Intensity (physics)
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2008-07-06T00:51:04Z
Srleffler
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rv. In physics, variables generally have only a single letter. "SA" is definitely nonstandard. "S" would be more common, but not as clear.
{{otheruses|Intensity (disambiguation)}}
In [[physics]], '''intensity''' is a [[Measurement|measure]] of the [[time averaging|time-averaged]] [[energy]] [[flux]]. The word "intensity" here is not synonymous with "[[wikt:strength|strength]]", "[[wikt:amplitude|amplitude]]", or "[[wikt:level|level]]", as it sometimes is in colloquial speech. For example, "the intensity of pressure" is meaningless, since the parameters of those variables do not match.
To find the intensity, take the energy density (that is, the energy per unit volume) and multiply it by the [[velocity]] at which the energy is moving. The resulting [[vector (spatial)|vector]] has the units of [[Power (physics)|power]] divided by [[area]] (i.e. watt/m²). It is possible to define the intensity of the water coming from a garden sprinkler, but intensity is used most frequently with [[wave]]s (i.e. [[sound]] or [[light]]).
==Mathematical description==
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 due to physics and geometry. Physically, [[conservation of energy]] applies. The consequence of this is that the net power coming from the source must be constant, thus:
:<math>P = \int I\, dA</math>
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. That ''P'' is a constant. If we integrate 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:
:<math>P = |I| \cdot A_{surf} = |I| \cdot 4\pi r^2 \,</math> <!-- "\,": other two equations get PNG treatment -->
where ''I'' is the intensity at the surface of the sphere, and ''r'' is the radius of the sphere. (<math>A_{surf} = 4\pi r^2 </math> is the expression for the surface area of a sphere). Solving for ''I'', we get:
:<math>|I| = \frac{P}{A_{surf}} = \frac{P}{4\pi r^2}</math>
If the medium is damped, then the intensity drops off more quickly than the above equation suggests.
Anything that can carry 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 [[energy density]] of the wave is given by
:<math>U = \frac{n^2 \epsilon_0}{2} |E|^2 </math>,
and the intensity is obtained multiplying this expression by the velocity of the wave, <math>c/n</math>:
:<math>I = \frac{c n \epsilon_0}{2} |E|^2</math>,
where ''n'' is the [[refractive index]], <math>c</math> is the [[speed of light]] in [[vacuum]] and <math>\epsilon_0</math> is the [[electric permittivity]] in vacuum.
==Intensity in photometry and radiometry==
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.
==See also==
*[[Sound intensity]]
*[[Magnitude (mathematics)|Magnitude]]
{{SI light units}}
{{SI radiometry units}}
[[Category:Optics]]
[[Category:Radiometry]]
[[Category:Physical quantity]]
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