View source for Physics:Rayleigh scattering

{{Short description|Light scattering by small particles}}
[[File:Leehasacamera - Sunset over the clouds (by).jpg|thumb|300x300px|Rayleigh scattering causes the blue color of the daytime sky and the reddening of the Sun at sunset.]]
'''Rayleigh scattering''' ({{IPAc-en|ˈ|r|eɪ|l|i}} {{respell|RAY|lee}}), named after the 19th-century British physicist Lord Rayleigh (John William Strutt),<ref>Lord Rayleigh (John Strutt) refined his theory of scattering in a series of papers; see Works.</ref> is the predominantly [[Physics:Elastic scattering|elastic scattering]] of [[Physics:Light|light]], or other [[Physics:Electromagnetic radiation|electromagnetic radiation]], by particles with a size much smaller than the [[Wavelength|wavelength]] of the radiation. For light frequencies well below the [[Physics:Resonance|resonance]] frequency of the scattering medium (normal [[Physics:Dispersion relation|dispersion]] regime), the amount of scattering is inversely proportional to the [[Fourth power|fourth power]] of the wavelength, e.g., a blue color is scattered much more than a red color as light propagates through air.

Rayleigh scattering results from the electric [[Physics:Polarizability|polarizability]] of the particles. The oscillating electric field of a light wave acts on the charges within a particle, causing them to move at the same frequency. The particle, therefore, becomes a small radiating [[Physics:Dipole|dipole]] whose radiation we see as scattered light. The particles may be individual atoms or molecules; it can occur when light travels through transparent solids and liquids, but is most prominently seen in [[Physics:Gas|gas]]es.

Rayleigh scattering of [[Astronomy:Sunlight|sunlight]] in Earth's atmosphere causes [[Astronomy:Diffuse sky radiation|diffuse sky radiation]], which is the reason for the blue color of the [[Astronomy:Daytime|daytime]] and [[Earth:Twilight|twilight]] [[Astronomy:Sky|sky]], as well as the [[Philosophy:Golden hour (photography)|yellowish]] to reddish hue of the low [[Astronomy:Sun|Sun]]. Sunlight is also subject to [[Physics:Raman scattering|Raman scattering]], which changes the rotational state of the molecules and gives rise to [[Physics:Polarization (waves)|polarization]] effects.<ref>{{cite journal|doi=10.1364/AO.20.000533|pmid=20309152|title=Rayleigh scattering|journal=Applied Optics|volume=20|issue=4|pages=533–5|year=1981|last1=Young|first1=Andrew T|bibcode=1981ApOpt..20..533Y}}</ref>

Scattering by particles with a size comparable to, or larger than, the wavelength of the light is typically treated by the Mie theory, the [[Physics:Discrete dipole approximation|discrete dipole approximation]] and other computational techniques. Rayleigh scattering applies to particles that are small with respect to wavelengths of light, and that are optically "soft" (i.e., with a [[Physics:Refractive index|refractive index]] close to 1). [[Physics:Anomalous diffraction theory|Anomalous diffraction theory]] applies to optically soft but larger particles.

==History==
In 1869, while attempting to determine whether any contaminants remained in the purified air he used for infrared experiments, [[Biography:John Tyndall|John Tyndall]] discovered that bright light scattering off nanoscopic particulates was faintly blue-tinted.<ref>{{Cite journal |last1=Tyndall |first1=John |title=On the blue colour of the sky, the polarization of skylight, and on the polarization of light by cloudy matter generally |journal=Proceedings of the Royal Society of London |date=1869 |volume=17 |pages=223–233 |doi=10.1098/rspl.1868.0033|doi-access=free }}</ref><ref>{{Cite web|url=https://www.bbvaopenmind.com/en/science/leading-figures/john-tyndall-the-man-who-explained-why-the-sky-is-blue/|title=John Tyndall, the Man who Explained Why the Sky is Blue|last=Conocimiento|first=Ventana al|date=2018-08-01|website=OpenMind|language=en-US|access-date=2019-03-31}}</ref> He conjectured that a similar scattering of sunlight gave the sky its [[Astronomy:Diffuse sky radiation|blue hue]], but he could not explain the preference for blue light, nor could atmospheric dust explain the intensity of the sky's color.

In 1871, Lord Rayleigh published two papers on the color and polarization of skylight to quantify [[Physics:Tyndall effect|Tyndall's effect]] in water droplets in terms of the tiny particulates' volumes and [[Physics:Refractive index|refractive indices]].<ref>{{cite journal |last1=Strutt |first1=Hon. J.W. |title=On the light from the sky, its polarization and colour |journal=The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science |date=1871 |volume=41 |issue=271 |pages=107–120 |doi=10.1080/14786447108640452}}</ref><ref>{{cite journal |last1=Strutt |first1=Hon. J.W. |title=On the light from the sky, its polarization and colour |journal=The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science |date=1871 |volume=41 |issue=273 |pages=274–279 |doi=10.1080/14786447108640479}}</ref><ref>{{cite journal |last1=Strutt |first1=Hon. J.W. |title=On the scattering of light by small particles |journal=The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science |date=1871 |volume=41 |issue=275 |pages=447–454 |doi=10.1080/14786447108640507}}</ref> In 1881, with the benefit of [[Biography:James Clerk Maxwell|James Clerk Maxwell]]'s 1865 [[Physics:History of Maxwell's equations|proof of the electromagnetic nature of light]], he showed that his equations followed from [[Physics:Electromagnetism|electromagnetism]].<ref>{{cite journal |last1=Rayleigh |first1=Lord |title=On the electromagnetic theory of light |journal=The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science |date=1881 |volume=12 |issue=73 |pages=81–101 |doi=10.1080/14786448108627074|url=https://zenodo.org/record/1431155 }}</ref> In 1899, he showed that they applied to individual molecules, with terms containing particulate volumes and refractive indices replaced with terms for molecular [[Physics:Polarizability|polarizability]].<ref>{{cite journal |last1=Rayleigh |first1=Lord |title=On the transmission of light through an atmosphere containing small particles in suspension, and on the origin of the blue of the sky |journal=The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science |date=1899 |volume=47 |issue=287 |pages=375–384 |doi=10.1080/14786449908621276|url=https://zenodo.org/record/1431249 }}</ref>

==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|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 [[Physics:Mie scattering|Mie scattering]], interference effects develop through [[Physics: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 [[Physics:Coherence|incoherent]] and the resulting [[Physics:Intensity|intensity]] is just the sum of the squares of the [[Physics:Amplitude|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 |url=https://courses.cit.cornell.edu/ece303/Lectures/lecture34.pdf|title=Cornell lectures |access-date=2 April 2014 }}</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 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 diameter ''d'' and [[Physics:Refractive index|refractive index]] ''n'' from a beam of unpolarized light of wavelength ''λ'' and intensity ''I''<sub>0</sub> is given by

<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 \left( \frac{d}{2} \right)^6</math><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>

where ''R'' is the distance to the particle and ''θ'' is the scattering angle. Averaging this over all angles gives the Rayleigh scattering cross-section<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{ 2 \pi^5}{3} \frac{d^6}{\lambda^4} \left( \frac{ n^2-1}{ n^2+2 } \right)^2</math><ref>Siegel, R., Howell, J.R., (2002). [https://cds.cern.ch/record/1505325/files/9781439805336_TOC.pdf ''Thermal radiation heat transfer'']. p. 480. New York, NY: Taylor & Francis. {{ISBN|1560329688}}</ref>

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, 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>{{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 at atmospheric pressure, where there are about {{val|2|e=25}} molecules per cubic meter, 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.

==From molecules==
[[File:Rayleigh sunlight scattering.svg|thumb|Figure showing the greater proportion of blue light scattered by the atmosphere relative to red light]]
The expression above can also be written in terms of individual molecules by expressing the dependence on refractive index in terms of the molecular [[Physics:Polarizability|polarizability]] ''α'', proportional to the dipole moment induced by the electric field of the light. In this case, the Rayleigh scattering intensity for a single particle is given in [[Centimetre–gram–second system of units|CGS-units]] by<ref>[http://hyperphysics.phy-astr.gsu.edu/hbase/atmos/blusky.html#c2 Rayleigh scattering]. Hyperphysics.phy-astr.gsu.edu. Retrieved on 2018-08-06.</ref>
<math display="block">I_s = I_0 \frac{8\pi^4\alpha^2}{\lambda^4 R^2}(1+\cos^2\theta)</math>
and in [[International System of Units|SI-units]] by
<math display="block">I_s = I_0 \frac{\pi^2\alpha^2}{{\varepsilon_0}^2 \lambda^4 R^2}\frac{1+\cos^2(\theta)}{2}</math>.

== Effect of fluctuations ==
When the dielectric constant <math>\epsilon</math> of a certain region of volume <math>V</math> is different from the average dielectric constant of the medium <math>\bar{\epsilon}</math>, then any incident light will be scattered according to the following equation<ref>{{Cite book|title=Statistical mechanics|last=McQuarrie, Donald A. (Donald Allan)|date=2000|publisher=University Science Books|isbn=1891389157|location=Sausalito, Calif.|pages=[https://archive.org/details/statisticalmecha00mcqu_0/page/62 62]|oclc=43370175|url=https://archive.org/details/statisticalmecha00mcqu_0/page/62}}</ref>

<math display="block">I=I_0\frac{\pi^2V^2\sigma_\epsilon^2}{2\lambda^4R^2} {\left (1+\cos^2\theta\right )}</math>where <math>\sigma_\epsilon^2</math> represents the [[Variance|variance]] of the fluctuation in the dielectric constant <math>\epsilon</math>.

== Cause of the blue color of the sky==
{{Main|Astronomy:Diffuse sky radiation}}

[[File:CircularPolarizer.jpg|thumb|right|Scattered blue light is [[Physics:Polarization (waves)|polarized]]. The picture on the right is shot through a polarizing filter: the polarizer transmits light that is linearly polarized in a specific direction.]]
The strong wavelength dependence of the scattering (~''λ''<sup>−4</sup>) means that shorter ([[Blue|blue]]) wavelengths are scattered more strongly than longer ([[Red|red]]) wavelengths. This results in the indirect blue light coming from all regions of the sky.  Rayleigh scattering is a good approximation of the manner in which light scattering occurs within various media for which scattering particles have a small size ([[Parameter|parameter]]).

A portion of the beam of light coming from the sun scatters off molecules of gas and other small particles in the atmosphere. Here, Rayleigh scattering primarily occurs through [[Astronomy:Sunlight|sunlight]]'s interaction with randomly located air molecules. It is this scattered light that gives the surrounding sky its brightness and its color. As previously stated, Rayleigh scattering is inversely proportional to the fourth power of wavelength, so that shorter wavelength violet and blue light will scatter more than the longer wavelengths (yellow and especially red light). However, the Sun, like any star, has its own spectrum and so ''I''<sub>0</sub> in the scattering formula above is not constant but falls away in the violet. In addition the oxygen in the Earth's atmosphere absorbs wavelengths at the edge of the ultra-violet region of the spectrum.  The resulting color, which appears like a pale blue, actually is a mixture of all the scattered colors, mainly blue and green.  Conversely, glancing toward the sun, the colors that were not scattered away—the longer wavelengths such as red and yellow light—are directly visible, giving the sun itself a slightly yellowish hue. Viewed from space, however, the sky is black and the sun is white.

The reddening of the sun is intensified when it is near the horizon because the light being received directly from it must pass through more of the atmosphere. The effect is further increased because the sunlight must pass through a greater proportion of the atmosphere nearer the earth's surface, where it is denser. This removes a significant proportion of the shorter wavelength (blue) and medium wavelength (green) light from the direct path to the observer. The remaining unscattered light is therefore mostly of longer wavelengths and appears more red.

Some of the scattering can also be from sulfate particles. For years after large [[Earth:Plinian eruption|Plinian eruption]]s, the blue cast of the sky is notably brightened by the persistent sulfate load of the stratospheric gases. Some works of the artist J. M. W. Turner may owe their vivid red colours to the eruption of Mount Tambora in his lifetime.<ref name="zerefos">{{Citation
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In locations with little [[Astronomy:Light pollution|light pollution]], the moonlit night sky is also blue, because moonlight is reflected sunlight, with a slightly lower [[Earth:Color temperature|color temperature]] due to the brownish color of the moon. The moonlit sky is not perceived as blue, however, because at low light levels human vision comes mainly from rod cells that do not produce any color perception ([[Biology:Purkinje effect|Purkinje effect]]).<ref>{{Citation |last=Choudhury |first=Asim Kumar Roy |title=Unusual visual phenomena and colour blindness |date=2014 |url=https://linkinghub.elsevier.com/retrieve/pii/B978085709229850005X |work=Principles of Colour and Appearance Measurement |pages=185–220 |publisher=Elsevier |language=en |doi=10.1533/9780857099242.185 |isbn=978-0-85709-229-8 |access-date=2022-03-29}}</ref>

==Of sound in amorphous solids==
Rayleigh scattering is also an important mechanism of wave scattering in amorphous solids such as glass, and is responsible for acoustic wave damping and phonon damping in glasses and granular matter at low or not too high temperatures.<ref>{{cite journal |last1=Mahajan |first1=Shivam |last2=Pica Ciamarra |first2=Massimo |title=Quasi-localized vibrational modes, boson peak and sound attenuation in model mass-spring networks |journal=SciPost Physics |year=2023 |volume=15 |issue=2 |doi=10.21468/SciPostPhys.15.2.069 |arxiv=2211.01137 |doi-access=free }}</ref> This is because in glasses at higher temperatures the Rayleigh-type scattering regime is obscured by the anharmonic damping (typically with a ~''λ''<sup>−2</sup> dependence on wavelength), which becomes increasingly more important as the temperature rises.

Rayleigh scattering in gases, strictly speaking, is induced by microscopic dipole fluctuations in the electromagnetic field of visible light. In amorphous solids, theories have been proposed which argue that Rayleigh-type scattering arises due to wave scattering from macroscopic spatial fluctuations in the elastic [[Physics:Shear modulus|shear modulus]].<ref>{{cite journal|last1=Schirmacher|first1=W.|last2=Ruocco|first2=G.|last3=Scopigno|first3=T.|title=Acoustic Attenuation in Glasses and its Relation with the Boson Peak|journal=Phys. Rev. Lett.|year=2007|volume=98|issue=2 |pages=025501|doi=10.1103/PhysRevLett.98.025501|pmid=17358618 |arxiv=cond-mat/0701112 |bibcode=2007PhRvL..98b5501S |s2cid=630096 }}</ref>
More recently, however, a Rayleigh-type quartic dependence of the damping coefficient on the sound wavelength, ~''λ''<sup>−4</sup>, has been derived from first principles based on wave scattering from microscopic motions of the atoms or particles (i.e. the microscopic building blocks of the solid), known as "nonaffine" motions, which are of crucial importance for the [[Physics:Elasticity|elasticity]] of amorphous solids. The effect has been derived by Baggioli & Zaccone<ref>{{cite journal|last1=Baggioli|first1=M.|last2=Zaccone|first2=A.|title=Theory of sound attenuation in amorphous solids from nonaffine motions|journal=J. Phys.: Condens. Matter|year=2022|volume=34|issue=21 |pages=215401|doi=10.1088/1361-648X/ac5d8b|pmid=35287118 |arxiv=2110.13446 |bibcode=2022JPCM...34u5401B |s2cid=239885429 }}</ref> and numerically confirmed, independently, by Szamel & Flenner.<ref>{{cite journal|last1=Szamel|first1=G.|last2=Flenner|first2=E.|title=Microscopic analysis of sound attenuation in low-temperature amorphous solids reveals quantitative importance of non-affine effects|journal=J. Chem. Phys.|year=2022|volume=156|issue=14 |pages=144502|doi=10.1063/5.0085199|pmid=35428393 |arxiv=2107.14254 |bibcode=2022JChPh.156n4502S |s2cid=247922827 }}</ref> The numerical analysis has also revealed that the  ~''λ''<sup>−4</sup> contribution from macroscopic fluctuations of shear modulus is quantitatively negligible compared to the  ~''λ''<sup>−4</sup> scattering contribution from nonaffine motions. Furthermore, the microscopic theory is able to recover the crossover from diffusive type ~''λ''<sup>−2</sup> scattering which dominates at lower wavevectors to the Rayleigh-type ~''λ''<sup>−4</sup> scattering at higher wavevectors.

==In amorphous solids – glasses – optical fibers==
Rayleigh scattering is an important component of the scattering of optical signals in optical fibers. Silica fibers are glasses,  disordered materials with microscopic variations of density and refractive index. These give rise to energy losses due to the scattered light, with the following coefficient:<ref>Rajagopal, K. (2008) ''Textbook on Engineering Physics'', PHI, New Delhi, part I, Ch. 3, {{ISBN|8120336658}}</ref>
<math display="block">\alpha_\text{scat} = \frac{8 \pi^3}{3 \lambda^4} n^8 p^2 k T_\text{f} \beta</math>

where ''n'' is the refraction index, ''p'' is the photoelastic coefficient of the glass, ''k'' is the [[Physics:Boltzmann constant|Boltzmann constant]], and ''β'' is the isothermal compressibility. ''T''<sub>f</sub> is a ''fictive temperature'', representing the temperature at which the density fluctuations are "frozen" in the material.

==In porous materials==
[[File:Why is the sky blue.jpg|thumb|Rayleigh scattering in [[Physics:Opalescence|opalescent]] glass: it appears blue from the side, but orange light shines through.<ref>[http://www.webexhibits.org/causesofcolor/14B.html Blue & red | Causes of Color]. Webexhibits.org. Retrieved on 2018-08-06.</ref>]]
Rayleigh-type ''λ''<sup>−4</sup> scattering can also be exhibited by porous materials. An example is the strong optical scattering by nanoporous materials.<ref name = Svensson>{{cite journal|doi=10.1063/1.3292210|title=Laser spectroscopy of gas confined in nanoporous materials|journal=Applied Physics Letters|volume=96|issue=2|pages=021107|year=2010|last1=Svensson|first1=Tomas|last2=Shen|first2=Zhijian|url=http://lup.lub.lu.se/search/ws/files/2070270/2370765.pdf|bibcode=2010ApPhL..96b1107S|arxiv=0907.5092|s2cid=53705149}}</ref> The strong contrast in refractive index between pores and solid parts of sintered alumina results in very strong scattering, with light completely changing direction each five micrometers on average. The ''λ''<sup>−4</sup>-type scattering is caused by the nanoporous structure (a narrow pore size distribution around ~70&nbsp;nm) obtained by [[Earth:Sintering|sintering]] monodispersive alumina powder.

==See also==
* {{annotated link|Physics:Rayleigh sky model}}
* {{annotated link|Physics:Optical phenomena}}
* {{annotated link|Physics:Dynamic light scattering}}
* {{annotated link|Physics:Raman scattering}}
* {{annotated link|Physics:Rayleigh–Gans approximation}}
* {{annotated link|Physics:Tyndall effect}}
* {{annotated link|Physics:Critical opalescence}}
* [[Software:HRS Computing|HRS Computing]] – scientific simulation software
* {{annotated link|Aerial perspective}}
* {{annotated link|Physics:Parametric process (optics)|Parametric process}}
* {{annotated link|Physics:Bragg's law}}

==Works==

* {{cite journal|doi=10.1080/14786447108640452|title=XV. On the light from the sky, its polarization and colour|journal=The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science|volume=41|issue=271|pages=107–120|year=1871|last1=Strutt|first1=J.W}}
* {{cite journal|doi=10.1080/14786447108640479|title=XXXVI. On the light from the sky, its polarization and colour|journal=The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science|volume=41|issue=273|pages=274–279|year=1871|last1=Strutt|first1=J.W}}
* {{cite journal|doi=10.1080/14786447108640507|title=LVIII. On the scattering of light by small particles|journal=The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science|volume=41|issue=275|pages=447–454|year=1871|last1=Strutt|first1=J.W}}
* {{cite journal|doi=10.1080/14786448108627074|title=X. On the electromagnetic theory of light|journal=The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science|volume=12|issue=73|pages=81–101|year=1881|last1=Rayleigh|first1=Lord|url=https://zenodo.org/record/1431155}}
* {{cite journal|doi=10.1080/14786449908621276|title=XXXIV. On the transmission of light through an atmosphere containing small particles in suspension, and on the origin of the blue of the sky|journal=The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science|volume=47|issue=287|pages=375–384|year=1899|last1=Rayleigh|first1=Lord|url=https://zenodo.org/record/1431249}}

==References==
{{Reflist}}


==Further reading==
{{Refbegin}}
*C.F. Bohren, D. Huffman, ''Absorption and scattering of light by small particles'', John Wiley, New York 1983. Contains a good description of the asymptotic behavior of Mie theory for small size parameter (Rayleigh approximation).
* {{cite book | last = Ditchburn | first =  R.W. | year = 1963 | title = Light |url=https://archive.org/details/light0000ditc | url-access = registration | edition = 2nd | pages = [https://archive.org/details/light0000ditc/page/582 582–585] | publisher = Blackie & Sons | location = London | isbn = 978-0-12-218101-6 }}
* {{cite journal | last = Chakraborti | first = Sayan |date=September 2007 | title = Verification of the Rayleigh scattering cross section | journal = [[Physics:American Journal of Physics|American Journal of Physics]] | volume = 75 | issue = 9 | pages = 824–826 | doi = 10.1119/1.2752825 |arxiv = physics/0702101 |bibcode = 2007AmJPh..75..824C | s2cid = 119100295 }}
* {{cite book | last = Ahrens | first = C. Donald | year = 1994 | title = Meteorology Today: an introduction to weather, climate, and the environment | edition = 5th | pages = [https://archive.org/details/meteorologytoday00ahre/page/88 88–89] | publisher = West Publishing Company | location = St. Paul MN | isbn = 978-0-314-02779-5 |url=https://archive.org/details/meteorologytoday00ahre/page/88 }}
* {{cite journal | last1 = Lilienfeld | first1 = Pedro | year = 2004| title = A Blue Sky History | journal = Optics and Photonics News | volume = 15 | issue = 6| pages = 32–39 | doi = 10.1364/OPN.15.6.000032 }} Gives a brief history of theories of why the sky is blue leading up to Rayleigh's discovery, and a brief description of Rayleigh scattering.
{{Refend}}

==External links==
* [http://hyperphysics.phy-astr.gsu.edu/hbase/atmos/blusky.html#c2 HyperPhysics description of Rayleigh scattering]
* [http://math.ucr.edu/home/baez/physics/General/BlueSky/blue_sky.html Full physical explanation of sky color, in simple terms]

{{DEFAULTSORT:Rayleigh Scattering}}
[[Category:Scattering, absorption and radiative transfer (optics)]]
[[Category:Atmospheric optical phenomena]]
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[[Category:Concepts in physics|Phenomena]]
[[Category:Physical phenomena]]

{{Sourceattribution|Rayleigh scattering}}