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{{other uses|Intensity (disambiguation)}}
This is a preview for the new '''MathML rendering mode''' (with SVG fallback), which is availble in production for registered users.
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]].


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.  
If you would like use the '''MathML''' rendering mode, you need a wikipedia user account that can be registered here [[https://en.wikipedia.org/wiki/Special:UserLogin/signup]]
* Only registered users will be able to execute this rendering mode.
* Note: you need not enter a email address (nor any other private information). Please do not use a password that you use elsewhere.


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]].
Registered users will be able to choose between the following three rendering modes:


==Mathematical description==
'''MathML'''
If a [[point source]] is radiating energy in all directions (producing a [[spherical wave]]), and no energy is absorbed or scattered by the medium, then the intensity decreases in proportion to distance from the object squared. This is an example of the [[inverse-square law]].
:<math forcemathmode="mathml">E=mc^2</math>


Applying the law of [[conservation of energy]], if the net power emanating is constant,
<!--'''PNG'''  (currently default in production)
:<math forcemathmode="png">E=mc^2</math>


:<math>P = \int \bold I\, \cdot \mathrm{d}\bold A</math>,
'''source'''
:<math forcemathmode="source">E=mc^2</math> -->


where ''P'' is the net power radiated, '''I''' is the intensity as a function of position, and d'''A''' is a [[differential element]] of a closed surface that contains the source.  
<span style="color: red">Follow this [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering link] to change your Math rendering settings.</span> You can also add a [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering-skin Custom CSS] to force the MathML/SVG rendering or select different font families. See [https://www.mediawiki.org/wiki/Extension:Math#CSS_for_the_MathML_with_SVG_fallback_mode these examples].


If one integrates over a surface of uniform intensity ''I'', for instance over a sphere centered around the point source, the equation becomes
==Demos==


:<math>P = |I| \cdot A_\mathrm{surf} = |I| \cdot 4\pi r^2 \,</math>, <!-- "\,": other two equations get PNG treatment -->
Here are some [https://commons.wikimedia.org/w/index.php?title=Special:ListFiles/Frederic.wang demos]:


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).


Solving for ''I'' gives
* accessibility:
** Safari + VoiceOver: [https://commons.wikimedia.org/wiki/File:VoiceOver-Mac-Safari.ogv video only], [[File:Voiceover-mathml-example-1.wav|thumb|Voiceover-mathml-example-1]], [[File:Voiceover-mathml-example-2.wav|thumb|Voiceover-mathml-example-2]], [[File:Voiceover-mathml-example-3.wav|thumb|Voiceover-mathml-example-3]], [[File:Voiceover-mathml-example-4.wav|thumb|Voiceover-mathml-example-4]], [[File:Voiceover-mathml-example-5.wav|thumb|Voiceover-mathml-example-5]], [[File:Voiceover-mathml-example-6.wav|thumb|Voiceover-mathml-example-6]], [[File:Voiceover-mathml-example-7.wav|thumb|Voiceover-mathml-example-7]]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-Audio-Windows7-InternetExplorer.ogg Internet Explorer + MathPlayer (audio)]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-SynchronizedHighlighting-WIndows7-InternetExplorer.png Internet Explorer + MathPlayer (synchronized highlighting)]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-Braille-Windows7-InternetExplorer.png Internet Explorer + MathPlayer (braille)]
** NVDA+MathPlayer: [[File:Nvda-mathml-example-1.wav|thumb|Nvda-mathml-example-1]], [[File:Nvda-mathml-example-2.wav|thumb|Nvda-mathml-example-2]], [[File:Nvda-mathml-example-3.wav|thumb|Nvda-mathml-example-3]], [[File:Nvda-mathml-example-4.wav|thumb|Nvda-mathml-example-4]], [[File:Nvda-mathml-example-5.wav|thumb|Nvda-mathml-example-5]], [[File:Nvda-mathml-example-6.wav|thumb|Nvda-mathml-example-6]], [[File:Nvda-mathml-example-7.wav|thumb|Nvda-mathml-example-7]].
** Orca: There is ongoing work, but no support at all at the moment [[File:Orca-mathml-example-1.wav|thumb|Orca-mathml-example-1]], [[File:Orca-mathml-example-2.wav|thumb|Orca-mathml-example-2]], [[File:Orca-mathml-example-3.wav|thumb|Orca-mathml-example-3]], [[File:Orca-mathml-example-4.wav|thumb|Orca-mathml-example-4]], [[File:Orca-mathml-example-5.wav|thumb|Orca-mathml-example-5]], [[File:Orca-mathml-example-6.wav|thumb|Orca-mathml-example-6]], [[File:Orca-mathml-example-7.wav|thumb|Orca-mathml-example-7]].
** From our testing, ChromeVox and JAWS are not able to read the formulas generated by the MathML mode.


:<math>|I| = \frac{P}{A_\mathrm{surf}} = \frac{P}{4\pi r^2}</math>.
==Test pages ==


If the medium is damped, then the intensity drops off more quickly than the above equation suggests.
To test the '''MathML''', '''PNG''', and '''source''' rendering modes, please go to one of the following test pages:
*[[Displaystyle]]
*[[MathAxisAlignment]]
*[[Styling]]
*[[Linebreaking]]
*[[Unique Ids]]
*[[Help:Formula]]


Anything that can transmit energy can have an intensity associated with it. For an [[electromagnetic wave]], if ''E'' is the [[complex amplitude]] of the [[electric field]], then the time-averaged [[energy density]] of the wave is given by
*[[Inputtypes|Inputtypes (private Wikis only)]]
:<math>\left\langle U \right \rangle = \frac{n^2 \epsilon_0}{2} |E|^2 </math>,
*[[Url2Image|Url2Image (private Wikis only)]]
and the intensity is obtained by multiplying this expression by the wave velocity, <math>c/n</math>:
==Bug reporting==
:<math>I = \frac{c n \epsilon_0}{2} |E|^2</math>,
If you find any bugs, please report them at [https://bugzilla.wikimedia.org/enter_bug.cgi?product=MediaWiki%20extensions&component=Math&version=master&short_desc=Math-preview%20rendering%20problem Bugzilla], or write an email to math_bugs (at) ckurs (dot) de .
 
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]].
 
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>
 
==Alternative definitions of "intensity"==
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]].
 
==See also==
*[[Sound intensity]]
*[[Magnitude (astronomy)]]
 
{{SI light units|1|self}}<!-- parameter 1 = table 1, parameter 2=compare page self reference -->
{{SI radiometry units|2|self}}<!-- parameter 1 = table 2, parameter 2=compare page self reference -->
 
== References ==
<references/>
 
{{DEFAULTSORT:Intensity (Physics)}}
[[Category:Optics]]
[[Category:Radiometry]]
[[Category:Physical quantities]]

Latest revision as of 23:52, 15 September 2019

This is a preview for the new MathML rendering mode (with SVG fallback), which is availble in production for registered users.

If you would like use the MathML rendering mode, you need a wikipedia user account that can be registered here [[1]]

  • Only registered users will be able to execute this rendering mode.
  • Note: you need not enter a email address (nor any other private information). Please do not use a password that you use elsewhere.

Registered users will be able to choose between the following three rendering modes:

MathML


Follow this link to change your Math rendering settings. You can also add a Custom CSS to force the MathML/SVG rendering or select different font families. See these examples.

Demos

Here are some demos:


Test pages

To test the MathML, PNG, and source rendering modes, please go to one of the following test pages:

Bug reporting

If you find any bugs, please report them at Bugzilla, or write an email to math_bugs (at) ckurs (dot) de .

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