Editing Cross section (physics) (section)

=== Scattering of light on extended bodies ===

In the context of scattering light on extended bodies, the scattering cross section, {{math|''σ''<sub>sc</sub>}}, describes the likelihood of light being scattered by a macroscopic particle. In general, the scattering cross section is different from the [[cross section (geometry)|geometrical cross section]] of a particle, as it depends upon the wavelength of light and the [[permittivity]] in addition to the shape and size of the particle. The total amount of scattering in a sparse medium is determined by the product of the scattering cross section and the number of particles present. In terms of area, the ''total cross section'' ({{math|''σ''}}) is the sum of the cross sections due to [[absorption cross section|absorption]], scattering, and [[luminescence]]:
:<math>\sigma = \sigma_\text{abs} + \sigma_\text{sc} + \sigma_\text{lum}.</math>

The total cross section is related to the [[absorbance]] of the light intensity through the [[Beer–Lambert law]], which says that absorbance is proportional to concentration: {{math|''A<sub>λ</sub>'' {{=}} ''Clσ''}}, where {{math|''A<sub>λ</sub>''}} is the absorbance at a given [[wavelength]] {{math|''λ''}}, {{math|''C''}} is the concentration as a [[number density]], and {{math|''l''}} is the [[Distance|path length]]. The extinction or [[absorbance]] of the radiation is the [[logarithm]] ([[decadic logarithm|decadic]] or, more usually, [[natural logarithm|natural]]) of the reciprocal of the [[transmittance]] {{mathcal|T}}:<ref name="Bajpai" />
: <math>A_\lambda = - \log \mathcal{T}.</math>

==== Relation to physical size ====
There is no simple relationship between the scattering cross section and the physical size of the particles, as the scattering cross section depends on the wavelength of radiation used. This can be seen when looking at a halo surrounding the Moon on a decently foggy evening: Red light photons experience a larger cross sectional area of water droplets than photons of higher energy.  The halo around the Moon thus has a perimeter of red light due to lower energy photons being scattering further from the center of the Moon. Photons from the rest of the visible spectrum are left within the center of the halo and perceived as white light.