# Wien displacement law

[2.13.6] An expression representing, in a functional form, the spectral radiance of a blackbody as a function of the wavelength and the temperature.

$L_{\lambda }=dI_{\lambda}/dA' = c_{1L}\left (\lambda \right )^{-5} \cdot f\left ( \lambda T \right )$

or

$L_{\lambda } T^{-5}=c_{1L}(\lambda T)^{-5} \cdot f(\lambda T)$

$f\left ( \lambda T \right )= e^{-(c_{2}/\lambda T)}$

The two principal corollaries of this law are:

$\lambda _{m} T = b$

$L _{m}/ T^{5} = b'$

These show how the maximum spectral radiance Lm and the wavelength λm at which it occurs are related to the absolute temperature T.

Note: The currently recommended value of b is 2.8978 x 10-3 m•K, or 2.8978 x 10-1 cm•K. From the Planck radiation law, and with the use of the values of b, c1, and c2 as given in that definition, b’ is found to be:

$4.0956 \cdot 10^{-14} \left ( W/cm^{2}\cdot sr\cdot \mu m\cdot K^{5} \right )$
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