I am drawing a blank when it comes to equation transformation. Wikipedia gives two equations for the spectral radiance of black body:
- First as a function of frequency $\nu$: $$I(\nu, T) = \frac{2 h \nu^3}{c^2}\cdot\frac{1}{e^\frac{h \nu}{k T} - 1}$$
- Then as a function of wavelength $\lambda$ : $$I'(\lambda, T) = \frac{2hc^2}{\lambda^5}\cdot\frac{1}{e^\frac{h c}{\lambda k T}-1}$$
And I don't see how they get $\lambda^5$ term. I'm assuming that the transformation is just $\nu \rightarrow c/\lambda$, but that gives $$ \frac{2 h \nu^3}{c^2} \Rightarrow \frac{2 hc}{\lambda^3} \neq \frac{2hc^2}{\lambda^5} $$
Similar transformation happens at other parts in the article also. I'm obviously missing something, likely completely trivial.