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Below are some important definitions for optics terms:

Given a gas composed of spherical particles of mass $ m $ and radius $ s $ and number density (particles per volume) $ n $, inside a rectangular slab of infinite size in the x and y directions but with finite height $ H $ in the z direction

We define the cross-section per particle $ \sigma $ as:

$ \sigma = \pi s^2 $

We define the column density as number density integrated along some path:

$ N = \int_0^H n \mathrm{d} x $

We define the opacity $ \kappa $ as the cross-section per unit mass of gas:

$ \kappa = \frac {\sigma}{m} $

We define the mass density (mass per volume) $ \rho $ as:

$ \rho = nm $

We define the optical depth $ \tau $ as:

$ \tau = \int_0^H n \sigma \mathrm{d} x = n \sigma H $