This article is about the optical phenomenon. For the magnetic phenomenon, seeRayleigh law. For the stochastic distribution, seeRayleigh distribution. For the wireless communication effect, seeRayleigh fading.
Rayleigh scattering causes the blue color of the daytime sky and the reddening of the Sun at sunset.
Rayleigh scattering (/ˈreɪli/RAY-lee) is the scattering or deflection oflight, or otherelectromagnetic radiation, by particles with a size much smaller than thewavelength of the radiation. For light frequencies well below theresonance frequency of the scattering medium (normaldispersion regime), the amount of scattering isinversely proportional to thefourth power 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 physicistLord Rayleigh (John William Strutt).[1]
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 bydramatically colored skies andmonochromatic rainbows.
Rayleigh scattering results from the electricpolarizability 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 radiatingdipole 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 ingases.
Scattering by particles with a size comparable to, or larger than, the wavelength of the light is typically treated by theMie theory, thediscrete 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 arefractive index close to 1).Anomalous diffraction theory applies to optically soft but larger particles.
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] He conjectured that a similar scattering of sunlight gave the sky itsblue hue, but he could not explain the preference for blue light, nor could atmospheric dust explain the intensity of the sky's color.
The size of a scattering particle is often parameterized by the ratio
wherer is the particle's radius,λ is thewavelength of the light andx is adimensionless 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 ofMie scattering, interference effects develop throughphase 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[9]) 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 isincoherent and the resultingintensity is just the sum of the squares of theamplitudes from each particle and therefore proportional to the inverse fourth power of the wavelength and the sixth power of its size.[10][11] The wavelength dependence is characteristic ofdipole scattering[10] 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 radiusr andrefractive indexn from a beam of unpolarized light of wavelengthλ and intensityI0 is given by[12]whereR is the observer's distance to the particle andθ is the scattering angle. Averaging this over all angles gives the Rayleighscattering cross-section of the particles in air:[13]Heren 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%.[14]
The major constituent of the atmosphere, nitrogen, has Rayleigh cross section of5.1×10−31 m2 at a wavelength of 532 nm (green light).[14] Over the length of one meter the fraction of light scattered can be approximated from the product of the cross-section and the particle density, that is number of particles per unit volume. For air at atmospheric pressure there are about2×1025 molecules per cubic meter, and the fraction scattered will be 10−5 for every meter of travel.[citation needed]
The strong wavelength dependence of the scattering (~λ−4) means that shorter (blue) wavelengths are scattered more strongly than longer (red) wavelengths.[citation needed]
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 molecularpolarizabilityα, 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 inCGS-units by[15]and inSI-units by
When thedielectric 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[16]
where represents thevariance of the fluctuation in the dielectric constant.
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 (~λ−4) means that shorter (blue) wavelengths are scattered more strongly than longer (red) 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.[17]
Some of the scattering can also be from sulfate particles. For years after largePlinian eruptions, the blue cast of the sky is notably brightened by the persistent sulfate load of thestratospheric gases. Some works of the artistJ. M. W. Turner may owe their vivid red colours to the eruption ofMount Tambora in his lifetime.[18]
In locations with littlelight pollution, the moonlit night sky is also blue, because moonlight is reflected sunlight, with a slightly lowercolor 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 fromrod cells that do not produce any color perception (Purkinje effect).[19]
Rayleigh scattering is also an important mechanism of wave scattering inamorphous 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.[20] This is because in glasses at higher temperatures the Rayleigh-type scattering regime is obscured by the anharmonic damping (typically with a ~λ−2 dependence on wavelength), which becomes increasingly more important as the temperature rises.
Rayleigh scattering is an important component of the scattering of optical signals inoptical 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:[21]
wheren is the refraction index,p is the photoelastic coefficient of the glass,k is theBoltzmann constant, andβ is the isothermal compressibility.Tf is afictive temperature, representing the temperature at which the density fluctuations are "frozen" in the material.
Rayleigh scattering inopalescent glass: it appears blue from the side, but orange light shines through.[22]
Rayleigh-typeλ−4 scattering can also be exhibited by porous materials. An example is the strong optical scattering by nanoporous materials.[23] The strong contrast in refractive index between pores and solid parts of sinteredalumina results in very strong scattering, with light completely changing direction each five micrometers on average. Theλ−4-type scattering is caused by the nanoporous structure (a narrow pore size distribution around ~70 nm) obtained bysintering monodispersive alumina powder.
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.
^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.
^Seinfeld, John H. and Pandis, Spyros N. (2006)Atmospheric Chemistry and Physics, 2nd Edition, John Wiley and Sons, New Jersey, Chapter 15.1.1,ISBN0471720186
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).
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.
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