﻿ Rayleighâ€“Jeans law

# Rayleighâ€“Jeans law

The Rayleigh-Jeans law describes the dependence of the radiation intensity of a black body of the wavelength of light at a given temperature in the framework of classical electrodynamics. It was the first time in 1900 by the English physicist John William Strutt, 3rd Baron Rayleigh described using the formula described by Rayleigh still had an incorrect prefactor. The correct formula was published five years later by the English physicist, astronomer and mathematician Sir James Jeans.

The Rayleigh-Jeans law provides useful values ​​at low frequencies, ie long wavelengths ( see picture). For small wavelengths, it provides far too large values ​​which the total radiation, integrated over the entire wavelength range, can strive towards infinity. This behavior has been called ultraviolet catastrophe. The behavior at small wavelengths, ie at high frequencies (and correspondingly high energy) is described in good approximation by the Wien law.

Only Max Planck found the correct explanation and summed with the Planck's radiation law, the Rayleigh-Jeans law and Wien's radiation law together.

If one chooses, it follows from the Planck's radiation law

Under the valid approximation for small exponents directly the Rayleigh-Jeans law:

Here, the temperature of the black body, the vacuum velocity of light and is the Boltzmann constant.

The adjacent graphs show a comparison of three radiation formulas according to Planck, Wien and Rayleigh - Jeans ( above in a linear, down in double-logarithmic representation). For large wavelengths shows a good agreement of the predictions according to Rayleigh - Jeans and Planck, to smaller wavelengths differs Rayleigh - Jeans increasingly strongly upwards. Vienna, however, describes the limit of small wavelengths ( here λ <5 microns ) very well, but is larger for wavelengths much too low.

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