Rayleigh–Jeans law

In <a href="/facts/Physics/a7aH2y08">physics</a>, the Rayleigh–Jeans law is an approximation to the <a href="/facts/Spectral_radiance/5kS1FhpD">spectral radiance</a> of <a href="/facts/Electromagnetic_radiation/Ynx7ujCW">electromagnetic radiation</a> as a function of <a href="/facts/Wavelength/kcJU0ymz">wavelength</a> from a <a href="/facts/Black_body/f0fHghDy">black body</a> 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 <a href="/facts/Spectral_radiance/5kS1FhpD">spectral radiance</a> (the power emitted per unit emitting area, per <a href="/facts/Steradian/PRCqT4n1">steradian</a>, per unit wavelength), 
 
 
 
 c
 
 
 {\displaystyle c}
 
 is the <a href="/facts/Speed_of_light/sKSQwdNx">speed of light</a>, 
 
 
 
 
 k
 
 B
 
 
 
 
 {\displaystyle k_{\text{B}}}
 
 is the <a href="/facts/Boltzmann_constant/5DIejyR3">Boltzmann constant</a>, and 
 
 
 
 T
 
 
 {\displaystyle T}
 
 is the <a href="/facts/Temperature/QyGe4gmj">temperature</a> in <a href="/facts/Kelvin/E3trzC4C">kelvins</a>. For <a href="/facts/Frequency/QUSbPaW8">frequency</a> 
 
 
 
 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 <a href="/facts/Classical_physics/gGnINVPE">classical physics</a> is commonly known as the <a href="/facts/Ultraviolet_catastrophe/rRM4PTQU">ultraviolet catastrophe</a>. <a href="/facts/Planck%2527s_law/7Umkdb9m">Planck's law</a>, which gives the correct radiation at all frequencies, has the Rayleigh–Jeans law as its low-frequency limit.

Rayleigh–Jeans law open-in-new

Rayleigh–Jeans law