ウィーンの変位則

${\displaystyle u(T')=\epsilon ^{4/3}u(T)}$

${\displaystyle T'=\epsilon ^{1/3}T}$

${\displaystyle \lambda '=\epsilon ^{-1/3}\lambda ={\frac {T}{T'}}\,\lambda }$

${\displaystyle u_{\lambda }(\lambda ';T')\,d\lambda '={\frac {T'^{4}}{T^{4}}}\,u_{\lambda }(\lambda ;T)\,d\lambda }$

${\displaystyle u_{\lambda }(\lambda ';T')={\frac {T'^{5}}{T^{5}}}\,u_{\lambda }(\lambda ;T)}$

${\displaystyle u_{\lambda }(\lambda ;T)=T^{5}F(\lambda T)}$

${\displaystyle \nu '={\frac {\lambda }{\lambda '}}\,\nu ={\frac {T'}{T}}\,\nu }$

${\displaystyle u_{\nu }(\nu ';T')\,d\nu '={\frac {T'^{4}}{T^{4}}}\,u_{\nu }(\nu ;T)\,d\nu }$

${\displaystyle u_{\nu }(\nu ';T')={\frac {T'^{3}}{T^{3}}}\,u_{\nu }(\nu ;T)}$

${\displaystyle u_{\nu }(\nu ;T)=T^{3}F'(\nu /T)}$

${\displaystyle u_{\lambda }(\lambda ;T)=T^{5}F(\lambda T)}$

${\displaystyle \left.{\frac {\partial u_{\lambda }}{\partial \lambda }}\right|_{\lambda =\lambda _{\text{max}}}=T^{6}\left.{\frac {dF}{dx}}\right|_{x=b}=0}$

${\displaystyle u_{\lambda }(\lambda ;T)={\frac {C\lambda ^{-5}}{e^{c_{2}/\lambda T}-1}};~C=8\pi hc,~c_{2}={\frac {hc}{k}}}$

${\displaystyle \left.{\frac {dF}{dx}}\right|_{x=b}=b^{-1}F(b)\left[{\frac {c_{2}/b}{1-e^{-c_{2}/b}}}-5\right]=0}$

${\displaystyle {\frac {c_{2}/b}{1-e^{-c_{2}/b}}}-5=0}$