The theory of radiative transfer describes how electromagnetic radiation travels through a medium. The matter can absorb, (re-)emit and/or scatter radiation and change its intensity. We will start with developing an equation which can describe how intensity changes in the absence of scattering as radiation travels through matter. Therefore,

Emission

Absorption

Thermal Radiative Transfer

We have

We know from Kirchhoff’s law:

Therefore,

or

This implies if , the radiation gets dimmer further we travel in the medium and if , then the radiation gets brighter. Thus, matter attempts to drive towards . If is constant:

so , explaining why optically thick emission resembles blackbody.

Scattering

In case of true absorption, the incident photon disappears and its energy is transferred to the material it was incident on. The material may