Optical Depth -- from Eric Weisstein's World of Physics

Thermodynamics "> Radiative Transfer v

Optical Depth

Optical depth gives a measure of how opaque a medium is to radiation passing through it. It is measured along the vertical optical path dz and, in the planetary science convention, is measured downwards from the top of the atmosphere, so that , and increases downward as z decreases. The differential optical depth is defined by

where K is the extinction coefficient, is the opacity, is the density, is the angle to the normal, and ds is the optical path. Defining , can be written
where n is the number density and is the cross section.

Integrating for normal incidence gives

where N is the column density.

Extinction Coefficient, Law of Atmospheres, Opacity, Optical Path, Radiative Transfer, Radiative Transfer Equation, Scale Height