Schwarzschild equation ($\frac{d{I}_{\lambda }}{ds}={\alpha }_{\lambda }(B_{\lambda }-I_{\lambda })$)

The absorption-and-emission transfer equation without scattering, often expressed along a ray as $d{I}_{\lambda }/ds=-{\alpha }_{\lambda }{I}_{\lambda }+{\alpha }_{\lambda }{B}_{\lambda }(T)$ in local thermal equilibrium. Its formal solution weights thermal emission by intervening transmission.