Mathematical derivation of $N(\lambda)d\lambda$

Question

We all know that in Rayleigh-Jeans law,

$$N(f)df ~=~ 8\pi f^2 df/c^3.$$

How do you derive $N(\lambda)d\lambda$?

I am sort of confused...

Answer 1

by wave theory $ \lambda =vT $ and $ f=1/T $ the waves move to the speed of light so

$ f= \frac{c}{\lambda} $ then $ d\lambda = -\frac{cdf}{f^{2}} $ simply replace in your equation.

i believe he is referring to $ f= \nu = 2\pi \omega $