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In
physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...
, the intensity or flux of
radiant energy Radiant may refer to: Computers, software, and video games * Radiant (software), a content management system * GtkRadiant, a level editor created by id Software for their games * Radiant AI, a technology developed by Bethesda Softworks for ''The ...
is the
power Power most often refers to: * Power (physics), meaning "rate of doing work" ** Engine power, the power put out by an engine ** Electric power * Power (social and political), the ability to influence people or events ** Abusive power Power may a ...
transferred per unit
area Area is the quantity that expresses the extent of a region on the plane or on a curved surface. The area of a plane region or ''plane area'' refers to the area of a shape A shape or figure is a graphics, graphical representation of an obje ...
, where the area is measured on the plane perpendicular to the direction of propagation of the energy. In the SI system, it has units
watt The watt (symbol: W) is the unit of power or radiant flux in the International System of Units (SI), equal to 1 joule per second or 1 kg⋅m2⋅s−3. It is used to quantify the rate of energy transfer. The watt is named after James Wa ...
s per
square metre The square metre ( international spelling as used by the International Bureau of Weights and Measures) or square meter (American spelling) is the unit of area in the International System of Units (SI) with symbol m2. It is the area of a square w ...
(W/m2), or kgs−3 in
base units A base unit (also referred to as a fundamental unit) is a unit adopted for measurement of a '' base quantity''. A base quantity is one of a conventionally chosen subset of physical quantities, where no quantity in the subset can be expressed in ter ...
. Intensity is used most frequently with
wave In physics, mathematics, and related fields, a wave is a propagating dynamic disturbance (change from equilibrium) of one or more quantities. Waves can be periodic, in which case those quantities oscillate repeatedly about an equilibrium (res ...
s such as acoustic waves (
sound In physics, sound is a vibration that propagates as an acoustic wave, through a transmission medium such as a gas, liquid or solid. In human physiology and psychology, sound is the ''reception'' of such waves and their ''perception'' by the ...
) or
electromagnetic wave In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, infrared, (visib ...
s such as
light Light or visible light is electromagnetic radiation that can be perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), corresponding to frequencies of 750–420 tera ...
or
radio wave Radio waves are a type of electromagnetic radiation with the longest wavelengths in the electromagnetic spectrum, typically with frequencies of 300 gigahertz (GHz) and below. At 300 GHz, the corresponding wavelength is 1 mm (short ...
s, in which case the ''average'' power transfer over one
period Period may refer to: Common uses * Era, a length or span of time * Full stop (or period), a punctuation mark Arts, entertainment, and media * Period (music), a concept in musical composition * Periodic sentence (or rhetorical period), a concept ...
of the wave is used. ''Intensity'' can be applied to other circumstances where energy is transferred. For example, one could calculate the intensity of the
kinetic energy In physics, the kinetic energy of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its accele ...
carried by drops of water from a
garden sprinkler An irrigation sprinkler (also known as a water sprinkler or simply a sprinkler) is a device used to irrigate (water) agricultural crops, lawns, landscapes, golf courses, and other areas. They are also used for cooling and for the control of airb ...
. The word "intensity" as used here is not synonymous with "
strength Strength may refer to: Physical strength *Physical strength, as in people or animals * Hysterical strength, extreme strength occurring when people are in life-and-death situations *Superhuman strength, great physical strength far above human c ...
", "
amplitude The amplitude of a periodic variable is a measure of its change in a single period (such as time or spatial period). The amplitude of a non-periodic signal is its magnitude compared with a reference value. There are various definitions of amplit ...
", "
magnitude Magnitude may refer to: Mathematics *Euclidean vector, a quantity defined by both its magnitude and its direction *Magnitude (mathematics), the relative size of an object *Norm (mathematics), a term for the size or length of a vector *Order of ...
", or "
level Level or levels may refer to: Engineering *Level (instrument), a device used to measure true horizontal or relative heights *Spirit level, an instrument designed to indicate whether a surface is horizontal or vertical *Canal pound or level *Regr ...
", as it sometimes is in colloquial speech. Intensity can be found by taking the
energy density In physics, energy density is the amount of energy stored in a given system or region of space per unit volume. It is sometimes confused with energy per unit mass which is properly called specific energy or . Often only the ''useful'' or extract ...
(energy per unit volume) at a point in space and multiplying it by the
velocity Velocity is the directional speed of an object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time (e.g. northbound). Velocity is a ...
at which the energy is moving. The resulting
vector Vector most often refers to: *Euclidean vector, a quantity with a magnitude and a direction *Vector (epidemiology), an agent that carries and transmits an infectious pathogen into another living organism Vector may also refer to: Mathematic ...
has the units of power divided by area (i.e.,
surface power density In physics and engineering, surface power density is power per unit area. Applications * The intensity of electromagnetic radiation can be expressed in W/m2. An example of such a quantity is the solar constant. * Wind turbines are often compared ...
).


Mathematical description

If 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 ...
is radiating energy in all directions (producing a
spherical wave The (two-way) wave equation is a second-order linear partial differential equation for the description of waves or standing wave fields — as they occur in classical physics — such as mechanical waves (e.g. water waves, sound waves and seis ...
), and no energy is absorbed or scattered by the medium, then the intensity decreases in proportion to the distance from the object squared. This is an example of the
inverse-square law In science, an inverse-square law is any scientific law stating that a specified physical quantity is inversely proportional to the square of the distance from the source of that physical quantity. The fundamental cause for this can be understo ...
. Applying the law of
conservation of energy In physics and chemistry, the law of conservation of energy states that the total energy of an isolated system remains constant; it is said to be ''conserved'' over time. This law, first proposed and tested by Émilie du Châtelet, means th ...
, if the net power emanating is constant, P = \int \mathbf I\, \cdot d\mathbf A, where ''P'' is the net power radiated, I is the intensity vector as a function of position, the magnitude is the intensity as a function of position, and ''d''A is a
differential element In mathematics, differential refers to several related notions derived from the early days of calculus, put on a rigorous footing, such as infinitesimal differences and the derivatives of functions. The term is used in various branches of mathe ...
of a closed surface that contains the source. If one integrates a uniform intensity, , over a surface that is perpendicular to the intensity vector, for instance over a sphere centered around the point source, the equation becomes P = , I, \cdot A_\mathrm = , I, \cdot 4\pi r^2 \,, where is the intensity at the surface of the sphere, ''r'' is the radius of the sphere, and A_\mathrm = 4\pi r^2 is the expression for the surface area of a sphere. Solving for gives , I, = \frac = \frac. If the medium is damped, then the intensity drops off more quickly than the above equation suggests. Anything that can transmit energy can have an intensity associated with it. For a monochromatic propagating electromagnetic wave, such as a
plane wave In physics, a plane wave is a special case of wave or field: a physical quantity whose value, at any moment, is constant through any plane that is perpendicular to a fixed direction in space. For any position \vec x in space and any time t, th ...
or a
Gaussian beam In optics, a Gaussian beam is a beam of electromagnetic radiation with high monochromaticity whose amplitude envelope in the transverse plane is given by a Gaussian function; this also implies a Gaussian intensity (irradiance) profile. This ...
, if ''E'' is the
complex amplitude Complex commonly refers to: * Complexity, the behaviour of a system whose components interact in multiple ways so possible interactions are difficult to describe ** Complex system, a system composed of many components which may interact with each ...
of the
electric field An electric field (sometimes E-field) is the physical field that surrounds electrically charged particles and exerts force on all other charged particles in the field, either attracting or repelling them. It also refers to the physical field fo ...
, then the time-averaged
energy density In physics, energy density is the amount of energy stored in a given system or region of space per unit volume. It is sometimes confused with energy per unit mass which is properly called specific energy or . Often only the ''useful'' or extract ...
of the wave, travelling in a non-magnetic material, is given by: \left\langle U \right \rangle = \frac , E, ^2, and the local intensity is obtained by multiplying this expression by the wave velocity, c/''n'': I = \frac , E, ^2, where ''n'' is the
refractive index In optics, the refractive index (or refraction index) of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium. The refractive index determines how much the path of light is bent, or ...
, c is the
speed of light The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit ...
in
vacuum A vacuum is a space devoid of matter. The word is derived from the Latin adjective ''vacuus'' for "vacant" or "void". An approximation to such vacuum is a region with a gaseous pressure much less than atmospheric pressure. Physicists often dis ...
and \varepsilon_0 is the
vacuum permittivity Vacuum permittivity, commonly denoted (pronounced "epsilon nought" or "epsilon zero"), is the value of the absolute dielectric permittivity of classical vacuum. It may also be referred to as the permittivity of free space, the electric consta ...
. For non-monochromatic waves, the intensity contributions of different spectral components can simply be added. The treatment above does not hold for arbitrary electromagnetic fields. For example, an
evanescent wave In electromagnetics, an evanescent field, or evanescent wave, is an oscillating electric and/or magnetic field that does not propagate as an electromagnetic wave but whose energy is spatially concentrated in the vicinity of the source (oscillati ...
may have a finite electrical amplitude while not transferring any power. The intensity should then be defined as the magnitude of the
Poynting vector In physics, the Poynting vector (or Umov–Poynting vector) represents the directional energy flux (the energy transfer per unit area per unit time) or '' power flow'' of an electromagnetic field. The SI unit of the Poynting vector is the watt ...
.


Alternative definitions

In
photometry Photometry can refer to: * Photometry (optics), the science of measurement of visible light in terms of its perceived brightness to human vision * Photometry (astronomy), the measurement of the flux or intensity of an astronomical object's electro ...
and
radiometry Radiometry is a set of techniques for measurement, measuring electromagnetic radiation, including visible light. Radiometric techniques in optics characterize the distribution of the radiation's power (physics), power in space, as opposed to phot ...
''intensity'' has a different meaning: it is the luminous or radiant power ''per unit
solid angle In geometry, a solid angle (symbol: ) is a measure of the amount of the field of view from some particular point that a given object covers. That is, it is a measure of how large the object appears to an observer looking from that point. The poi ...
''. This can cause confusion in
optics Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behaviour of visible, ultraviole ...
, where ''intensity'' can mean any of
radiant intensity In radiometry, radiant intensity is the radiant flux emitted, reflected, transmitted or received, per unit solid angle, and spectral intensity is the radiant intensity per unit frequency or wavelength, depending on whether the spectrum is taken ...
,
luminous intensity In photometry, luminous intensity is a measure of the wavelength-weighted power emitted by a light source in a particular direction per unit solid angle, based on the luminosity function, a standardized model of the sensitivity of the human eye. ...
or
irradiance In radiometry, irradiance is the radiant flux ''received'' by a ''surface'' per unit area. The SI unit of irradiance is the watt per square metre (W⋅m−2). The CGS unit erg per square centimetre per second (erg⋅cm−2⋅s−1) is often used ...
, depending on the background of the person using the term.
Radiance In radiometry, radiance is the radiant flux emitted, reflected, transmitted or received by a given surface, per unit solid angle per unit projected area. Radiance is used to characterize diffuse emission and reflection of electromagnetic radiatio ...
is also sometimes called ''intensity'', especially by astronomers and astrophysicists, and in
heat transfer Heat transfer is a discipline of thermal engineering that concerns the generation, use, conversion, and exchange of thermal energy (heat) between physical systems. Heat transfer is classified into various mechanisms, such as thermal conduction, ...
.


See also

*
Field strength In physics, field strength means the ''magnitude'' of a vector-valued field (e.g., in volts per meter, V/m, for an electric field ''E''). For example, an electromagnetic field results in both electric field strength and magnetic field strength. As ...
*
Sound intensity Sound intensity, also known as acoustic intensity, is defined as the power carried by sound waves per unit area in a direction perpendicular to that area. The SI unit of intensity, which includes sound intensity, is the watt per square meter (W/m2 ...
*
Magnitude (astronomy) In astronomy, magnitude is a unitless measure of the brightness Brightness is an attribute of visual perception in which a source appears to be radiating or reflecting light. In other words, brightness is the perception elicited by the lumi ...


References

{{DEFAULTSORT:Intensity (Physics) Optics Radiometry Physical quantities