Rayleigh-Jean's Tail

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

Equations

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 Tail

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

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