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

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...

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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 $f= \nu = 2\pi \omega$
I believe you mean $\omega = 2 \pi f$ –  kleingordon Aug 10 '12 at 22:09