The Rayleigh-Jean's Law describes the spectral radiance of electromagnetic radiation at all wavelengths from a black body at a given temperature through classical arguments. The Rayleign-Jeans law agrees with experimental results at large wavelengths but strongly disagrees at short wavelengths.

Think high wavelength, low frequency


For wavelength $ \lambda $, it is:

$ B _\lambda (T) = \frac {2ckT}{\lambda^4} $

For frequency $ \nu $, it is:

$ B _\nu (T) = \frac {2 \nu^2 kT}{c^2} $

Recognizing the Rayleigh-Jean's TailEdit

We can simplify Plank's Law when the following inequality holds:

$ \frac {h\nu}{kT} \ll 1 $