Rayleigh scattering

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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) and the whole surface re-radiates with the same phase. Because the particles are randomly positioned, the scattered light

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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. This is because in glasses at higher temperatures the Rayleigh-type scattering regime is obscured by the anharmonic damping (typically with a

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Due to Rayleigh scattering, red and orange colors are more visible during sunset because the blue and violet light has been scattered out of the direct path. Due to removal of such colors, these colors are scattered by

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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

1387:) wavelengths. This results in the indirect blue and violet light coming from all regions of the sky. The human eye responds to this wavelength combination as if it were a combination of blue and white light. 1129: 1611:

scattering can also be exhibited by porous materials. An example is the strong optical scattering by nanoporous materials. The strong contrast in refractive index between pores and solid parts of sintered

1454:. 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: 719:

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%.

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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

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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

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of the wavelength (e.g., a blue color is scattered much more than a red color as light propagates through air). The phenomenon is named after the 19th-century British physicist

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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

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from each particle and therefore proportional to the inverse fourth power of the wavelength and the sixth power of its size. The wavelength dependence is characteristic of

1313: 1073: 257:. In 1899, he showed that they applied to individual molecules, with terms containing particulate volumes and refractive indices replaced with terms for molecular 226:

discovered that bright light scattering off nanoscopic particulates was faintly blue-tinted. He conjectured that a similar scattering of sunlight gave the sky its

773:, 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 1093: 553:{\displaystyle I_{s}=I_{0}{\frac {1+\cos ^{2}\theta }{2R^{2}}}\left({\frac {2\pi }{\lambda }}\right)^{4}\left({\frac {n^{2}-1}{n^{2}+2}}\right)^{2}r^{6}} 360:

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

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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

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The expression above can also be written in terms of individual molecules by expressing the dependence on refractive index in terms of the molecular

2576:, John Wiley, New York 1983. Contains a good description of the asymptotic behavior of Mie theory for small size parameter (Rayleigh approximation). 708:{\displaystyle \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}.} 774: 1814:"XXXIV. On the transmission of light through an atmosphere containing small particles in suspension, and on the origin of the blue of the sky" 743:

at a wavelength of 532 nm (green light). This means that about a fraction 10 of the light will be scattered for every meter of travel.

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The fraction of light scattered by scattering particles over the unit travel length (e.g., meter) is the number of particles per unit volume

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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.

2054:"On the transmission of light through an atmosphere containing small particles in suspension, and on the origin of the blue of the sky" 2310: 1037:{\displaystyle I_{s}=I_{0}{\frac {\pi ^{2}\alpha ^{2}}{{\varepsilon _{0}}^{2}\lambda ^{4}R^{2}}}{\frac {1+\cos ^{2}(\theta )}{2}}} 274: 2735: 230:, but he could not explain the preference for blue light, nor could atmospheric dust explain the intensity of the sky's color. 222:

In 1869, while attempting to determine whether any contaminants remained in the purified air he used for infrared experiments,

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times the cross-section. For example, air has a refractive index of 1.0002793 at atmospheric pressure, where there are about

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molecules per cubic meter, and therefore the major constituent of the atmosphere, nitrogen, has a Rayleigh cross section of

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Scattering by particles with a size comparable to, or larger than, the wavelength of the light is typically treated by the

1909:"On the blue colour of the sky, the polarization of skylight, and on the polarization of light by cloudy matter generally" 1252:{\displaystyle I=I_{0}{\frac {\pi ^{2}V^{2}\sigma _{\epsilon }^{2}}{2\lambda ^{4}R^{2}}}{\left(1+\cos ^{2}\theta \right)}} 17: 1620:-type scattering is caused by the nanoporous structure (a narrow pore size distribution around ~70 nm) obtained by 250: 82: 2220:

Sneep, Maarten; Ubachs, Wim (2005). "Direct measurement of the Rayleigh scattering cross section in various gases".

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results in very strong scattering, with light completely changing direction each five micrometers on average. The

1664: 1338: 2484: 2282: 2162: 2755: 1262: 897: 203: 2349: 2750: 211: 2760: 2609: 1704: 1098: 2715: 131: 2350:"Atmospheric effects of volcanic eruptions as seen by famous artists and depicted in their paintings" 1547:{\displaystyle \alpha _{\text{scat}}={\frac {8\pi ^{3}}{3\lambda ^{4}}}n^{8}p^{2}kT_{\text{f}}\beta } 1413:, the moonlit night sky is also blue, because moonlight is reflected sunlight, with a slightly lower 762:

Figure showing the greater proportion of blue light scattered by the atmosphere relative to red light

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Rayleigh scattering causes the blue color of the daytime sky and the reddening of the Sun at sunset.

2435:"Quasi-localized vibrational modes, boson peak and sound attenuation in model mass-spring networks" 1652: 750:) means that shorter (blue) wavelengths are scattered more strongly than longer (red) wavelengths. 569: 2710: 2254: 331: 2099: 889:{\displaystyle I_{s}=I_{0}{\frac {8\pi ^{4}\alpha ^{2}}{\lambda ^{4}R^{2}}}(1+\cos ^{2}\theta )} 2274: 2268: 2174:

Cox, A.J. (2002). "An experiment to measure Mie and Rayleigh total scattering cross sections".

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dependence on wavelength), which becomes increasingly more important as the temperature rises.

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Chakraborti, Sayan (September 2007). "Verification of the Rayleigh scattering cross section".

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Lord Rayleigh (John Strutt) refined his theory of scattering in a series of papers; see

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Zerefos, C. S.; Gerogiannis, V. T.; Balis, D.; Zerefos, S. C.; Kazantzidis, A. (2007),

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Rayleigh scattering is an important component of the scattering of optical signals in

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Barnett, C.E. (1942). "Some application of wavelength turbidimetry in the infrared".

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Strutt, J.W (1871). "XXXVI. On the light from the sky, its polarization and colour".

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Strutt, Hon. J.W. (1871). "On the light from the sky, its polarization and colour".

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Strutt, Hon. J.W. (1871). "On the light from the sky, its polarization and colour".

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Strutt, J.W (1871). "XV. On the light from the sky, its polarization and colour".

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Some of the scattering can also be from sulfate particles. For years after large

39: 2241: 1124:, then any incident light will be scattered according to the following equation 2745: 2058: