Editing Beer–Lambert law (section)

=== In-atmosphere astronomy ===
The Bouguer–Lambert law may be applied to describe the attenuation of solar or stellar radiation as it travels through the atmosphere. In this case, there is scattering of radiation as well as absorption. The optical depth for a slant path is {{math|1=''{{prime|τ}}'' = ''mτ''}}, where {{mvar|τ}} refers to a vertical path, {{mvar|m}} is called the [[airmass|relative airmass]], and for a plane-parallel atmosphere it is determined as {{math|1=''m'' = sec ''θ''}} where {{mvar|θ}} is the [[zenith angle]] corresponding to the given path. The Bouguer-Lambert law for the atmosphere is usually written
<math display="block">T = \exp \big( -m(\tau_\mathrm{a} + \tau_\mathrm{g} + \tau_\mathrm{RS} + \tau_\mathrm{NO_2} + \tau_\mathrm{w} + \tau_\mathrm{O_3} + \tau_\mathrm{r} + \cdots) \bigr),</math>
where each {{mvar|&tau;<sub>x</sub>}} is the optical depth whose subscript identifies the source of the absorption or scattering it describes:
* {{math|a}} refers to [[aerosols]] (that absorb and scatter);
* {{math|g}} are uniformly mixed gases (mainly [[carbon dioxide]] (CO<sub>2</sub>)  and molecular [[oxygen]] (O<sub>2</sub>) which only absorb);
* {{math|{{chem2|NO2}}}} is [[nitrogen dioxide]], mainly due to urban pollution (absorption only);
* {{math|RS}} are effects due to [[Raman scattering]] in the atmosphere;
* {{math|w}} is [[water vapour]] [[water absorption|absorption]];
* {{math|{{chem2|O3}}}} is [[ozone]] (absorption only);
* {{mvar|r}} is [[Rayleigh scattering]] from molecular [[oxygen]] ({{chem2|O2}}) and [[nitrogen]] ({{chem2|N2}}) (responsible for the blue color of the sky);
* the selection of the attenuators which have to be considered depends on the wavelength range and can include various other compounds. This can include [[tetraoxygen]], [[HONO]], [[formaldehyde]], [[glyoxal]], a series of halogen radicals and others.

{{mvar|m}} is the ''optical mass'' or ''[[airmass]] factor'', a term approximately equal (for small and moderate values of {{mvar|θ}}) to {{tmath|\tfrac{1}{\cos \theta},}} where {{mvar|θ}} is the observed object's [[celestial coordinate system|zenith angle]] (the angle measured from the direction perpendicular to the Earth's surface at the observation site). This equation can be used to retrieve {{math|''τ''<sub>a</sub>}}, the aerosol [[optical depth|optical thickness]], which is necessary for the correction of satellite images and also important in accounting for the role of aerosols in climate.