IEVref:845-24-005ID:
Language:enStatus: Standard
Term: Planck's law
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Definition: 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.


Publication date:2020-12
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