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Area Lighting / Emission, optical properties of materials

IEV ref 845-24-005

en
Planck's law
law giving the spectral distribution of radiance of a Planckian radiator as a function of wavelength and temperature

L e,λ (λ,T)= L e (λ,T) λ = c 1 π λ 5 ( e c 2 λT 1) 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaieYdi9WrpeeC0lXdh9vqqj=hEeea0xXdbb a9frFj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXd bPYxe9vr0=vr0=vqpWqaaeaaciWacmGadaGadeaaeaGaauaaaOqaai aadYeadaWgaaWcbaGaaiyzaiaacYcacqaH7oaBaeqaaOGaaiikaiab eU7aSjaacYcacaWGubGaaiykaiabg2da9maalaaabaGaeyOaIyRaam itamaaBaaaleaacaGGLbaabeaakiaacIcacqaH7oaBcaGGSaGaamiv aiaacMcaaeaacqGHciITcqaH7oaBaaGaeyypa0ZaaSaaaeaacaWGJb WaaSbaaSqaaiaaigdaaeqaaaGcbaacdaGae8hWdahaaiabeU7aSnaa CaaaleqabaGaeyOeI0IaaGynaaaakiaacIcacaqGLbWaaWbaaSqabe aadaWcaaqaaiaadogadaWgaaadbaGaaGOmaaqabaaaleaacqaH7oaB caWGubaaaaaakiabgkHiTiaaigdacaGGPaWaaWbaaSqabeaacqGHsi slcaaIXaaaaaaa@5ED6@

where Le,λ is the spectral radiance, λ is the wavelength in vacuum, T is the thermodynamic temperature, c 1  =2 π h  c 0 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaieYdi9WrpeeC0lXdh9vqqj=hEeea0xXdbb a9frFj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXd bPYxe9vr0=vr0=vqpWqaaeaaciWaamGadaGadeaaeaGaauaaaOqaaa baaaaaaaaapeGaam4ya8aadaWgaaWcbaWdbiaaigdaa8aabeaak8qa caGGGcGaeyypa0JaaGOmaiaacckacqaHapaCcaGGGcGaamiAaiaacc kapaGaam4yamaaDaaaleaacaaIWaaabaGaaGOmaaaaaaa@44E5@ , c 2  =h  c 0  / k MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaieYdi9WrpeeC0lXdi9qqqj=hEeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meaabaGacmaadiWaaiWabaabaiaafaaake aaqaaaaaaaaaWdbiaadogapaWaaSbaaSqaa8qacaaIYaaapaqabaGc peGaaiiOaiabg2da9iaadIgacaGGGcGaam4ya8aadaWgaaWcbaWdbi aaicdaa8aabeaak8qacaGGGcGaai4laiaacckacaWGRbaaaa@45FE@ , h is the Planck constant, c0 is the speed of light in vacuum, and k is the Boltzmann constant

Note 1 to entry: The formula is sometimes written with c 1 π Ω 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaieYdi9WrpeeC0lXdh9vqqj=hEeea0xXdbb a9frFj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXd bPYxe9vr0=vr0=vqpWqaaeaaciWacmGadaGadeaaeaGaauaaaOqaam aalaaabaGaam4yamaaBaaaleaacaaIXaaabeaaaOqaaGWaaiab=b8a WjaaysW7cqqHPoWvdaWgaaWcbaGaaGimaaqabaaaaaaa@3EC6@ instead of c 1 π MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaieYdi9WrpeeC0lXdh9vqqj=hEeea0xXdbb a9frFj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXd bPYxe9vr0=vr0=vqpWqaaeaaciWacmGadaGadeaaeaGaauaaaOqaam aalaaabaGaam4yamaaBaaaleaacaaIXaaabeaaaOqaaGWaaiab=b8a Wbaaaaa@3AC5@ , where Ω0 is the solid angle of magnitude 1 sr.

Note 2 to entry: For a detector in a medium of refractive index n, the measured radiance is n2Le,λ(λ, T).

Note 3 to entry: Planck's law can also be expressed to give the spectral distribution of radiant exitance, Me,λ(λ, T); the first factor in the formula is then c1 instead of c 1 π MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaieYdi9WrpeeC0lXdh9vqqj=hEeea0xXdbb a9frFj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXd bPYxe9vr0=vr0=vqpWqaaeaaciWacmGadaGadeaaeaGaauaaaOqaam aalaaabaGaam4yamaaBaaaleaacaaIXaaabeaaaOqaaGWaaiab=b8a Wbaaaaa@3AC5@ .

Note 4 to entry: Both quantities (radiance and radiant exitance) apply to the unpolarized radiation as emitted.

Note 5 to entry: For the up-to-date values of the Planck constant, h, the speed of light in vacuum, c0, and the Boltzmann constant, k, see CODATA.

Note 6 to entry: This entry was numbered 845-04-05 in IEC 60050-845:1987.


fr
loi de Planck, f
loi donnant la répartition spectrale de la luminance énergétique d'un radiateur de Planck en fonction de la longueur d'onde et de la température

L e,λ (λ,T)= L e (λ,T) λ = c 1 π λ 5 ( e c 2 λT 1) 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaieYdi9WrpeeC0lXdh9vqqj=hEeea0xXdbb a9frFj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXd bPYxe9vr0=vr0=vqpWqaaeaaciWacmGadaGadeaaeaGaauaaaOqaai aadYeadaWgaaWcbaGaaiyzaiaacYcacqaH7oaBaeqaaOGaaiikaiab eU7aSjaacYcacaWGubGaaiykaiabg2da9maalaaabaGaeyOaIyRaam itamaaBaaaleaacaGGLbaabeaakiaacIcacqaH7oaBcaGGSaGaamiv aiaacMcaaeaacqGHciITcqaH7oaBaaGaeyypa0ZaaSaaaeaacaWGJb WaaSbaaSqaaiaaigdaaeqaaaGcbaacdaGae8hWdahaaiabeU7aSnaa CaaaleqabaGaeyOeI0IaaGynaaaakiaacIcacaqGLbWaaWbaaSqabe aadaWcaaqaaiaadogadaWgaaadbaGaaGOmaaqabaaaleaacqaH7oaB caWGubaaaaaakiabgkHiTiaaigdacaGGPaWaaWbaaSqabeaacqGHsi slcaaIXaaaaaaa@5ED6@

Le,λ est la luminance spectrale, λ est la longueur d'onde dans le vide, T est la température thermodynamique, c 1  =2 π h  c 0 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaieYdi9WrpeeC0lXdh9vqqj=hEeea0xXdbb a9frFj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXd bPYxe9vr0=vr0=vqpWqaaeaaciWaamGadaGadeaaeaGaauaaaOqaaa baaaaaaaaapeGaam4ya8aadaWgaaWcbaWdbiaaigdaa8aabeaak8qa caGGGcGaeyypa0JaaGOmaiaacckacqaHapaCcaGGGcGaamiAaiaacc kapaGaam4yamaaDaaaleaacaaIWaaabaGaaGOmaaaaaaa@44E5@ , c 2  =h  c 0  / k MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaieYdi9WrpeeC0lXdi9qqqj=hEeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meaabaGacmaadiWaaiWabaabaiaafaaake aaqaaaaaaaaaWdbiaadogapaWaaSbaaSqaa8qacaaIYaaapaqabaGc peGaaiiOaiabg2da9iaadIgacaGGGcGaam4ya8aadaWgaaWcbaWdbi aaicdaa8aabeaak8qacaGGGcGaai4laiaacckacaWGRbaaaa@45FE@ , h est la constante de Planck, c0 est la vitesse de la lumière dans le vide, et k est la constante de Boltzmann

Note 1 à l'article: La formule s'écrit parfois avec c 1 π Ω 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaieYdi9WrpeeC0lXdh9vqqj=hEeea0xXdbb a9frFj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXd bPYxe9vr0=vr0=vqpWqaaeaaciWacmGadaGadeaaeaGaauaaaOqaam aalaaabaGaam4yamaaBaaaleaacaaIXaaabeaaaOqaaGWaaiab=b8a WjaaysW7cqqHPoWvdaWgaaWcbaGaaGimaaqabaaaaaaa@3EC6@ au lieu de c 1 π MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaieYdi9WrpeeC0lXdh9vqqj=hEeea0xXdbb a9frFj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXd bPYxe9vr0=vr0=vqpWqaaeaaciWacmGadaGadeaaeaGaauaaaOqaam aalaaabaGaam4yamaaBaaaleaacaaIXaaabeaaaOqaaGWaaiab=b8a Wbaaaaa@3AC5@ , où Ω0 est l'angle solide de 1 sr.

Note 2 à l'article: Pour un récepteur dans un milieu d'indice de réfraction n, la luminance énergétique mesurée est n2Le,λ(λ, T).

Note 3 à l'article: La loi de Planck peut aussi être exprimée pour donner la répartition spectrale de l'exitance énergétique, Me,λ(λ, T); dans la formule, le premier facteur est alors c1 au lieu de c 1 π MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaieYdi9WrpeeC0lXdh9vqqj=hEeea0xXdbb a9frFj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXd bPYxe9vr0=vr0=vqpWqaaeaaciWacmGadaGadeaaeaGaauaaaOqaam aalaaabaGaam4yamaaBaaaleaacaaIXaaabeaaaOqaaGWaaiab=b8a Wbaaaaa@3AC5@ .

Note 4 à l'article: Les deux grandeurs (luminance et exitance énergétiques) s'appliquent au rayonnement non polarisé tel qu'il est émis.

Note 5 à l'article: Pour les valeurs actualisées de la constante de Planck, h, la vitesse de la lumière dans le vide, c0, et la constante de Boltzmann, k, voir CODATA.

Note 6 à l'article: Cet article était numéroté 845-04-05 dans l'IEC 60050-845:1987.


ar
قانون بلانك

de
Plancksches Gesetz, n

it
legge di Planck

ko
플랑크 법칙

ja
プランクの放射則

pl
prawo Plancka, n

pt
lei de Planck

zh
普朗克定律

Publication date: 2020-12
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