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Wikipedia says that Planck's law is:

$$B_\nu (\nu, T) = \frac{2h\nu^3}{c^2}\times \frac{1}{e^{h\nu /(k_BT)} - 1}$$

So, to convert this to wavelength, I substituted $\nu = \frac{c}{\lambda}$ which gave me:

$$B_\lambda(\lambda, T) = \frac{2hc}{\lambda^3}\times \frac{1}{e^{hc/(\lambda k_BT)} - 1}$$

However, Wikipedia says that:

$$B_\lambda(\lambda, T) = \frac{2hc^2}{\lambda^5}\times \frac{1}{e^{hc/(\lambda k_BT)} - 1}$$

What did I do wrong?

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    $\begingroup$ physics.stackexchange.com/q/13611 $\endgroup$
    – user18764
    Commented Aug 25, 2017 at 18:09
  • $\begingroup$ In the link : Planck's law you read the first few lines. Be careful to continue in paragraph "Correspondence between spectral variable forms" : \begin{equation} B\left( \lambda,T\right)\mathrm{d}\lambda=-B\left[ \nu( \lambda),T\right]\mathrm{d}\nu \tag{01} \end{equation} $\endgroup$
    – Frobenius
    Commented Aug 25, 2017 at 18:20

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