Editing Rayleigh scattering (section)

==Small size parameter approximation==
The size of a scattering particle is often parameterized by the ratio

<math display="block"> x = \frac{2 \pi r} {\lambda}</math>

where ''r'' is the particle's radius, ''λ'' is the [[wavelength]] of the light and ''x'' is a [[dimensionless parameter]] that characterizes the particle's interaction with the incident radiation such that: Objects with x ≫ 1 act as geometric shapes, scattering light according to their projected area. At the intermediate x ≃ 1 of [[Mie scattering]], interference effects develop through [[phase (waves)|phase]] variations over the object's surface. Rayleigh scattering applies to the case when the scattering particle is very small (x ≪ 1, with a particle size < 1/10 of wavelength<ref>[http://hyperphysics.phy-astr.gsu.edu/hbase/atmos/blusky.html Blue Sky and Rayleigh Scattering]. Hyperphysics.phy-astr.gsu.edu. Retrieved on 2018-08-06.</ref>) and the whole surface re-radiates with the same phase. Because the particles are randomly positioned, the scattered light arrives at a particular point with a random collection of phases; it is [[coherence (physics)|incoherent]] and the resulting [[intensity (physics)|intensity]] is just the sum of the squares of the [[amplitude]]s from each particle and therefore proportional to the inverse fourth power of the wavelength and the sixth power of its size.<ref name="Cornell">{{Cite web |last=Rana |first=Farhan  |title=Electromagnetic Scattering |url=https://courses.cit.cornell.edu/ece303/Lectures/lecture34.pdf |access-date=2 April 2014 |website=ECE303 Electromagnetic Fields and Waves}}</ref><ref>{{cite journal|last=Barnett|first=C.E.|title=Some application of wavelength turbidimetry in the infrared|journal=J. Phys. Chem.|year=1942|volume=46|issue=1|pages=69–75|doi=10.1021/j150415a009}}</ref> The wavelength dependence is characteristic of [[Dipole radiation|dipole scattering]]<ref name=Cornell/> and the volume dependence will apply to any scattering mechanism. In detail, the intensity of light scattered by any one of the small spheres of radius ''r'' and [[refractive index]] ''n'' from a beam of unpolarized light of wavelength ''λ'' and intensity ''I''<sub>0</sub> is given by<ref>Seinfeld, John H. and Pandis, Spyros N. (2006) ''Atmospheric Chemistry and Physics, 2nd Edition'', John Wiley and Sons, New Jersey, Chapter 15.1.1, {{ISBN|0471720186}}</ref>
<math display="block"> I_s = I_0 \frac{ 1+\cos^2 \theta }{2 R^2} \left( \frac{ 2 \pi }{ \lambda } \right)^4 \left( \frac{ n^2-1}{ n^2+2 } \right)^2 r^6</math>
where ''R'' is the observer's distance to the particle and ''θ'' is the scattering angle. Averaging this over all angles gives the Rayleigh [[scattering cross-section]] of the  particles in air:<ref>{{cite journal|last=Cox|first=A.J.|title=An experiment to measure Mie and Rayleigh total scattering cross sections|journal=American Journal of Physics|year=2002|volume=70|issue=6|page=620|doi=10.1119/1.1466815|bibcode = 2002AmJPh..70..620C |s2cid=16699491}}</ref>
<math display="block"> \sigma_\text{s} = \frac{ 8 \pi}{3}  \left( \frac{2\pi}{\lambda}\right)^4 \left( \frac{ n^2-1}{ n^2+2 } \right)^2 r^6 .</math>
Here ''n'' is the refractive index of the spheres that approximate the molecules of the gas; the index of the gas surrounding the spheres is neglected, an approximation that introduces an error of less than 0.05%.<ref name=SneepUbacks/>

The fraction of light scattered by scattering particles over the unit travel length (e.g., meter) is the number of particles per unit volume ''N'' times the cross-section. For example, air has a refractive index of 1.0002793 at atmospheric pressure, where there are about {{val|2|e=25}} molecules per cubic meter, and therefore the major constituent of the atmosphere, nitrogen, has a Rayleigh cross section of {{val|5.1|e=-31|u=m<sup>2</sup>}} at a wavelength of 532&nbsp;nm (green light).<ref name=SneepUbacks>{{cite journal | last1 = Sneep | first1 = Maarten | last2 = Ubachs | first2 = Wim | year = 2005 | title = Direct measurement of the Rayleigh scattering cross section in various gases | doi = 10.1016/j.jqsrt.2004.07.025 | journal = Journal of Quantitative Spectroscopy and Radiative Transfer | volume = 92 | issue = 3| pages = 293–310 |bibcode = 2005JQSRT..92..293S }}</ref> This means that  about a fraction 10<sup>−5</sup> of the light will be scattered for every meter of travel.

The strong wavelength dependence of the scattering (~''λ''<sup>−4</sup>) means that shorter (blue) wavelengths are scattered more strongly than longer (red) wavelengths.