Rayleigh–Jeans law
In physics, the Rayleigh–Jeans Law attempts to describe the spectral radiance of electromagnetic radiation at all wavelengths from a black body at a given temperature through classical arguments. For wavelength λ, it is:
where c is the speed of light, kB is the Boltzmann constant and T is the temperature in kelvins. For frequency ν, the expression is instead
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, and its resolution was a foundational aspect of the development of quantum mechanics in the early 20th century.
In 1900, the British physicist Lord Rayleigh derived the λ−4 dependence of the Rayleigh–Jeans law based on classical physical arguments and empirical facts. A more complete derivation, which included the proportionality constant, was presented by Rayleigh and Sir James Jeans in 1905. The Rayleigh–Jeans law revealed an important error in physics theory of the time. The law predicted an energy output that diverges towards infinity as wavelength approaches zero (as frequency tends to infinity) and measurements of energy output at short wavelengths disagreed with this prediction.
In 1900 Max Planck empirically obtained an expression for black-body radiation expressed in terms of wavelength λ = c/ν (Planck's law):
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