Shows the relative wavelengths of the electromagnetic waves of three different colours of
(blue, green, and red) with a distance scale in micrometers along the x-axis.
Maxwell derived a
wave form of the electric and magnetic equations, thus uncovering the wave-like nature of electric and magnetic fields and their
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.
 Maxwell’s equations were confirmed by
Heinrich Hertz through experiments with radio waves.
Maxwell's equations, a spatially varying
electric field is always associated with a
magnetic field 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 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 fact, magnetic fields may be viewed as relativistic distortions of electric fields, 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 affect 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
In electromagnetic radiation (such as microwaves from an antenna, shown here) the term applies only to the parts of the
that radiate into infinite space and decrease in intensity by an
of power, so that the total radiation energy that crosses through an imaginary spherical surface is the same, no matter how far away from the antenna the spherical surface is drawn. Electromagnetic radiation thus includes the
part of the electromagnetic field around a transmitter. A part of the "near-field" close to the transmitter, forms part of the changing
, but does not count as electromagnetic radiation.
Maxwell's equations established that some charges and currents ("sources") produce a local type of
electromagnetic field near them that does not have the behaviour of EMR. Currents directly produce a magnetic field, but it is of a
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 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 inside a
transformer, or the feedback behaviour that happens close to the coil of a
metal detector. Typically, near-fields have a powerful effect on their own sources, causing an increased “load” (decreased
electrical reactance) 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 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 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 of EM radiation always decreases with the inverse square of distance from the source; this is called the
inverse-square law. This is in contrast to dipole parts of the EM field close to the source (the near-field), which varies in power according to an inverse cube power law, and thus does not transport a conserved amount of energy over distances, but instead fades 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).
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.
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. Note that the electric and magnetic fields in such a wave are in-phase with each other, reaching minima and maxima together
An alternate view of the wave shown above.
Electrodynamics is the
physics of electromagnetic radiation, and
electromagnetism 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 fields, all magnetic and electric field vectors add together according to
 For example, in optics two or more coherent lightwaves may interact and by constructive or destructive
interference yield a resultant irradiance deviating from the sum of the component irradiances of the individual lightwaves.
Since light is an oscillation it is 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
crystals, interactions can occur between light and static electric and magnetic fields — these interactions include the
Faraday effect and the
refraction, a wave crossing from one medium to another of different
density alters its
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
spectrum passing through a prism, because of the wavelength-dependent
refractive index of the
prism material (
dispersion); that is, each component wave within the composite light is bent a different amount.
EM radiation exhibits both wave properties and
particle properties at the same time (see
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 too 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
 When a single photon is sent through an
interferometer, it passes through both paths, interfering with itself, as waves do, yet is detected by a
photomultiplier or other sensitive detector only once.
quantum theory of the interaction between electromagnetic radiation and matter such as electrons is described by the theory of
Electromagnetic waves can be
polarized, reflected, refracted,
diffracted or interfere with each other.
Representation of the electric field vector of a wave of circularly polarized electromagnetic radiation.
Electromagnetic radiation is a
transverse wave, 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 in order to satisfy the two
Maxwell equations that specify how one is produced from the other. 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, 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 math section below).
An important aspect of light's nature is its frequency. The frequency of a wave is its rate of oscillation and is measured in
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
A wave 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 the size of buildings to very short gamma rays smaller than atom nuclei. Frequency is inversely proportional to wavelength, according to the equation:
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. 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. 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 (EMI) or as it is more commonly known as,
radio-frequency interference (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
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
black bodies. Physicists struggled with this problem, which later became known as the
ultraviolet catastrophe, unsuccessfully for many years. In 1900,
Max Planck developed a new theory of
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
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
proton. A photon has an energy, E, proportional to its frequency, f, by
where h is
Planck's constant, is the wavelength and c is the
speed of light. This is sometimes known as the
 In quantum theory (see
first quantization) 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:
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, 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
As a photon is absorbed by an
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
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
electrons also exhibited 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 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, 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 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
When any wire (or other conducting object such as an
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),
frequency. As particles, light is a stream of
photons. Each has an energy related to the frequency of the wave given by
Planck's relation E = hf, where E is the energy of the photon, h = 6.626 × 10−34 J·s is
Planck's constant, 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, relative to the observer, regardless of the observer's velocity. (This observation led to Einstein's development of the theory of
In a medium (other than vacuum),
velocity factor or
refractive index 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
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
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.