Rayleigh scattering
Rayleigh scattering (/ˈreɪli/ RAY-lee), named after the 19th-century British physicist Lord Rayleigh (John William Strutt),[1] is the predominantly elastic scattering of light, or other electromagnetic radiation, by particles with a size much smaller than the wavelength of the radiation. For light frequencies well below the resonance frequency of the scattering medium (normal dispersion regime), the amount of scattering is inversely proportional to the 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 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 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 gases.
Rayleigh scattering of sunlight in Earth's atmosphere causes diffuse sky radiation, which is the reason for the blue color of the daytime and twilight sky, as well as the yellowish to reddish hue of the low Sun. Sunlight is also subject to Raman scattering, which changes the rotational state of the molecules and gives rise to polarization effects.[2]
Scattering by particles with a size comparable to, or larger than, the wavelength of the light is typically treated by the Mie theory, the 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 refractive index close to 1). Anomalous diffraction theory applies to optically soft but larger particles.
History[edit]
In 1869, while attempting to determine whether any contaminants remained in the purified air he used for infrared experiments, John Tyndall discovered that bright light scattering off nanoscopic particulates was faintly blue-tinted.[3][4] He conjectured that a similar scattering of sunlight gave the sky its 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 Tyndall's effect in water droplets in terms of the tiny particulates' volumes and refractive indices.[5][6][7] In 1881, with the benefit of James Clerk Maxwell's 1865 proof of the electromagnetic nature of light, he showed that his equations followed from electromagnetism.[8] In 1899, he showed that they applied to individual molecules, with terms containing particulate volumes and refractive indices replaced with terms for molecular polarizability.[9]
Small size parameter approximation[edit]
The size of a scattering particle is often parameterized by the ratio
where r is the particle's radius,
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 2×1025 molecules per cubic meter, and therefore the major constituent of the atmosphere, nitrogen, has a Rayleigh cross section of 5.1×10−31 m2 at a wavelength of 532 nm (green light).[15] This means that about a fraction 10−5 of the light will be scattered for every meter of travel.
The strong wavelength dependence of the scattering (~
From molecules[edit]
The expression above can also be written in terms of individual molecules by expressing the dependence on refractive index in terms of the molecular polarizability
Effect of fluctuations[edit]
When the dielectric constant of a certain region of volume is different from the average dielectric constant of the medium , then any incident light will be scattered according to the following equation[17]
Cause of the blue color of the sky[edit]
The blue color of the sky is a consequence of three factors:[18]
- the blackbody spectrum of sunlight coming into the Earth's atmosphere,
- Rayleigh scattering of that light off oxygen and nitrogen molecules, and
- the response of the human visual system.
The strong wavelength dependence of the Rayleigh scattering (~
Some of the scattering can also be from sulfate particles. For years after large Plinian eruptions, 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.[19]
In locations with little light pollution, the moonlit night sky is also blue, because moonlight is reflected sunlight, with a slightly lower 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 (Purkinje effect).[20]
Of sound in amorphous solids[edit]
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.[21] This is because in glasses at higher temperatures the Rayleigh-type scattering regime is obscured by the anharmonic damping (typically with a ~
In amorphous solids – glasses – optical fibers[edit]
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:[22]
where n is the refraction index, p is the photoelastic coefficient of the glass, k is the Boltzmann constant, and
In porous materials[edit]
Rayleigh-type
See also[edit]
- Rayleigh sky model
- Rician fading
- Optical phenomena – Observable events that result from the interaction of light and matter
- Dynamic light scattering – Technique for determining size distribution of particles
- Raman scattering – Inelastic scattering of photons by matter
- Rayleigh–Gans approximation
- Tyndall effect – Scattering of light by tiny particles in a colloidal suspension
- Critical opalescence
- HRS Computing – scientific simulation software
- Marian Smoluchowski – Polish physicist (1872–1917)
- Rayleigh criterion – Ability of any image-forming device to distinguish small details of an object
- Aerial perspective – Atmospheric effects on the appearance of a distant object
- Parametric process – Interacting phenomenon between light and matter
- Bragg's law – Physical law regarding scattering angles of radiation through a medium
Works[edit]
- Strutt, J.W (1871). "XV. On the light from the sky, its polarization and colour". The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science. 41 (271): 107–120. doi:10.1080/14786447108640452.
- Strutt, J.W (1871). "XXXVI. On the light from the sky, its polarization and colour". The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science. 41 (273): 274–279. doi:10.1080/14786447108640479.
- Strutt, J.W (1871). "LVIII. On the scattering of light by small particles". The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science. 41 (275): 447–454. doi:10.1080/14786447108640507.
- Rayleigh, Lord (1881). "X. On the electromagnetic theory of light". The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science. 12 (73): 81–101. doi:10.1080/14786448108627074.
- Rayleigh, Lord (1899). "XXXIV. On the transmission of light through an atmosphere containing small particles in suspension, and on the origin of the blue of the sky". The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science. 47 (287): 375–384. doi:10.1080/14786449908621276.
References[edit]
- ^ Lord Rayleigh (John Strutt) refined his theory of scattering in a series of papers; see Works.
- ^ Young, Andrew T (1981). "Rayleigh scattering". Applied Optics. 20 (4): 533–5. Bibcode:1981ApOpt..20..533Y. doi:10.1364/AO.20.000533. PMID 20309152.
- ^ Tyndall, John (1869). "On the blue colour of the sky, the polarization of skylight, and on the polarization of light by cloudy matter generally". Proceedings of the Royal Society of London. 17: 223–233. doi:10.1098/rspl.1868.0033.
- ^ Conocimiento, Ventana al (2018-08-01). "John Tyndall, the Man who Explained Why the Sky is Blue". OpenMind. Retrieved 2019-03-31.
- ^ Strutt, Hon. J.W. (1871). "On the light from the sky, its polarization and colour". The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science. 41 (271): 107–120. doi:10.1080/14786447108640452.
- ^ Strutt, Hon. J.W. (1871). "On the light from the sky, its polarization and colour". The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science. 41 (273): 274–279. doi:10.1080/14786447108640479.
- ^ Strutt, Hon. J.W. (1871). "On the scattering of light by small particles". The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science. 41 (275): 447–454. doi:10.1080/14786447108640507.
- ^ Rayleigh, Lord (1881). "On the electromagnetic theory of light". The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science. 12 (73): 81–101. doi:10.1080/14786448108627074.
- ^ Rayleigh, Lord (1899). "On the transmission of light through an atmosphere containing small particles in suspension, and on the origin of the blue of the sky". The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science. 47 (287): 375–384. doi:10.1080/14786449908621276.
- ^ Blue Sky and Rayleigh Scattering. Hyperphysics.phy-astr.gsu.edu. Retrieved on 2018-08-06.
- ^ a b "Cornell lectures" (PDF). Retrieved 2 April 2014.
- ^ Barnett, C.E. (1942). "Some application of wavelength turbidimetry in the infrared". J. Phys. Chem. 46 (1): 69–75. doi:10.1021/j150415a009.
- ^ 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
- ^ Cox, A.J. (2002). "An experiment to measure Mie and Rayleigh total scattering cross sections". American Journal of Physics. 70 (6): 620. Bibcode:2002AmJPh..70..620C. doi:10.1119/1.1466815. S2CID 16699491.
- ^ a b Sneep, Maarten; Ubachs, Wim (2005). "Direct measurement of the Rayleigh scattering cross section in various gases". Journal of Quantitative Spectroscopy and Radiative Transfer. 92 (3): 293–310. Bibcode:2005JQSRT..92..293S. doi:10.1016/j.jqsrt.2004.07.025.
- ^ Rayleigh scattering. Hyperphysics.phy-astr.gsu.edu. Retrieved on 2018-08-06.
- ^ McQuarrie, Donald A. (Donald Allan) (2000). Statistical mechanics. Sausalito, Calif.: University Science Books. pp. 62. ISBN 1891389157. OCLC 43370175.
- ^ a b Smith, Glenn S. (2005-07-01). "Human color vision and the unsaturated blue color of the daytime sky". American Journal of Physics. 73 (7): 590–597. doi:10.1119/1.1858479. ISSN 0002-9505.
- ^ Zerefos, C. S.; Gerogiannis, V. T.; Balis, D.; Zerefos, S. C.; Kazantzidis, A. (2007), "Atmospheric effects of volcanic eruptions as seen by famous artists and depicted in their paintings" (PDF), Atmospheric Chemistry and Physics, 7 (15): 4027–4042, Bibcode:2007ACP.....7.4027Z, doi:10.5194/acp-7-4027-2007
- ^ Choudhury, Asim Kumar Roy (2014), "Unusual visual phenomena and colour blindness", Principles of Colour and Appearance Measurement, Elsevier, pp. 185–220, doi:10.1533/9780857099242.185, ISBN 978-0-85709-229-8, retrieved 2022-03-29
- ^ Mahajan, Shivam; Pica Ciamarra, Massimo (2023). "Quasi-localized vibrational modes, boson peak and sound attenuation in model mass-spring networks". SciPost Physics. 15 (2). arXiv:2211.01137. doi:10.21468/SciPostPhys.15.2.069.
- ^ Rajagopal, K. (2008) Textbook on Engineering Physics, PHI, New Delhi, part I, Ch. 3, ISBN 8120336658
- ^ Blue & red | Causes of Color. Webexhibits.org. Retrieved on 2018-08-06.
- ^ Svensson, Tomas; Shen, Zhijian (2010). "Laser spectroscopy of gas confined in nanoporous materials" (PDF). Applied Physics Letters. 96 (2): 021107. arXiv:0907.5092. Bibcode:2010ApPhL..96b1107S. doi:10.1063/1.3292210. S2CID 53705149.
Further reading[edit]
- 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).
- Ditchburn, R.W. (1963). Light (2nd ed.). London: Blackie & Sons. pp. 582–585. ISBN 978-0-12-218101-6.
- Chakraborti, Sayan (September 2007). "Verification of the Rayleigh scattering cross section". American Journal of Physics. 75 (9): 824–826. arXiv:physics/0702101. Bibcode:2007AmJPh..75..824C. doi:10.1119/1.2752825. S2CID 119100295.
- Ahrens, C. Donald (1994). Meteorology Today: an introduction to weather, climate, and the environment (5th ed.). St. Paul MN: West Publishing Company. pp. 88–89. ISBN 978-0-314-02779-5.
- Lilienfeld, Pedro (2004). "A Blue Sky History". Optics and Photonics News. 15 (6): 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.