View source for Luminous intensity

{{short description|Visible light per unit solid angle}}
{{See also|Light intensity (disambiguation)}}
{{Infobox physical quantity
| name =luminous intensity
| width =
| background =
| image = Luminosity.svg
| caption = [[Photopic vision|Photopic]] (black) and [[scotopic vision|scotopic]] (green) luminosity functions.<ref name="scvl" group=c/> The photopic includes the CIE 1931 standard<ref name="ciexyz31" group=c/> (solid), the Judd–Vos 1978 modified data<ref name="vljv" group=c/> (dashed), and the Sharpe, Stockman, Jagla & Jägle 2005 data<ref name="ssvl2" group=c/> (dotted). The horizontal axis is wavelength in [[Nanometre|nm]].
| unit = [[candela]]
| otherunits = {{ubl|[[candlepower]]|[[Hefnerkerze]]}}
| symbols = ''I''<sub>v</sub>
| baseunits = cd
| dimension = '''J'''
| extensive =
| intensive =
| conserved =
| transformsas =
| derivations =
}}
In [[Photometry (optics)|photometry]], '''luminous intensity''' is a measure of the [[wavelength]]-weighted [[Power (physics)|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]]. The [[SI]] unit of luminous intensity is the [[candela]]&nbsp;(cd), an [[SI base unit]].

Photometry deals with the measurement of visible light as perceived by human eyes. The human eye can only see light in the [[visible spectrum]] and has different sensitivities to [[light]] of different wavelengths within the spectrum. When adapted for bright conditions ([[photopic vision]]), the eye is most sensitive to greenish-yellow light at 555&nbsp;nm. Light with the same [[radiant intensity]] at other wavelengths has a lower luminous intensity. The curve which measures the response of the human eye to light is a defined standard, known as the [[luminosity function]]. This curve, denoted ''V''(&lambda;) or <math>\textstyle \overline{y}(\lambda)</math>, is based on an average of widely differing experimental data from scientists using different measurement techniques. For instance, the measured responses of the eye to violet light varied by a factor of ten {{Citation needed|reason=Which study showed this?|date=February 2018}} .

==Relationship to other measures==
Luminous intensity should not be confused with another photometric unit, [[luminous flux]], which is the total perceived power emitted in all directions. Luminous intensity is the perceived power ''per unit solid angle''. If a lamp has a 1 lumen bulb and the optics of the lamp are set up to focus the light evenly into a 1 [[steradian]] beam, then the beam would have a luminous intensity of 1 candela. If the optics were changed to concentrate the beam into 1/2 steradian then the source would have a luminous intensity of 2 candela. The resulting beam is narrower and brighter, though its luminous flux remains unchanged.

Luminous intensity is also not the same as the [[radiant intensity]], the corresponding objective [[physical quantity]] used in the measurement science of [[radiometry]].

==Units==
Like other SI base units, the candela has an [[operational definition]]&mdash;it is defined by the description of a physical process that will produce one candela of luminous intensity. By definition, if one constructs a light source that emits monochromatic green light with a frequency of 540&nbsp;THz, and that has a radiant intensity of 1/683&nbsp;[[watt]]s per [[steradian]] in a given direction, that light source will emit one candela in the specified direction.<ref>{{Cite web
 | title = Base unit definitions: Candela
 | work = The NIST Reference on Constants, Units, and Uncertainty
 | url = http://physics.nist.gov/cuu/Units/candela.html
 | accessdate = 8 February 2008
 }}</ref>

The frequency of light used in the definition corresponds to a wavelength in a vacuum of 555&nbsp;nm, which is near the peak of the eye's response to light. If the source emitted uniformly in all directions, the total [[radiant flux]] would be about 18.40&nbsp;mW, since there are 4&pi;&nbsp;steradians in a sphere. A typical candle produces very roughly one candela of luminous intensity.

Prior to the definition of the candela, a variety of units for luminous intensity were used in various countries. These were typically based on the brightness of the flame from a "standard candle" of defined composition, or the brightness of an incandescent filament of specific design. One of the best-known of these standards was the [[England|English]] standard: [[candlepower]]. One candlepower was the light produced by a pure [[spermaceti]] candle weighing one sixth of a pound and burning at a rate of 120&nbsp;[[Grain (mass)|grains]] per hour. Germany, Austria, and Scandinavia used the [[Hefnerkerze]], a unit based on the output of a [[Hefner lamp]].<ref>{{Cite web|url=http://www.sizes.com/units/hefner.htm |title=Hefner unit, or Hefner candle |work=Sizes.com |date=30 May 2007 |accessdate=25 February 2009}}</ref> In 1881, [[Jules Violle]] proposed the ''[[Violle]]'' as a unit of luminous intensity, and it was notable as the first unit of light intensity that did not depend on the properties of a particular lamp. All of these units were superseded by the definition of the candela.

==Usage==
The luminous intensity for monochromatic light of a particular wavelength &lambda; is given by

:<math>I_\mathrm{v} = 683 \cdot \overline{y}(\lambda) \cdot I_\mathrm{e},</math>

where

:''I''<sub>v</sub> is the luminous intensity in candelas&nbsp;(cd),
:''I''<sub>e</sub> is the radiant intensity in watts per steradian&nbsp;(W/sr),
:<math>\textstyle \overline{y}(\lambda)</math> is the [[Luminosity function|standard luminosity function]].

If more than one wavelength is present (as is usually the case), one must sum or integrate over the [[spectrum]] of wavelengths present to get the luminous intensity:

<!-- TBD: Is integral from 0 to infinity really correct, or should it better be 380nm to 780nm here? -->
:<math>I_\mathrm{v} = 683 \int^\infin_0 \overline{y}(\lambda) \cdot \frac{dI_\mathrm{e}(\lambda)}{d\lambda} \, d\lambda.</math>

==See also==
* [[Brightness]]
* [[International System of Quantities]]
* [[Radiance]]
==References==
<references/>
===Curve data===
{{reflist|group=c|refs=
<ref name="scvl">{{cite web
 | title    = CIE Scotopic luminosity curve (1951)
 | url     = http://www.cvrl.org/database/text/lum/scvl.htm
 | archiveurl = https://web.archive.org/web/20081228115119/http://www.cvrl.org/database/text/lum/scvl.htm
 | archivedate = 2008-12-28
 }}</ref>
<ref name="ciexyz31">{{cite web
 | title    = CIE (1931) 2-deg color matching functions
 | url     = http://www.cvrl.org/database/text/cmfs/ciexyz31.htm
 | archiveurl = https://web.archive.org/web/20081228084047/http://www.cvrl.org/database/text/cmfs/ciexyz31.htm
 | archivedate = 2008-12-28
 }}</ref>
<ref name="vljv">{{cite web
 | title    = Judd–Vos modified CIE 2-deg photopic luminosity curve (1978)
 | url     = http://www.cvrl.org/database/text/lum/vljv.htm
 | archiveurl = https://web.archive.org/web/20081228083025/http://www.cvrl.org/database/text/lum/vljv.htm
 | archivedate = 2008-12-28
 }}</ref>
<ref name="ssvl2">{{cite web
 | title    = Sharpe, Stockman, Jagla & Jägle (2005) 2-deg V*(l) luminous efficiency function
 | url     = http://www.cvrl.org/database/text/lum/ssvl2.htm
 | archiveurl = https://web.archive.org/web/20070927222337/http://www.cvrl.org/database/text/lum/ssvl2.htm
 | archivedate = 2007-09-27
 }}</ref>
}}
{{SI_light_units}}
{{SI base quantities}}
{{Use dmy dates|date=September 2010}}

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[[Category:Physical quantities]]
[[Category:SI base quantities]]
[[Category:Photometry]]