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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