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| {{other uses|Intensity (disambiguation)}}
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| In [[physics]], '''intensity''' is the [[Power (physics)|power]] transferred per unit [[area]]. In the [[SI]] system, it has units watts per metre squared (W/m<sup>2</sup>). It is used most frequently with [[wave]]s (e.g. [[sound]] or [[light]]), in which case the [[time averaging|''average'']] power transfer over one [[Period (physics)|period]] 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]] carried by drops of water from a [[garden sprinkler]].
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| The word "intensity" as used here is not synonymous with "[[wikt:strength|strength]]", "[[wikt:amplitude|amplitude]]", "[[wikt:magnitude|magnitude]]", or "[[wikt:level|level]]", as it sometimes is in colloquial speech.
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| Intensity can be found by taking the [[energy density]] (energy per unit volume) at a point in space and multiplying it by the [[velocity]] at which the energy is moving. The resulting [[Vector (geometry)|vector]] has the units of [[Power (physics)|power]] divided by [[area]].
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| ==Mathematical description==
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| If a [[point source]] is radiating energy in ''three dimensions'' and there is no energy lost to the medium, then the intensity decreases in proportion to distance from the object squared. This is an example of the [[inverse-square law]].
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| Applying the law of [[conservation of energy]], if the net power emanating is constant,
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| :<math>P = \int I\, \cdot dA</math>,
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| where ''P'' is the net power radiated, ''I'' is the intensity as a function of position, and ''dA'' is a [[differential element]] of a closed surface that contains the source.
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| If one integrates over a surface of uniform intensity ''I'', for instance over a sphere centered around a point source radiating equally in all directions, the equation becomes
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| :<math>P = |I| \cdot A_\mathrm{surf} = |I| \cdot 4\pi r^2 \,</math>, <!-- "\,": other two equations get PNG treatment -->
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| where ''I'' is the intensity at the surface of the sphere, and ''r'' is the radius of the sphere. (<math>A_\mathrm{surf} = 4\pi r^2 </math> is the expression for the surface area of a sphere).
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| Solving for ''I'' gives
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| :<math>|I| = \frac{P}{A_\mathrm{surf}} = \frac{P}{4\pi r^2}</math>.
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| If the medium is damped, then the intensity drops off more quickly than the above equation suggests.
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| Anything that can transmit energy can have an intensity associated with it. For an [[electromagnetic wave]], if ''E'' is the [[complex number|complex]] [[amplitude]] of the [[electric field]], then the time-averaged [[energy density]] of the wave is given by
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| :<math>\left\langle U \right \rangle = \frac{n^2 \epsilon_0}{2} |E|^2 </math>,
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| and the intensity is obtained by multiplying this expression by the velocity of the wave, <math>c/n</math>:
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| :<math>I = \frac{c n \epsilon_0}{2} |E|^2</math>, | |
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| where ''n'' is the [[refractive index]], <math>c</math> is the [[speed of light]] in [[vacuum]] and <math>\epsilon_0</math> is the [[vacuum permittivity]].
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| The treatment above does not hold for electromagnetic fields that are not radiating, such as for an [[evanescent wave]]. In these cases, the intensity can be defined as the magnitude of the [[Poynting vector]].<ref>{{cite web |work=Encyclopedia of Laser Physics and Technology |title=Optical Intensity |url=http://www.rp-photonics.com/optical_intensity.html |publisher=RP Photonics |first=Rüdiger |last=Paschotta}}</ref>
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| ==Alternative definitions of "intensity"==
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| In [[photometry (optics)|photometry]] and [[radiometry]] ''intensity'' has a different meaning: it is the luminous or radiant power ''per unit [[solid angle]]''. This can cause confusion in [[optics]], where ''intensity'' can mean any of [[radiant intensity]], [[luminous intensity]] or [[irradiance]], depending on the background of the person using the term. [[Radiance]] is also sometimes called ''intensity'', especially by astronomers and astrophysicists, and in [[heat transfer]].
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| ==See also==
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| *[[Sound intensity]]
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| *[[Magnitude (astronomy)]]
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| {{SI light units|1|self}}<!-- parameter 1 = table 1, parameter 2=compare page self reference -->
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| {{SI radiometry units|2|self}}<!-- parameter 1 = table 2, parameter 2=compare page self reference -->
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| == References ==
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| <references/>
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| {{DEFAULTSORT:Intensity (Physics)}}
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| [[Category:Optics]]
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| [[Category:Radiometry]]
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| [[Category:Physical quantities]]
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