View source for Physics:Luminous intensity

{{short description|Visible light per unit solid angle}}
{{Infobox physical quantity
| name =luminous intensity
| width =
| background =
| unit = [[Candela|candela]]
| otherunits = {{ubl|[[Candlepower|candlepower]]|[[Hefnerkerze]]}}
| symbols = {{math|''I''<sub>v</sub>}}
| baseunits = cd
| dimension = <math>\mathsf{J}</math>
| extensive =
| intensive =
| conserved =
| transformsas =
| derivations =
}}
In [[Physics:Photometry (optics)|photometry]], '''luminous intensity''' is a measure of the [[Wavelength|wavelength]]-weighted [[Physics:Power|power]] emitted by a light source in a particular direction per unit [[Solid angle|solid angle]], based on the [[Physics:Luminosity function|luminosity function]], a standardized model of the sensitivity of the [[Biology:Human eye|human eye]]. The SI unit of luminous intensity is the [[Candela|candela]]&nbsp;(cd), an [[SI base unit]].

==Measurement==
Photometry deals with the measurement of visible light as perceived by human eyes. The human eye can only see light in the [[Physics:Visible spectrum|visible spectrum]] and has different sensitivities to [[Physics:Light|light]] of different wavelengths within the spectrum. When adapted for bright conditions ([[Biology:Photopic vision|photopic vision]]), the eye is most sensitive to yellow-green light at 555&nbsp;nm. Light with the same [[Physics:Radiant intensity|radiant intensity]] at other wavelengths has a lower luminous intensity. The curve which represents  the response of the human eye to light is a defined standard function {{math|{{overline|''y''}}(λ)}} or {{math|''V''(λ)}}  established by the International Commission on Illumination (CIE, for ''Commission Internationale de l'Éclairage'') and standardized in collaboration with the [[Organization:International Organization for Standardization|ISO]]. <ref>{{cite book | url=https://www.iso.org/standard/83178.html | title=ISO/CIE 23539:2023 CIE TC 2-93 Photometry — The CIE system of physical photometry | publisher=ISO/CIE | date=2023 | language=en | doi=10.25039/IS0.CIE.23539.2023}}</ref>

Luminous intensity of artificial light sources is typically measured using and a [[Physics:Goniophotometer|goniophotometer]] outfitted with a [[Physics:Photometer|photometer]] or a spectroradiometer. <ref>{{cite book |last1=Schneider |first1=T. |last2=Young |first2=R. |last3=Bergen |first3=T. |last4=Dam-Hansen |first4=C |last5=Goodman |first5=T. |last6=Jordan |first6=W. |last7=Lee |first7=D.-H |last8=Okura |first8=T. |last9=Sperfeld |first9=P. |last10=Thorseth |first10=A |last11=Zong |first11=Y. |title=CIE 250:2022 Spectroradiometric Measurement of Optical Radiation Sources |date=2022 |publisher=CIE - International Commission on Illumination |location=Vienna |isbn=978-3-902842-23-7 |url=https://orbit.dtu.dk/en/publications/cie-2502022-spectroradiometric-measurement-of-optical-radiation-s}}</ref>
{{SI light units}}

==Relationship to other measures==
[[File:photometry_radiometry_units.svg|thumb|upright=1.5|Comparison of photometric and radiometric quantities]]
Luminous intensity should not be confused with another photometric unit, [[Physics:Luminous flux|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|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 [[Physics:Radiant intensity|radiant intensity]], the corresponding objective [[Physics:Physical quantity|physical quantity]] used in the measurement science of [[Astronomy:Radiometry|radiometry]].

==Units==
Like other SI base units, the candela has an [[Philosophy:Operational definition|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|watt]]s per [[Steradian|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
 | access-date = 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 1 candela source emitted uniformly in all directions, the total [[Physics:Radiant flux|radiant flux]] would be about 18.40&nbsp;mW, since there are 4&pi;&nbsp;steradians in a sphere.  Note that a typical modern candle produces very roughly one candela while releasing heat at roughly 80 W.

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 {{wipe|England}} standard: [[Candlepower|candlepower]]. One candlepower was the light produced by a pure [[Chemistry:Spermaceti|spermaceti]] candle weighing one sixth of a pound and burning at a rate of 120&nbsp;grains per hour. Germany, Austria, and Scandinavia used the [[Hefnerkerze]], a unit based on the output of a [[Physics:Hefner lamp|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 |access-date=25 February 2009}}</ref> In 1881, [[Biography:Jules Violle|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==
thumb |[[Photopic vision|Photopic (black) and [[Biology:Scotopic vision|scotopic]] (green) luminosity functions.<ref name="scvl" group=c/> The photopic includes the CIE 1931 standard<ref name="ciexyz31" group=c/><ref name="ciexyz31_curve" 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]].]]
The luminous intensity for monochromatic light of a particular wavelength &lambda; is given by
<math display="block">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 [[Physics:Radiant intensity|radiant intensity]] in watts per steradian&nbsp; (W/sr),
*<math display="inline"> \overline{y}(\lambda)</math> is the [[Physics: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|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 display="block">I_\mathrm{v} = 683 \int_0^\infty \overline{y}(\lambda) \cdot \frac{dI_\mathrm{e}(\lambda)}{d\lambda} \, d\lambda.</math>

==See also==
* [[Physics:Brightness|Brightness]]
* [[Physics:International System of Quantities|International System of Quantities]]
* [[Physics:Radiance|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
 | archive-url = https://web.archive.org/web/20081228115119/http://www.cvrl.org/database/text/lum/scvl.htm
 | archive-date = 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
 | archive-url = https://web.archive.org/web/20081228084047/http://www.cvrl.org/database/text/cmfs/ciexyz31.htm
 | archive-date = 2008-12-28
 }}</ref>
<ref name="ciexyz31_curve">{{cite web
 | title    = CIE 'physiologically-relevant' luminous efficiency functions
 | url     = http://www.cvrl.org/lumindex.htm
 | archive-url = https://web.archive.org/web/20190707084652/http://www.cvrl.org/lumindex.htm
 | archive-date = 2019-07-07
 }}</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
 | archive-url = https://web.archive.org/web/20081228083025/http://www.cvrl.org/database/text/lum/vljv.htm
 | archive-date = 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
 | archive-url = https://web.archive.org/web/20070927222337/http://www.cvrl.org/database/text/lum/ssvl2.htm
 | archive-date = 2007-09-27
 }}</ref>
}}


{{DEFAULTSORT:Luminous Intensity}}
[[Category:SI base quantities]]
[[Category:Photometry]]
[[Category:Electromagnetic quantities]]

{{Sourceattribution|Luminous intensity}}