rayleigh-jeans

In physics, the Rayleigh–Jeans law is an approximation to the spectral radiance of electromagnetic radiation as a function of wavelength from a black body at a given temperature through classical arguments. For wavelength λ, it is





B

λ


(
T
)
=



2
c

k

B


T


λ

4




,


{\displaystyle B_{\lambda }(T)={\frac {2ck_{\text{B}}T}{\lambda ^{4}}},}


where




B

λ




{\displaystyle B_{\lambda }}

is the spectral radiance (the power emitted per unit emitting area, per steradian, per unit wavelength),



c


{\displaystyle c}

is the speed of light,




k

B




{\displaystyle k_{\text{B}}}

is the Boltzmann constant, and



T


{\displaystyle T}

is the temperature in kelvins. For frequency



ν


{\displaystyle \nu }

, the expression is instead





B

ν


(
T
)
=



2

ν

2



k

B


T


c

2




.


{\displaystyle B_{\nu }(T)={\frac {2\nu ^{2}k_{\text{B}}T}{c^{2}}}.}


The Rayleigh–Jeans law agrees with experimental results at large wavelengths (low frequencies) but strongly disagrees at short wavelengths (high frequencies). This inconsistency between observations and the predictions of classical physics is commonly known as the ultraviolet catastrophe. Planck's law, which gives the correct radiation at all frequencies, has the Rayleigh–Jeans law as its low-frequency limit.

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