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:

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