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Area Lighting / Emission, optical properties of materials

IEV ref845-04-05

en
Planck's law
law giving the spectral concentration 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@+=feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgaruavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGeaGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaqFn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=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@5DC5@

Le, radiance
λ, wavelength in vacuum
T, thermodynamic temperature
c1 = 2π20
c2 =0/k
h, Planck's constant
c0, velocity (speed) of light in vacuum
k, the Boltzmann constant

Note 1 – The formula is sometimes written with c 1 π Ω 0 MathType@MTEF@5@5@+=feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgaruavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGeaGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaqFn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpeWZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaamaalaaabaGaam4yamaaBaaaleaacaaIXaaabeaaaOqaaGWaaiab=b8aWjabfM6axnaaBaaaleaacaGGVbaabeaaaaaaaa@3BA9@ instead of c 1 π MathType@MTEF@5@5@+=feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgaruavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGeaGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaqFn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpeWZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaamaalaaabaGaam4yamaaBaaaleaacaaIXaaabeaaaOqaaGWaaiab=b8aWbaaaaa@38FC@ , where Ω0 is the solid angle of magnitude 1 steradian.

Note 2 – For a detector in a medium of refractive index n, the measured radiance is n2 Le λ(λ, T)

Note 3 – Planck's law can be also expressed to give the spectral concentration of radiant exitance Me, λ(λ, T); the first factor in the formula (1), is then c1 instead of c1/π.

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


fr
loi de Planck, f
loi donnant la densité 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@+=feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgaruavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGeaGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaqFn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=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@5DC5@

Le, luminance énergétique
λ , longueur d'onde dans le vide
T, température thermodynamique
c1 = 2π20
c2 =0/k
h, constante de Planck
c0 vitesse de la lumière dans le vide
k, constante de Boltzmann

Note 1 – On écrit parfois la formule avec c 1 π Ω 0 MathType@MTEF@5@5@+=feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgaruavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGeaGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaqFn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpeWZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaamaalaaabaGaam4yamaaBaaaleaacaaIXaaabeaaaOqaaGWaaiab=b8aWjabfM6axnaaBaaaleaacaGGVbaabeaaaaaaaa@3BA9@ au lieu de c 1 π MathType@MTEF@5@5@+=feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgaruavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGeaGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaqFn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpeWZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaamaalaaabaGaam4yamaaBaaaleaacaaIXaaabeaaaOqaaGWaaiab=b8aWbaaaaa@38FC@ , où Ω0 est l'angle solide de 1 stéradian.

Note 2 – Pour un récepteur dans un milieu d'indice de réfraction n, la luminance énergétique mesurée est n2 Le, λ(λ, T)

Note 3 – La loi de Planck peut aussi être exprimée pour donner la densité spectrale de l'exitance énergétique Me, λ(λ, T); dans la formule (1), le premier facteur est alors c1 au lieu de c1/π.

Note 4 – Ces deux grandeurs (luminance et exitance) s'appliquent au rayonnement tel qu'il est émis, c'est-à-dire non polarisé.


ar
قانون بلانك

de
Plancksches Gesetz, n

es
ley de Planck

fi
Planckin laki

it
legge di Planck

ko
플랑크 법칙

ja
プランクの放射則

no
nb Plancks lov

nn Plancks lov

pl
prawo Plancka

pt
lei de Planck

sv
Plancks lag

Publication date: 1987
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