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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
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(6) |
where N is the column density.
 Extinction Coefficient, Law of Atmospheres, Opacity, Optical Path, Radiative Transfer, Radiative Transfer Equation, Scale Height
© 1996-2007 Eric W. Weisstein
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