Radiative Transfer Equation -- from Eric Weisstein's World of Physics

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Radiative Transfer Equation

Consider the change in power in a pencil of radiation upon passing through an infinitesimal length of material,

where is the power lost, is the volume of material through which the pencil passes, is the incident power, is the intensity in erg cm^-2 sterradian^-1 s^-1, J is the emissivity in erg cm^-3 s^-1 sterradian^-1, and

is the extinction coefficient in cm^-1. Dividing (1) through by yields

The quantities in this equation are frequency dependent, so the law is often written as

where these are now specific quantities valid at a given frequency. This is the radiative transfer equation. If J = 0, this reduces to Lambert's law

Extinction Coefficient, Lambert's Law, Radiative Transfer Equation--Isothermal Blackbody, Two-Stream Approximation