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[[Image:Image-Metal-reflectance.png|thumb|right|400px|''Spectral reflectance curves'' for [[aluminium]] (Al), [[silver]] (Ag), and [[gold]] (Au) metal [[mirror]]s at normal incidence.]]
This is a preview for the new '''MathML rendering mode''' (with SVG fallback), which is availble in production for registered users.


'''Reflectivity''' or '''reflectance''' is the fraction of incident electromagnetic power that is reflected at an interface, in contrast to the [[reflection coefficient]], which is the ratio of the reflected to incident [[electric field]].<ref name="Klein">[http://www.amazon.com/dp/0471872970 Klein and Furtak, ''Optics'']</ref>
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.


== Reflectance ==
Registered users will be able to choose between the following three rendering modes:
[[File:Fresnel reflection coefficients.svg|thumb|Fresnel reflection coefficients for a boundary surface between air and a variable material in dependence of the complex refractive index and the angle of incidence]]
The reflectance or reflectivity is the square of the magnitude of the reflection coefficient.<ref>E. Hecht (2001). Optics (4th ed.). Pearson Education. ISBN 0-8053-8566-5.</ref> The reflection coefficient can be expressed as a [[complex number]] as determined by the [[Fresnel equation]]s for a single layer, whereas the reflectance (or reflectivity) is always a positive [[real number]].


According to the CIE (the International Commission on Illumination),<ref name="CIE">[http://www.cie.co.at/ CIE (the International Commission on Illumination)]</ref> '''reflectivity''' is distinguished from '''reflectance''' by the fact that reflectivity is a value that applies to ''thick'' reflecting objects.<ref name="ILV">[http://www.cie.co.at/index.php/index.php?i_ca_id=306 CIE International Lighting Vocabulary]</ref> When reflection occurs from thin layers of material, internal reflection effects can cause the reflectance to vary with surface thickness. Reflectivity is the limit value of reflectance as the sample becomes thick; it is the intrinsic reflectance of the surface, hence irrespective of other parameters such as the reflectance of the rear surface.  Another way to interpret this is that the reflectance is the fraction of electromagnetic power reflected from a specific sample, while reflectivity is a property of the material itself, which would be measured on a perfect machine if the material filled half of all space.<ref name="Grant">[http://www.amazon.com/dp/081947245X Palmer and Grant, ''The Art of Radiometry'']</ref>
'''MathML'''
:<math forcemathmode="mathml">E=mc^2</math>


The ''reflectance spectrum'' or [[spectral reflectance curve]] is the plot of the reflectance as a function of wavelength.
<!--'''PNG'''  (currently default in production)
:<math forcemathmode="png">E=mc^2</math>


==Surface type==
'''source'''
Going back to the fact that reflectivity is a directional property, most surfaces can be divided into those that give [[specular reflection]] and those that give [[diffuse reflection]].
:<math forcemathmode="source">E=mc^2</math> -->


* For specular surfaces, such as glass or polished metal, reflectivity will be nearly zero at all angles except at the appropriate reflected angle - that is, reflected radiation will follow a different path from incident radiation for all cases other than radiation normal to the surface.
<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].


* For diffuse surfaces, such as matte white paint, reflectivity is uniform; radiation is reflected in all angles equally or near-equally. Such surfaces are said to be [[Lambertian reflectance|Lambertian]].
==Demos==


Most real objects have some mixture of diffuse and specular reflective properties.
Here are some [https://commons.wikimedia.org/w/index.php?title=Special:ListFiles/Frederic.wang demos]:


== Water reflectivity ==
[[Image:Water reflectivity.jpg|thumb|right|400px|Reflectivity of smooth water at 20°C (refractive index=1.333)]]


Reflection occurs when light moves from a medium with one [[index of refraction]] into a second medium with a different index of refraction.
* 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.


Specular reflection from a body of water is calculated by the [[Fresnel equations]].<ref name="Ottav">Ottaviani, M. and Stamnes, K. and Koskulics, J. and Eide, H. and Long, S.R. and Su, W. and Wiscombe, W., 2008: 'Light Reflection from Water Waves: Suitable Setup for a Polarimetric Investigation under Controlled Laboratory Conditions''. Journal of Atmospheric and Oceanic Technology, '''25 (5)''', 715--728.</ref> Fresnel reflection is directional and therefore does not contribute significantly to [[albedo]] which is primarily diffuse reflection.
==Test pages ==


A real water surface may be wavy. Reflectivity assuming a flat surface as given by the [[Fresnel equations]] can be adjusted to account for [[waviness]].
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]]


==Grating efficiency==
*[[Inputtypes|Inputtypes (private Wikis only)]]
 
*[[Url2Image|Url2Image (private Wikis only)]]
The generalization of reflectance to a [[diffraction grating]], which disperses light by [[wavelength]], is called '''diffraction efficiency'''.
==Bug reporting==
 
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 .
==Applications==
Reflectivity is an important concept in the fields of [[optics]], [[solar thermal energy]], [[telecommunication]] and [[radar]].
 
==See also==
* [[Bidirectional reflectance distribution function]]
* [[Emissivity]]
* [[Lambert's cosine law]]
* [[Transmittance]]
* [[Sun path]]
* [[Light Reflectance Value]]
 
==References==
{{Refimprove|date=December 2008}}
{{Reflist}}
 
==External links==
{{Wiktionary|reflectivity}}
* [http://www.tvu.com/metalreflectivityLR.jpg reflectivity of metals (chart)]
* [http://www.graphics.cornell.edu/online/measurements/reflectance/index.html Reflectance Data] Painted surfaces etc.
* [http://www.gratinglab.com/information/handbook/chapter9.asp Grating efficiency]
 
[[Category:Geometrical optics]]
[[Category:Thermodynamics]]

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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