or "Void (astronomy), void". An approximation to such vacuum is a region with a gaseous pressure m ...
, Maxwell concluded that light itself is an EM wave. Maxwell's equations were confirmed by
Heinrich Hertz Heinrich Rudolf Hertz ( ; ; 22 February 1857 – 1 January 1894) was a German who first conclusively proved the existence of the predicted by 's . The unit of frequency, , was named the "" in his honor.
through experiments with radio waves. Maxwell realized that since a lot of physics is symmetrical and mathematically artistic in a way, that there must also be a symmetry between electricity and magnetism. He realized that light is a combination of electricity and magnetism and thus that the two must be tied together. According to
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), s ...
, a spatially varying
electric field An electric field (sometimes E-field) is the physical field that surrounds electrically-charged particle In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' ' ...

is always associated with a
magnetic field A magnetic field is a vector field In vector calculus and physics, a vector field is an assignment of a vector to each point in a subset of space. For instance, a vector field in the plane can be visualised as a collection of arrows with ...

that changes over time. Likewise, a spatially varying magnetic field is associated with specific changes over time in the electric field. In an electromagnetic wave, the changes in the electric field are always accompanied by a wave in the magnetic field in one direction, and vice versa. This relationship between the two occurs without either type of field causing the other; rather, they occur together in the same way that time and space changes occur together and are interlinked in
special relativity 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 ...
. In fact, magnetic fields can be viewed as electric fields in another frame of reference, and electric fields can be viewed as magnetic fields in another frame of reference, but they have equal significance as physics is the same in all frames of reference, so the close relationship between space and time changes here is more than an analogy. Together, these fields form a propagating electromagnetic wave, which moves out into space and need never again interact with the source. The distant EM field formed in this way by the acceleration of a charge carries energy with it that "radiates" away through space, hence the term.

### Near and far fields

Maxwell's equations established that some charges and currents ("sources") produce a local type of
electromagnetic field An electromagnetic field (also EM field or EMF) is a classical (i.e. non-quantum) field Field may refer to: Expanses of open ground * Field (agriculture), an area of land used for agricultural purposes * Airfield, an aerodrome that lacks the in ...
near them that does ''not'' have the behaviour of EMR. Currents directly produce a magnetic field, but it is of a
magnetic dipole A magnetic dipole is the limit of either a closed loop of electric current An electric current is a stream of charged particles, such as electrons or ions, moving through an electrical conductor or space. It is measured as the net rate of flow of ...
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 The electric dipole moment is a measure of the separation of positive and negative electrical charge Electricity is the set of physical phenomena associated with the presence and motion Image:Leaving Yongsan Station.jpg, 300px, Motion inv ...

type electrical field, but this also declines with distance. These fields make up the near-field near the EMR source. Neither of these behaviours are responsible for EM radiation. Instead, they cause electromagnetic field behaviour that only efficiently transfers power to a receiver very close to the source, such as the
magnetic induction Electromagnetic or magnetic induction is the production of an electromotive force In electromagnetism and electronics, electromotive force (emf, denoted \mathcal and measured in volts) is the electrical action produced by a non-electrical sour ...

inside a
transformer A transformer is a passive electrical device that transfers electrical energy from one electrical circuit to another, or multiple Electrical network, circuits. A varying current in any one coil of the transformer produces a varying magnetic flux ...

, or the feedback behaviour that happens close to the coil of a
metal detector A metal detector is an instrument that detects the presence of metal A metal (from Ancient Greek, Greek μέταλλον ''métallon'', "mine, quarry, metal") is a material that, when freshly prepared, polished, or fractured, shows a lustr ...

. Typically, near-fields have a powerful effect on their own sources, causing an increased "load" (decreased
electrical reactance In electrical circuits, reactance is the opposition presented to alternating current Alternating current (AC) is an electric current which periodically reverses direction and changes its magnitude continuously with time in contrast to direct cu ...

) in the source or transmitter, whenever energy is withdrawn from the EM field by a receiver. Otherwise, these fields do not "propagate" freely out into space, carrying their energy away without distance-limit, but rather oscillate, returning their energy to the transmitter if it is not received by a receiver. By contrast, the EM far-field is composed of ''radiation'' that is free of the transmitter in the sense that (unlike the case in an electrical transformer) the transmitter requires the same power to send these changes in the fields out, whether the signal is immediately picked up or not. This distant part of the electromagnetic field ''is'' "electromagnetic radiation" (also called the
far-field The near field and far field are regions of the electromagnetic field An electromagnetic field (also EM field or EMF) is a classical (i.e. non-quantum) field Field may refer to: Expanses of open ground * Field (agriculture), an area of lan ...
). 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 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 ...
, the amount of power passing through any spherical surface drawn around the source is the same. Because such a surface has an area proportional to the square of its distance from the source, the
power density Power density is the amount of power Power typically refers to: * Power (physics) In physics, power is the amount of energy transferred or converted per unit time. In the International System of Units, the unit of power is the watt, equal to ...
of EM radiation always decreases with the inverse square of the distance from the source; this is called the
inverse-square law 420px, S represents the light source, while r represents the measured points. The lines represent the flux emanating from the sources and fluxes. The total number of flux lines depends on the strength of the light source and is constant with in ...

. This is in contrast to dipole parts of the EM field close to the source (the near-field), which vary in power according to an inverse cube power law, and thus do ''not'' transport a conserved amount of energy over distances, but instead fade with distance, with its energy (as noted) rapidly returning to the transmitter or absorbed by a nearby receiver (such as a transformer secondary coil). The far-field (EMR) depends on a different mechanism for its production than the near-field, and upon different terms in Maxwell's equations. Whereas the magnetic part of the near-field is due to currents in the source, the magnetic field in EMR is due only to the local change in the electric field. In a similar way, while the electric field in the near-field is due directly to the charges and charge-separation in the source, the electric field in EMR is due to a change in the local magnetic field. Both processes for producing electric and magnetic EMR fields have a different dependence on distance than do near-field dipole electric and magnetic fields. That is why the EMR type of EM field becomes dominant in power "far" from sources. The term "far from sources" refers to how far from the source (moving at the speed of light) any portion of the outward-moving EM field is located, by the time that source currents are changed by the varying source potential, and the source has therefore begun to generate an outwardly moving EM field of a different phase. A more compact view of EMR is that the far-field that composes EMR is generally that part of the EM field that has traveled sufficient distance from the source, that it has become completely disconnected from any feedback to the charges and currents that were originally responsible for it. Now independent of the source charges, the EM field, as it moves farther away, is dependent only upon the accelerations of the charges that produced it. It no longer has a strong connection to the direct fields of the charges, or to the velocity of the charges (currents). 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 electromagnetic near-field, and do not comprise EM radiation.

## Properties

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 carried by electromagneti ...
is the
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 succession of eve ...

of electromagnetic radiation, and
electromagnetism 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 electromagnet ...

is the physical phenomenon associated with the theory of electrodynamics. Electric and magnetic fields obey the properties of 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 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 ...
fields, all magnetic and electric field vectors add together according to
vector addition 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 ...

. For example, in optics two or more coherent light waves may interact and by constructive or destructive
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 ...
yield a resultant irradiance deviating from the sum of the component irradiances of the individual light waves. 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 A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macrosco ...

s, interactions can occur between light and static electric and magnetic fields—these interactions include the
Faraday effect The Faraday effect or Faraday rotation, sometimes referred to as the magneto-optic Faraday effect (MOFE), is a physical magneto-optical phenomenon. The Faraday effect causes a polarization rotation which is proportional to the projection of the m ...

and the
Kerr effect The Kerr effect, also called the quadratic electro-optic (QEO) effect, is a change in the refractive index In optics, the refractive index (also known as refraction index or index of refraction) of a optical medium, material is a dimensionless ...
. In
refraction 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 ...

, a wave crossing from one medium to another of different
density The density (more precisely, the volumetric mass density; also known as specific mass), of a substance is its per unit . The symbol most often used for density is ''ρ'' (the lower case Greek letter ), although the Latin letter ''D'' can also ...

alters its 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 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 ...

. Light of composite wavelengths (natural sunlight) disperses into a visible
spectrum A spectrum (plural ''spectra'' or ''spectrums'') is a condition that is not limited to a specific set of values but can vary, without gaps, across a Continuum (theory), continuum. The word was first used scientifically in optics to describe the ...

passing through a prism, because of the wavelength-dependent
refractive index In optics, the refractive index (also known as refraction index or index of refraction) of a optical medium, material is a dimensionless number that describes how fast EM radiation, light travels through the material. It is defined as :n = \frac ...

of the
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 ...

material (
dispersion Dispersion may refer to: Economics and finance *Dispersion (finance), a measure for the statistical distribution of portfolio returns *Price dispersion, a variation in prices across sellers of the same item *Wage dispersion, the amount of variation ...
); that is, each component wave within the composite light is bent a different amount. EM radiation exhibits both wave properties and
particle In the Outline of physical science, physical sciences, a particle (or corpuscule in older texts) is a small wikt:local, localized physical body, object to which can be ascribed several physical property, physical or chemical property, chemical p ...
properties at the same time (see ). 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''. Demonstrating that the light itself is quantized, not merely its interaction with matter, is a more subtle affair. Some experiments display both the wave and particle natures of electromagnetic waves, such as the self-interference of a single
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 ...

. When a single photon is sent through an
interferometer . The two light rays with a common source combine at the half-silvered mirror to reach the detector. They may either interfere constructively (strengthening in intensity) if their light waves arrive in phase, or interfere destructively (weakening i ...

, it passes through both paths, interfering with itself, as waves do, yet is detected by a
photomultiplierA photomultiplier is a device that converts incident photons into an electrical signal. Kinds of photomultiplier include: * Photomultiplier tube, a vacuum tube A vacuum tube, an electron tube, valve (British usage) or tube (North America), i ...

or other sensitive detector only once. A quantum theory of the interaction between electromagnetic radiation and matter such as electrons is described by the theory of
quantum electrodynamics In particle physics Particle physics (also known as high energy physics) is a branch of that studies the nature of the particles that constitute and . Although the word ' can refer to various types of very small objects (e.g. , gas particles ...
. Electromagnetic waves can be polarized, reflected, refracted,
diffracted Diffraction refers to various phenomena that occur when a wave In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that ...

or interfere with each other.

## Wave model

In homogeneous, isotropic media, electromagnetic radiation is a , meaning that its oscillations are perpendicular to the direction of energy transfer and travel. The electric and magnetic parts of the field stand in a fixed ratio of strengths to satisfy the two
Maxwell 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), s ...
that specify how one is produced from the other. In dissipation-less (lossless) media, these E and B fields are also in phase, with both reaching maxima and minima at the same points in space (see illustrations). A common misconception is that the E and B fields in electromagnetic radiation are out of phase because a change in one produces the other, and this would produce a phase difference between them as sinusoidal functions (as indeed happens in
electromagnetic induction Electromagnetic or magnetic induction is the production of an electromotive force In electromagnetism and electronics, electromotive force (emf, denoted \mathcal and measured in volts) is the electrical action produced by a non-electrical sour ...

, and in the near-field close to antennas). However, in the far-field EM radiation which is described by the two source-free Maxwell curl operator equations, a more correct description is that a time-change in one type of field is proportional to a space-change in the other. These derivatives require that the E and B fields in EMR are in-phase (see mathematics section below). An important aspect of light's nature is its
frequency Frequency is the number of occurrences of a repeating event per unit of time A unit of time is any particular time Time is the indefinite continued sequence, progress of existence and event (philosophy), events that occur in an apparen ...

. The frequency of a wave is its rate of oscillation and is measured in
hertz The hertz (symbol: Hz) is the unit Unit may refer to: Arts and entertainment * UNIT Unit may refer to: Arts and entertainment * UNIT, a fictional military organization in the science fiction television series ''Doctor Who'' * Unit of action ...

, the 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 Dispersion may refer to: Economics and finance *Dispersion (finance), a measure for the statistical distribution of portfolio returns *Price dispersion, a variation in prices across sellers of the same item *Wage dispersion, the amount of variation ...

. 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 In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is the distance between consecutive corresponding points of the same phase (waves), phase on the wave, such as two adja ...

. 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: :$\displaystyle v=f\lambda$ where ''v'' is the speed of the wave ('' 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 The electromagnetic wave equation is a second-order partial differential equation that describes the propagation of electromagnetic waves through a Medium (optics), medium or in a vacuum. It is a Wave equation#Scalar wave equation in three space d ...
. 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 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 ...
into its
frequency spectrum The power spectrum S_(f) of a time series x(t) describes the distribution of power Power typically refers to: * Power (physics) In physics, power is the amount of energy transferred or converted per unit time. In the International System ...
, or individual sinusoidal components, each of which contains a single frequency, amplitude and phase. Such a component wave is said to be ''monochromatic''. A monochromatic electromagnetic wave can be characterized by its frequency or wavelength, its peak amplitude, its phase relative to some reference phase, its direction of propagation, and its polarization. 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. An example of interference caused by EMR is
electromagnetic interference Electromagnetic interference (EMI), also called radio-frequency interference (RFI) when in the radio frequency Radio frequency (RF) is the oscillation Oscillation is the repetitive variation, typically in time, of some measure about a cent ...
(EMI) or as it is more commonly known as,
radio-frequency interference File:Analog TV EMI.jpg, 300px, Electromagnetic interference in analog TV signal Electromagnetic interference (EMI), also called radio-frequency interference (RFI) when in the radio frequency spectrum, is a disturbance generated by an external sourc ...
(RFI). Additionally, multiple polarization signals can be combined (i.e. interfered) to form new states of polarization, which is known as parallel polarization state generation. The energy in electromagnetic waves is sometimes called
radiant energy 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. "Ph ...
.

## Particle model and quantum theory

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 . Physicists struggled with this problem unsuccessfully for many years. It later became known as the
ultraviolet catastrophe The ultraviolet catastrophe, also called the Rayleigh–Jeans catastrophe, was the prediction of late 19th century/early 20th century classical physics Classical physics is a group of physics Physics (from grc, φυσική (ἐπι ...
. In 1900,
Max Planck Max Karl Ernst Ludwig Planck, (; ; 23 April 1858 – 4 October 1947) was a German German(s) may refer to: Common uses * of or related to Germany * Germans, Germanic ethnic group, citizens of Germany or people of German ancestry * For citi ...

developed a new theory of
black-body radiation Black-body radiation is the within or surrounding a body in with its environment, emitted by a (an idealized opaque, non-reflective body). It has a specific spectrum of wavelengths, inversely related to intensity that depend only on the bod ...
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 . 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 ...

proposed that light quanta be regarded as real particles. Later the particle of light was given the name
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 ...

, to correspond with other particles being described around this time, such as the
electron The electron is a subatomic particle (denoted by the symbol or ) whose electric charge is negative one elementary charge. Electrons belong to the first generation (particle physics), generation of the lepton particle family, and are general ...

and
proton A proton is a subatomic particle, symbol or , with a positive electric charge of +1''e'' elementary charge and a mass slightly less than that of a neutron. Protons and neutrons, each with masses of approximately one atomic mass unit, are collecti ...

. A photon has an energy, ''E'', proportional to its frequency, ''f'', by : $E = hf = \frac \,\!$ where ''h'' is , $\lambda$ is the wavelength and ''c'' is the
speed of light The speed of light in vacuum A vacuum is a space devoid of matter. The word is derived from the Latin adjective ''vacuus'' for "vacant" or "Void (astronomy), void". An approximation to such vacuum is a region with a gaseous pressure m ...
. This is sometimes known as the Planck–Einstein equation. In quantum theory (see
first quantization A first quantization of a physical system is a possibly semiclassical treatment of quantum mechanics Quantum mechanics is a fundamental Scientific theory, theory in physics that provides a description of the physical properties of nature at ...
) the energy of the photons is thus directly proportional to the frequency of the EMR wave. Likewise, the momentum ''p'' of a photon is also proportional to its frequency and inversely proportional to its wavelength: : $p = = = .$ 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 Frequency is the number of occurrences of a repeating event per unit of time A unit of time is any particular time Time is the indefinite continued sequence, progress of existence and event (philosophy), events that occur in an apparen ...

'', 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 in vain to find an explanation. In 1905, Einstein explained this puzzle by resurrecting the particle theory of light to explain the observed effect. 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. As a photon is absorbed by an atom, it Excited state, excites the atom, elevating an
electron The electron is a subatomic particle (denoted by the symbol or ) whose electric charge is negative one elementary charge. Electrons belong to the first generation (particle physics), generation of the lepton particle family, and are general ...

to a higher
energy level A quantum mechanical 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 ...
(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.

## Wave–particle duality

The modern theory that explains the nature of light includes the notion of wave–particle duality. More generally, the theory states that everything has both a particle nature and a wave nature, and various experiments can be done to bring out one or the other. The particle nature is more easily discerned using an object with a large mass. A bold proposition by Louis de Broglie in 1924 led the scientific community to realize that matter (e.g.
electron The electron is a subatomic particle (denoted by the symbol or ) whose electric charge is negative one elementary charge. Electrons belong to the first generation (particle physics), generation of the lepton particle family, and are general ...

s) also exhibits wave–particle duality.

## Wave and particle effects of electromagnetic radiation

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 beam. For instance, dark bands in the light emitted by a distant star are due to the atoms in the star's atmosphere. A similar phenomenon occurs for 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. An example is the Emission (electromagnetic radiation), emission spectrum of nebulae. 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 aid various chemical determinations for the composition of gases lit from behind (absorption spectra) and for glowing gases (emission spectra). Spectroscopy (for example) determines what chemical elements comprise a particular star. Spectroscopy is also used in the determination of the distance of a star, using the red shift.

## Propagation speed

When any wire (or other conducting object such as an antenna (electronics), antenna) conducts alternating current, electromagnetic radiation is propagated at the same frequency as the current. In many such situations it is possible to identify an electrical dipole moment that arises from separation of charges due to the exciting electrical potential, and this dipole moment oscillates in time, as the charges move back and forth. This oscillation at a given frequency gives rise to changing electric and magnetic fields, which then set the electromagnetic radiation in motion. At the quantum level, electromagnetic radiation is produced when the wavepacket of a charged particle oscillates or otherwise accelerates. Charged particles in a stationary state do not move, but a superposition of such states may result in a transition state that has an electric dipole moment that oscillates in time. This oscillating dipole moment is responsible for the phenomenon of radiative transition between quantum states of a charged particle. Such states occur (for example) in atoms when photons are radiated as the atom shifts from one stationary state to another. As a wave, light is characterized by a velocity (the
speed of light The speed of light in vacuum A vacuum is a space devoid of matter. The word is derived from the Latin adjective ''vacuus'' for "vacant" or "Void (astronomy), void". An approximation to such vacuum is a region with a gaseous pressure m ...
),
wavelength In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is the distance between consecutive corresponding points of the same phase (waves), phase on the wave, such as two adja ...

, and
frequency Frequency is the number of occurrences of a repeating event per unit of time A unit of time is any particular time Time is the indefinite continued sequence, progress of existence and event (philosophy), events that occur in an apparen ...

. As particles, light is a stream of
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 ...

s. Each has an energy related to the frequency of the wave given by Max Planck, Planck's relation ''E = hf'', where ''E'' is the energy of the photon, ''h'' is , 6.626 × 10−34 J·s, and ''f'' is the frequency of the wave. One rule is obeyed regardless of circumstances: EM radiation in a vacuum travels at the
speed of light The speed of light in vacuum A vacuum is a space devoid of matter. The word is derived from the Latin adjective ''vacuus'' for "vacant" or "Void (astronomy), void". An approximation to such vacuum is a region with a gaseous pressure m ...
, ''relative to the observer'', regardless of the observer's velocity. (This observation led to Einstein's development of the theory of
special relativity 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 ...
.) In a medium (other than vacuum), velocity of propagation, velocity factor or
refractive index In optics, the refractive index (also known as refraction index or index of refraction) of a optical medium, material is a dimensionless number that describes how fast EM radiation, light travels through the material. It is defined as :n = \frac ...

are considered, depending on frequency and application. Both of these are ratios of the speed in a medium to speed in a vacuum.

## Special theory of relativity

By the late nineteenth century, various experimental anomalies could not be explained by the simple wave theory. One of these anomalies involved a controversy over the speed of light. The speed of light and other EMR predicted by Maxwell's equations did not appear unless the equations were modified in a way first suggested by George Francis FitzGerald, FitzGerald and Hendrik Lorentz, Lorentz (see history of special relativity), or else otherwise that speed would depend on the speed of observer relative to the "medium" (called luminiferous aether) which supposedly "carried" the electromagnetic wave (in a manner analogous to the way air carries sound waves). Experiments failed to find any observer effect. In 1905, Einstein proposed that space and time appeared to be velocity-changeable entities for light propagation and all other processes and laws. These changes accounted for the constancy of the speed of light and all electromagnetic radiation, from the viewpoints of all observers—even those in relative motion.

# History of discovery

Electromagnetic radiation of wavelengths other than those of visible light were discovered in the early 19th century. The discovery of
infrared Infrared (IR), sometimes called infrared light, is electromagnetic radiation (EMR) with wavelengths longer than those of Light, visible light. It is therefore invisible to the human eye. IR is generally understood to encompass wavelengths from ...

radiation is ascribed to astronomer William Herschel, who published his results in 1800 before the Royal Society of London. Herschel used a glass Triangular prism (optics), prism to refract light from the Sun and detected invisible rays that caused heating beyond the red part of the spectrum, through an increase in the temperature recorded with a thermometer. These "calorific rays" were later termed infrared. In 1801, German physicist Johann Wilhelm Ritter discovered
ultraviolet Ultraviolet (UV) is a form of electromagnetic radiation In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that stud ...

in an experiment similar to Herschel's, using sunlight and a glass prism. Ritter noted that invisible rays near the violet edge of a solar spectrum dispersed by a triangular prism darkened silver chloride preparations more quickly than did the nearby violet light. Ritter's experiments were an early precursor to what would become photography. Ritter noted that the ultraviolet rays (which at first were called "chemical rays") were capable of causing chemical reactions. In 1862–64
James Clerk Maxwell James Clerk Maxwell (13 June 1831 – 5 November 1879) was a Scottish scientist A scientist is a person who conducts Scientific method, scientific research to advance knowledge in an Branches of science, area of interest. In classica ...

developed equations for the electromagnetic field which suggested that waves in the field would travel with a speed that was very close to the known speed of light. Maxwell therefore suggested that visible light (as well as invisible infrared and ultraviolet rays by inference) all consisted of propagating disturbances (or radiation) in the electromagnetic field. Radio waves were first produced deliberately by
Heinrich Hertz Heinrich Rudolf Hertz ( ; ; 22 February 1857 – 1 January 1894) was a German who first conclusively proved the existence of the predicted by 's . The unit of frequency, , was named the "" in his honor.
in 1887, using electrical circuits calculated to produce oscillations at a much lower frequency than that of visible light, following recipes for producing oscillating charges and currents suggested by Maxwell's equations. Hertz also developed ways to detect these waves, and produced and characterized what were later termed
radio wave Radio waves are a type of electromagnetic radiation In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies ma ...
s and
microwave Microwave is a form of electromagnetic radiation In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies mat ...

s.James Jeans, Jeans, James (1947
The Growth of Physical Science
Cambridge University Press
Wilhelm Röntgen discovered and named X-rays. After experimenting with high voltages applied to an evacuated tube on 8 November 1895, he noticed a fluorescence on a nearby plate of coated glass. In one month, he discovered X-rays' main properties. The last portion of the EM spectrum to be discovered was associated with radioactivity. Henri Becquerel found that uranium salts caused fogging of an unexposed photographic plate through a covering paper in a manner similar to X-rays, and Marie Curie discovered that only certain elements gave off these rays of energy, soon discovering the intense radiation of radium. The radiation from pitchblende was differentiated into alpha rays (alpha particles) and beta rays (beta particles) by Ernest Rutherford through simple experimentation in 1899, but these proved to be charged particulate types of radiation. However, in 1900 the French scientist Paul Villard discovered a third neutrally charged and especially penetrating type of radiation from radium, and after he described it, Rutherford realized it must be yet a third type of radiation, which in 1903 Rutherford named
gamma ray A gamma ray, also known as gamma radiation (symbol γ or \gamma), is a penetrating form of electromagnetic radiation In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, it ...
s. In 1910 British physicist William Henry Bragg demonstrated that gamma rays are electromagnetic radiation, not particles, and in 1914 Rutherford and Edward Andrade measured their wavelengths, finding that they were similar to X-rays but with shorter wavelengths and higher frequency, although a 'cross-over' between X and gamma rays makes it possible to have X-rays with a higher energy (and hence shorter wavelength) than gamma rays and vice versa. The origin of the ray differentiates them, gamma rays tend to be natural phenomena originating from the unstable nucleus of an atom and X-rays are electrically generated (and hence man-made) unless they are as a result of bremsstrahlung X-radiation caused by the interaction of fast moving particles (such as beta particles) colliding with certain materials, usually of higher atomic numbers.

# Electromagnetic spectrum

EM radiation (the designation 'radiation' excludes static electric and magnetic and near and far field, near fields) is classified by wavelength into radio wave, radio,
microwave Microwave is a form of electromagnetic radiation In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies mat ...

,
infrared Infrared (IR), sometimes called infrared light, is electromagnetic radiation (EMR) with wavelengths longer than those of Light, visible light. It is therefore invisible to the human eye. IR is generally understood to encompass wavelengths from ...

, visible spectrum, visible,
ultraviolet Ultraviolet (UV) is a form of electromagnetic radiation In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that stud ...

,
X-ray An X-ray, or, much less commonly, X-radiation, is a penetrating form of high-energy electromagnetic radiation. Most X-rays have a wavelength ranging from 10 Picometre, picometers to 10 Nanometre, nanometers, corresponding to frequency ...

s and gamma rays. Arbitrary electromagnetic waves can be expressed by
Fourier analysis 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 ...
in terms of sinusoidal monochromatic waves, which in turn can each be classified into these regions of the EMR spectrum. For certain classes of EM waves, the waveform is most usefully treated as ''random'', and then spectral analysis must be done by slightly different mathematical techniques appropriate to random or stochastic processes. In such cases, the individual frequency components are represented in terms of their ''power'' content, and the phase information is not preserved. Such a representation is called the power spectral density of the random process. Random electromagnetic radiation requiring this kind of analysis is, for example, encountered in the interior of stars, and in certain other very wideband forms of radiation such as the Zero point field, Zero point wave field of the electromagnetic vacuum. The behavior of EM radiation and its interaction with matter depends on its frequency, and changes qualitatively as the frequency changes. Lower frequencies have longer wavelengths, and higher frequencies have shorter wavelengths, and are associated with photons of higher energy. There is no fundamental limit known to these wavelengths or energies, at either end of the spectrum, although photons with energies near the Planck energy or exceeding it (far too high to have ever been observed) will require new physical theories to describe.

## Radio and microwave

When radio waves impinge upon a Electrical conductor, conductor, they couple to the conductor, travel along it and radio frequency induction, induce an electric current on the conductor surface by moving the electrons of the conducting material in correlated bunches of charge. Such effects can cover macroscopic distances in conductors (such as radio antennas), since the wavelength of radiowaves is long. Electromagnetic radiation phenomena with wavelengths ranging from as long as one meter to as short as one millimeter are called microwaves; with frequencies between 300 MHz (0.3 GHz) and 300 GHz. At radio and microwave frequencies, EMR interacts with matter largely as a bulk collection of charges which are spread out over large numbers of affected atoms. In electrical conductors, such induced bulk movement of charges (electric currents) results in absorption of the EMR, or else separations of charges that cause generation of new EMR (effective reflection of the EMR). An example is absorption or emission of radio waves by antennas, or absorption of microwaves by water or other molecules with an electric dipole moment, as for example inside a microwave oven. These interactions produce either electric currents or heat, or both.

## Infrared

Like radio and microwave, infrared (IR) also is reflected by metals (and also most EMR, well into the ultraviolet range). However, unlike lower-frequency radio and microwave radiation, Infrared EMR commonly interacts with dipoles present in single molecules, which change as atoms vibrate at the ends of a single chemical bond. It is consequently absorbed by a wide range of substances, causing them to increase in temperature as the vibrations dissipate as heat. The same process, run in reverse, causes bulk substances to radiate in the infrared spontaneously (see thermal radiation section below). Infrared radiation is divided into spectral subregions. While different subdivision schemes exist, the spectrum is commonly divided as near-infrared (0.75–1.4 μm), short-wavelength infrared (1.4–3 μm), mid-wavelength infrared (3–8 μm), long-wavelength infrared (8–15 μm) and far infrared (15–1000 μm).

## Visible light

Natural sources produce EM radiation across the spectrum. EM radiation with a
wavelength In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is the distance between consecutive corresponding points of the same phase (waves), phase on the wave, such as two adja ...

between approximately 400 nanometre, nm and 700 nm is directly detected by the human eye and perceived as visible light. Other wavelengths, especially nearby infrared (longer than 700 nm) and ultraviolet (shorter than 400 nm) are also sometimes referred to as light. As frequency increases into the visible range, photons have enough energy to change the bond structure of some individual molecules. It is not a coincidence that this happens in the visible range, as the Visual system, mechanism of vision involves the change in bonding of a single molecule, retinal, which absorbs a single photon. The change in retinal causes a change in the shape of the rhodopsin protein it is contained in, which starts the biochemical process that causes the retina of the human eye to sense the light. Photosynthesis becomes possible in this range as well, for the same reason. A single molecule of chlorophyll is excited by a single photon. In plant tissues that conduct photosynthesis, carotenoids act to quench electronically excited chlorophyll produced by visible light in a process called non-photochemical quenching, to prevent reactions that would otherwise interfere with photosynthesis at high light levels. infrared sensing in snakes, Animals that detect infrared make use of small packets of water that change temperature, in an essentially thermal process that involves many photons. Infrared, microwaves and radio waves are known to damage molecules and biological tissue only by bulk heating, not excitation from single photons of the radiation. Visible light is able to affect only a tiny percentage of all molecules. Usually not in a permanent or damaging way, rather the photon excites an electron which then emits another photon when returning to its original position. This is the source of color produced by most dyes. Retinal is an exception. When a photon is absorbed the retinal permanently changes structure from cis to trans, and requires a protein to convert it back, i.e. reset it to be able to function as a light detector again. Limited evidence indicate that some reactive oxygen species are created by visible light in skin, and that these may have some role in photoaging, in the same manner as ultraviolet A.

## Ultraviolet

As frequency increases into the ultraviolet, photons now carry enough energy (about three electron volts or more) to excite certain doubly bonded molecules into permanent chemical rearrangement. In DNA, this causes lasting damage. DNA is also indirectly damaged by reactive oxygen species produced by ultraviolet A (UVA), which has energy too low to damage DNA directly. This is why ultraviolet at all wavelengths can damage DNA, and is capable of causing cancer, and (for UVB) skin burns (sunburn) that are far worse than would be produced by simple heating (temperature increase) effects. This property of causing molecular damage that is out of proportion to heating effects, is characteristic of all EMR with frequencies at the visible light range and above. These properties of high-frequency EMR are due to quantum effects that permanently damage materials and tissues at the molecular level. At the higher end of the ultraviolet range, the energy of photons becomes large enough to impart enough energy to electrons to cause them to be liberated from the atom, in a process called photoionisation. The energy required for this is always larger than about 10 electron volt (eV) corresponding with wavelengths smaller than 124 nm (some sources suggest a more realistic cutoff of 33 eV, which is the energy required to ionize water). This high end of the ultraviolet spectrum with energies in the approximate ionization range, is sometimes called "extreme UV." Ionizing UV is strongly filtered by the Earth's atmosphere.

## X-rays and gamma rays

Electromagnetic radiation composed of photons that carry minimum-ionization energy, or more, (which includes the entire spectrum with shorter wavelengths), is therefore termed
ionizing radiation Ionizing radiation (or ionising radiation), including nuclear radiation, consists of s or s that have sufficient to s or s by detaching s from them. The particles generally travel at a speed that is greater than 1% of , and the electromagnetic w ...
. (Many other kinds of ionizing radiation are made of non-EM particles). Electromagnetic-type ionizing radiation extends from the extreme ultraviolet to all higher frequencies and shorter wavelengths, which means that all X-rays and gamma rays qualify. These are capable of the most severe types of molecular damage, which can happen in biology to any type of biomolecule, including mutation and cancer, and often at great depths below the skin, since the higher end of the X-ray spectrum, and all of the gamma ray spectrum, penetrate matter.

# Atmosphere and magnetosphere

Most UV and X-rays are blocked by absorption first from molecular nitrogen, and then (for wavelengths in the upper UV) from the electronic excitation of dioxygen and finally ozone at the mid-range of UV. Only 30% of the Sun's ultraviolet light reaches the ground, and almost all of this is well transmitted. Visible light is well transmitted in air, as it is not energetic enough to excite nitrogen, oxygen, or ozone, but too energetic to excite molecular vibrational frequencies of water vapor. Absorption bands in the infrared are due to modes of vibrational excitation in water vapor. However, at energies too low to excite water vapor, the atmosphere becomes transparent again, allowing free transmission of most microwave and radio waves. Finally, at radio wavelengths longer than 10 meters or so (about 30 MHz), the air in the lower atmosphere remains transparent to radio, but plasma in certain layers of the ionosphere begins to interact with radio waves (see skywave). This property allows some longer wavelengths (100 meters or 3 MHz) to be reflected and results in shortwave radio beyond line-of-sight. However, Ionosphere#D layer, certain ionospheric effects begin to block incoming radiowaves from space, when their frequency is less than about 10 MHz (wavelength longer than about 30 meters).

# Thermal and electromagnetic radiation as a form of heat

The basic structure 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 ultimately composed of atoms, which are made up of interacting subatomic particl ...

# Biological effects

ionizing radiation Ionizing radiation (or ionising radiation), including nuclear radiation, consists of s or s that have sufficient to s or s by detaching s from them. The particles generally travel at a speed that is greater than 1% of , and the electromagnetic w ...
due to the ability of photons of this radiation to produce ions and free radicals in materials (including living tissue). Since such radiation can severely damage life at energy levels that produce little heating, it is considered far more dangerous (in terms of damage-produced per unit of energy, or power) than the rest of the electromagnetic spectrum.

## Use as weapon

The heat ray is an application of EMR that makes use of microwave frequencies to create an unpleasant heating effect in the upper layer of the skin. A publicly known heat ray weapon called the Active Denial System was developed by the US military as an experimental weapon to deny the enemy access to an area. A death ray is a theoretical weapon that delivers heat ray based on electromagnetic energy at levels that are capable of injuring human tissue. An inventor of a death ray, Harry Grindell Matthews, claimed to have lost sight in his left eye while working on his death ray weapon based on a microwave magnetron from the 1920s (a normal microwave oven creates a tissue damaging cooking effect inside the oven at around 2 kV/m).

# Derivation from electromagnetic theory

Electromagnetic waves are predicted by the classical laws of electricity and magnetism, known as
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), s ...
. There are nontrivial solutions of the homogeneous Maxwell's equations (without charges or currents), describing ''waves'' of changing electric and magnetic fields. Beginning with Maxwell's equations in vacuum, free space: :where ::$\mathbf$ and $\mathbf$ are the
electric field An electric field (sometimes E-field) is the physical field that surrounds electrically-charged particle In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' ' ...

(measured in Volt, V/m or Newtons, N/Coulomb, C) and the
magnetic field A magnetic field is a vector field In vector calculus and physics, a vector field is an assignment of a vector to each point in a subset of space. For instance, a vector field in the plane can be visualised as a collection of arrows with ...

(measured in Tesla (unit), T or Weber (unit), Wb/m2), respectively; ::$\nabla \cdot X$ yields the divergence and $\nabla \times X$ the curl (mathematics), curl of a vector field $X;$ ::$\frac$ and $\frac$ are partial derivatives (rate of change in time, with location fixed) of the magnetic and electric field; ::$\mu_0$ is the permeability (electromagnetism), permeability of a vacuum (4$\pi$ x 10−7 (Henry (unit), H/m)), and $\varepsilon_0$ is the permittivity of a vacuum (8.85×10−12 (Farad (unit), F/m)); :: Besides the trivial solution ::$\mathbf=\mathbf=\mathbf,$ useful solutions can be derived with the following vector calculus identities, vector identity, valid for all vectors $\mathbf$ in some vector field: ::$\nabla \times \left\left( \nabla \times \mathbf \right\right) = \nabla \left\left( \nabla \cdot \mathbf \right\right) - \nabla^2 \mathbf.$ Taking the curl of the second Maxwell equation () yields: Evaluating the left hand side of () with the above identity and simplifying using (), yields: Evaluating the right hand side of () by exchanging the sequence of derivations and inserting the fourth yields: Combining () and () again, gives a vector-valued differential equation for the electric field, solving the homogeneous Maxwell equations: Taking the curl of the fourth Maxwell equation () results in a similar differential equation for a magnetic field solving the homogeneous Maxwell equations: Both differential equations have the form of the general wave equation for waves propagating with speed $c_0,$ where $f$ is a function of time and location, which gives the amplitude of the wave at some time at a certain location: :$\nabla^2 f = \frac \frac$ This is also written as: ::$\Box f = 0$ where $\Box$ denotes the so-called d'Alembert operator, which in Cartesian coordinates is given as: ::$\Box = \nabla^2 - \frac \frac = \frac + \frac + \frac - \frac \frac \$ Comparing the terms for the speed of propagation, yields in the case of the electric and magnetic fields: ::$c_0 = \frac.$ This is the
speed of light The speed of light in vacuum A vacuum is a space devoid of matter. The word is derived from the Latin adjective ''vacuus'' for "vacant" or "Void (astronomy), void". An approximation to such vacuum is a region with a gaseous pressure m ...
in vacuum. Thus Maxwell's equations connect the vacuum permittivity $\varepsilon_0$, the vacuum permeability $\mu_0$, and the speed of light, ''c''0, via the above equation. This relationship had been discovered by Wilhelm Eduard Weber and Rudolf Kohlrausch prior to the development of Maxwell's electrodynamics, however Maxwell was the first to produce a field theory consistent with waves traveling at the speed of light. These are only two equations versus the original four, so more information pertains to these waves hidden within Maxwell's equations. A generic vector wave for the electric field has the form :$\mathbf = \mathbf_0 f\left\left( \hat \cdot \mathbf - c_0 t \right\right)$ Here, $\mathbf_0$ is the constant amplitude, $f$ is any second differentiable function, $\hat$ is a unit vector in the direction of propagation, and  is a position vector. $f\left\left( \hat \cdot \mathbf - c_0 t \right\right)$ is a generic solution to the wave equation. In other words, :$\nabla^2 f\left\left( \hat \cdot \mathbf - c_0 t \right\right) = \frac \frac f\left\left( \hat \cdot \mathbf - c_0 t \right\right),$ for a generic wave traveling in the $\hat$ direction. From the first of Maxwell's equations, we get :$\nabla \cdot \mathbf = \hat \cdot \mathbf_0 f\text{'}\left\left( \hat \cdot \mathbf - c_0 t \right\right) = 0$ Thus, :$\mathbf \cdot \hat = 0$ which implies that the electric field is orthogonal to the direction the wave propagates. The second of Maxwell's equations yields the magnetic field, namely, :$\nabla \times \mathbf = \hat \times \mathbf_0 f\text{'}\left\left( \hat \cdot \mathbf - c_0 t \right\right) = -\frac$ Thus, :$\mathbf = \frac \hat \times \mathbf$ The remaining equations will be satisfied by this choice of $\mathbf,\mathbf$. The electric and magnetic field waves in the far-field travel at the speed of light. They have a special restricted orientation and proportional magnitudes, $E_0 = c_0 B_0$, which can be seen immediately from the Poynting vector. The electric field, magnetic field, and direction of wave propagation are all orthogonal, and the wave propagates in the same direction as $\mathbf \times \mathbf$. Also, E and B far-fields in free space, which as wave solutions depend primarily on these two Maxwell equations, are in-phase with each other. This is guaranteed since the generic wave solution is first order in both space and time, and the curl operator on one side of these equations results in first-order spatial derivatives of the wave solution, while the time-derivative on the other side of the equations, which gives the other field, is first-order in time, resulting in the same phase shift for both fields in each mathematical operation. From the viewpoint of an electromagnetic wave traveling forward, the electric field might be oscillating up and down, while the magnetic field oscillates right and left. This picture can be rotated with the electric field oscillating right and left and the magnetic field oscillating down and up. This is a different solution that is traveling in the same direction. This arbitrariness in the orientation with respect to propagation direction is known as polarization (waves), polarization. On a quantum level, it is described as photon polarization. The direction of the polarization is defined as the direction of the electric field. More general forms of the second-order wave equations given above are available, allowing for both non-vacuum propagation media and sources. Many competing derivations exist, all with varying levels of approximation and intended applications. One very general example is a form of the electric field equation, which was factorized into a pair of explicitly directional wave equations, and then efficiently reduced into a single uni-directional wave equation by means of a simple slow-evolution approximation.

* Antenna measurement * Bioelectromagnetism * Bolometer * Control of electromagnetic radiation * Electromagnetic pulse * Electromagnetic radiation and health * Evanescent wave coupling * Finite-difference time-domain method * Gravitational wave * Helicon (physics), Helicon * Impedance of free space * Radiation reaction * Risks and benefits of sun exposure * Sinusoidal plane-wave solutions of the electromagnetic wave equation

# References

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"Electromagnetism"
– a chapter from an online textbook
''Electromagnetic Waves from Maxwell's Equations''
o
Project PHYSNET

An Introduction to The Wigner Distribution in Geometric Optics

Introduction to light and electromagnetic radiation
course video from the Khan Academy
Lectures on electromagnetic waves
course video and notes from MIT Professor Walter Lewin