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48-578: Rayleigh may refer to: Science [ edit ] Rayleigh scattering Rayleigh–Jeans law Rayleigh waves Rayleigh (unit) , a unit of photon flux named after the 4th Baron Rayleigh Rayl , rayl or Rayleigh, two units of specific acoustic impedance and characteristic acoustic impedance, named after the 3rd Baron Rayleigh Rayleigh criterion in angular resolution Rayleigh distribution Rayleigh fading Rayleigh law on low-field magnetization Rayleigh length Rayleigh number ,

96-577: A Nobel Prize in 1904 Robert John Strutt, 4th Baron Rayleigh , physicist; son of John William Strutt Fictional name [ edit ] Silvers Rayleigh , a fictional character in One Piece Places [ edit ] Rayleigh, British Columbia , Canada Rayleigh, Essex , England Rayleigh (lunar crater) Rayleigh (Martian crater) See also [ edit ] [REDACTED] Look up rayleigh in Wiktionary,

144-496: A dimensionless number for a fluid associated with buoyancy driven flow Rayleigh quotient Rayleigh–Ritz method Plateau–Rayleigh instability explains why a falling stream of fluid breaks up into smaller packets Rayleigh–Taylor instability an instability of an interface between two fluids Title of nobility [ edit ] Baron Rayleigh Charlotte Mary Gertrude Strutt, 1st Baroness Rayleigh John William Strutt, 3rd Baron Rayleigh , physicist, winner of

192-529: A low-pressure gas. The number density can be related to the molecular weight M {\displaystyle M} and mass density ρ {\displaystyle \rho } through N V = N A ρ M {\displaystyle {\tfrac {N}{V}}={\tfrac {N_{\mathrm {A} }\rho }{M}}} , adjusting the final form of our equation to include molar refractivity: This equation allows us to relate bulk property ( refractive index ) to

240-536: A molecule's internal structure. "Polarizability" should not be confused with the intrinsic magnetic or electric dipole moment of an atom, molecule, or bulk substance; these do not depend on the presence of an external field. Electric polarizability is the relative tendency of a charge distribution, like the electron cloud of an atom or molecule , to be distorted from its normal shape by an external electric field . The polarizability α {\displaystyle \alpha } in isotropic media

288-402: A random collection of phases; it is incoherent and the resulting intensity is just the sum of the squares of the amplitudes 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 dipole scattering and the volume dependence will apply to any scattering mechanism. In detail,

336-483: A scattering particle is often parameterized by the ratio x = 2 π r λ {\displaystyle x={\frac {2\pi r}{\lambda }}} 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

384-554: 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. In 1869, while attempting to determine whether any contaminants remained in

432-502: 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. This is because in glasses at higher temperatures the Rayleigh-type scattering regime is obscured by the anharmonic damping (typically with a ~ λ dependence on wavelength), which becomes increasingly more important as

480-437: Is caused by the nanoporous structure (a narrow pore size distribution around ~70 nm) obtained by sintering monodispersive alumina powder. Polarizability Polarizability usually refers to the tendency of matter, when subjected to an electric field , to acquire an electric dipole moment in proportion to that applied field. It is a property of particles with an electric charge . When subject to an electric field,

528-778: Is defined as the ratio of the induced dipole moment p {\displaystyle \mathbf {p} } of an atom to the electric field E {\displaystyle \mathbf {E} } that produces this dipole moment. Polarizability has the SI units of C·m ·V = A ·s ·kg while its cgs unit is cm . Usually it is expressed in cgs units as a so-called polarizability volume, sometimes expressed in Å = 10 cm . One can convert from SI units ( α {\displaystyle \alpha } ) to cgs units ( α ′ {\displaystyle \alpha '} ) as follows: where ε 0 {\displaystyle \varepsilon _{0}} ,

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576-623: Is defined, so that: The elements describing the response parallel to the applied electric field are those along the diagonal. A large value of α y x {\displaystyle \alpha _{yx}} here means that an electric-field applied in the x {\displaystyle x} -direction would strongly polarize the material in the y {\displaystyle y} -direction. Explicit expressions for α {\displaystyle \alpha } have been given for homogeneous anisotropic ellipsoidal bodies. The matrix above can be used with

624-572: Is different from Wikidata All article disambiguation pages All disambiguation pages Rayleigh scattering 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

672-491: 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. Scattering by particles with

720-697: Is related to the average electric susceptibility of the medium by the Clausius–Mossotti relation : where R is the molar refractivity , N A {\displaystyle N_{\text{A}}} is the Avogadro constant , α c {\displaystyle \alpha _{c}} is the electronic polarizability, p is the density of molecules, M is the molar mass , and ε r = ϵ / ϵ 0 {\displaystyle \varepsilon _{\mathrm {r} }=\epsilon /\epsilon _{0}}

768-441: Is the electric permittivity constant and χ e {\displaystyle \chi _{\text{e}}} is the electric susceptibility . Using this proportionality, we find the local field as F = 1 3 ( ε r + 2 ) E {\displaystyle \mathbf {F} ={\tfrac {1}{3}}(\varepsilon _{\mathrm {r} }+2)\mathbf {E} } which can be used in

816-665: Is the 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: σ s = 8 π 3 ( 2 π λ ) 4 ( n 2 − 1 n 2 + 2 ) 2 r 6 . {\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}.} Here n

864-406: Is the material's relative permittivity or dielectric constant (or in optics, the square of the refractive index ). Polarizability for anisotropic or non-spherical media cannot in general be represented as a scalar quantity. Defining α {\displaystyle \alpha } as a scalar implies both that applied electric fields can only induce polarization components parallel to

912-708: Is the refraction index, p is the photoelastic coefficient of the glass, k is the Boltzmann constant , and β is the isothermal compressibility. T f is a fictive temperature , representing the temperature at which the density fluctuations are "frozen" in the material. Rayleigh-type λ 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 alumina results in very strong scattering, with light completely changing direction each five micrometers on average. The λ -type scattering

960-526: 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%. 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 × 10 molecules per cubic meter, and therefore

1008-400: The y {\displaystyle y} -direction the induced polarization would be the same in magnitude but appear in the y {\displaystyle y} component of p {\displaystyle \mathbf {p} } . Many crystalline materials have directions that are easier to polarize than others and some even become polarized in directions perpendicular to

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1056-931: The dielectric constant ϵ {\displaystyle \epsilon } of a certain region of volume V {\displaystyle V} is different from the average dielectric constant of the medium ϵ ¯ {\displaystyle {\bar {\epsilon }}} , then any incident light will be scattered according to the following equation I = I 0 π 2 V 2 σ ϵ 2 2 λ 4 R 2 ( 1 + cos 2 ⁡ θ ) {\displaystyle I=I_{0}{\frac {\pi ^{2}V^{2}\sigma _{\epsilon }^{2}}{2\lambda ^{4}R^{2}}}{\left(1+\cos ^{2}\theta \right)}} where σ ϵ 2 {\displaystyle \sigma _{\epsilon }^{2}} represents

1104-493: The vacuum permittivity , is ~8.854 × 10 (F/m). If the polarizability volume in cgs units is denoted α ′ {\displaystyle \alpha '} the relation can be expressed generally (in SI) as α = 4 π ε 0 α ′ {\displaystyle \alpha =4\pi \varepsilon _{0}\alpha '} . The polarizability of individual particles

1152-437: The variance of the fluctuation in the dielectric constant ϵ {\displaystyle \epsilon } . The blue color of the sky is a consequence of three factors: The strong wavelength dependence of the Rayleigh scattering (~ λ ) 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

1200-772: The alkane's less electronegative sp carbons. Ground state electron configuration models often describe molecular or bond polarization during chemical reactions poorly, because reactive intermediates may be excited, or be the minor, alternate structures in a chemical equilibrium with the initial reactant. Magnetic polarizability defined by spin interactions of nucleons is an important parameter of deuterons and hadrons . In particular, measurement of tensor polarizabilities of nucleons yields important information about spin-dependent nuclear forces. The method of spin amplitudes uses quantum mechanics formalism to more easily describe spin dynamics. Vector and tensor polarization of particle/nuclei with spin S ≥ 1 are specified by

1248-411: The applied electric field , and the same thing happens with non-spherical bodies. Some molecules and materials with this sort of anisotropy are optically active , or exhibit linear birefringence of light. To describe anisotropic media a polarizability rank two tensor or 3 × 3 {\displaystyle 3\times 3} matrix α {\displaystyle \alpha }

1296-523: The color and polarization of skylight to quantify Tyndall's effect in water droplets in terms of the tiny particulates' volumes and refractive indices . 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 . In 1899, he showed that they applied to individual molecules, with terms containing particulate volumes and refractive indices replaced with terms for molecular polarizability . The size of

1344-543: The definition of polarization and simplified with ε r = 1 + N α ε 0 V {\displaystyle \varepsilon _{\mathrm {r} }=1+{\tfrac {N\alpha }{\varepsilon _{0}V}}} to get P = ε 0 ( ε r − 1 ) E {\displaystyle \mathbf {P} =\varepsilon _{0}(\varepsilon _{\mathrm {r} }-1)\mathbf {E} } . These two terms can both be set equal to

1392-1178: The dependence on refractive index in terms of the molecular 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 CGS-units by I s = I 0 8 π 4 α 2 λ 4 R 2 ( 1 + cos 2 ⁡ θ ) {\displaystyle I_{s}=I_{0}{\frac {8\pi ^{4}\alpha ^{2}}{\lambda ^{4}R^{2}}}(1+\cos ^{2}\theta )} and in SI-units by I s = I 0 π 2 α 2 ε 0 2 λ 4 R 2 1 + cos 2 ⁡ ( θ ) 2 . {\displaystyle I_{s}=I_{0}{\frac {\pi ^{2}\alpha ^{2}}{{\varepsilon _{0}}^{2}\lambda ^{4}R^{2}}}{\frac {1+\cos ^{2}(\theta )}{2}}.} When

1440-549: The dipole moment per unit cell . Note that the local electric field seen by a molecule is generally different from the macroscopic electric field that would be measured externally. This discrepancy is taken into account by the Clausius–Mossotti relation (below) which connects the bulk behaviour ( polarization density due to an external electric field according to the electric susceptibility χ = ε r − 1 {\displaystyle \chi =\varepsilon _{\mathrm {r} }-1} ) with

1488-511: The eruption of Mount Tambora in his lifetime. 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 ). Rayleigh scattering

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1536-478: The field and that the x , y {\displaystyle x,y} and z {\displaystyle z} directions respond in the same way to the applied electric field. For example, an electric field in the x {\displaystyle x} -direction can only produce an x {\displaystyle x} component in p {\displaystyle \mathbf {p} } and if that same electric field were applied in

1584-411: The field due to matter within the sphere, E i n = − P 3 ε 0 {\displaystyle \mathbf {E} _{\mathrm {in} }={\tfrac {-\mathbf {P} }{3\varepsilon _{0}}}} We can then define the local field as the macroscopic field without the contribution of the internal field: The polarization is proportional to

1632-554: The free dictionary. Raleigh (disambiguation) for a different spelling Topics referred to by the same term [REDACTED] This disambiguation page lists articles associated with the title Rayleigh . If an internal link led you here, you may wish to change the link to point directly to the intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=Rayleigh&oldid=872773884 " Categories : Disambiguation pages Place name disambiguation pages Hidden categories: Short description

1680-708: 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 0 is given by I s = I 0 1 + cos 2 ⁡ θ 2 R 2 ( 2 π λ ) 4 ( n 2 − 1 n 2 + 2 ) 2 r 6 {\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}} where R

1728-636: The interactions between molecules are considered by comparing a local field to the macroscopic field. Analyzing a cubic crystal lattice , we can imagine an isotropic spherical region to represent the entire sample. Giving the region the radius a {\displaystyle a} , the field would be given by the volume of the sphere times the dipole moment per unit volume P . {\displaystyle \mathbf {P} .} We can call our local field F {\displaystyle \mathbf {F} } , our macroscopic field E {\displaystyle \mathbf {E} } , and

1776-421: The intermediate x ≃ 1 of Mie scattering , interference effects develop through 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 ) 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

1824-419: The macroscopic field by P = ε 0 ( ε r − 1 ) E = χ e ε 0 E {\displaystyle \mathbf {P} =\varepsilon _{0}(\varepsilon _{r}-1)\mathbf {E} =\chi _{\text{e}}\varepsilon _{0}\mathbf {E} } where ε 0 {\displaystyle \varepsilon _{0}}

1872-493: The major constituent of the atmosphere, nitrogen, has a Rayleigh cross section of 5.1 × 10  m 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. The strong wavelength dependence of the scattering (~ λ ) means that shorter (blue) wavelengths are scattered more strongly than longer (red) wavelengths. The expression above can also be written in terms of individual molecules by expressing

1920-510: The molar refractivity equation and other data to produce density data for crystallography. Each polarizability measurement along with the refractive index associated with its direction will yield a direction specific density that can be used to develop an accurate three dimensional assessment of molecular stacking in the crystal. This relationship was first observed by Linus Pauling . Polarizability and molecular property are related to refractive index and bulk property. In crystalline structures,

1968-427: The molecular polarizability α {\displaystyle \alpha } due to the local field. Magnetic polarizability likewise refers to the tendency for a magnetic dipole moment to appear in proportion to an external magnetic field . Electric and magnetic polarizabilities determine the dynamical response of a bound system (such as a molecule or crystal) to external fields, and provide insight into

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2016-424: The molecular property (polarizability) as a function of frequency. Generally, polarizability increases as the volume occupied by electrons increases. In atoms, this occurs because larger atoms have more loosely held electrons in contrast to smaller atoms with tightly bound electrons. On rows of the periodic table , polarizability therefore decreases from left to right. Polarizability increases down on columns of

2064-428: The negatively charged electrons and positively charged atomic nuclei are subject to opposite forces and undergo charge separation . Polarizability is responsible for a material's dielectric constant and, at high (optical) frequencies, its refractive index . The polarizability of an atom or molecule is defined as the ratio of its induced dipole moment to the local electric field; in a crystalline solid, one considers

2112-450: The other, eliminating the E {\displaystyle \mathbf {E} } term giving us We can replace the relative permittivity ε r {\displaystyle \varepsilon _{\mathrm {r} }} with refractive index n {\displaystyle n} , since ε r = n 2 {\displaystyle \varepsilon _{\mathrm {r} }=n^{2}} for

2160-610: The periodic table. Likewise, larger molecules are generally more polarizable than smaller ones. Water is a very polar molecule, but alkanes and other hydrophobic molecules are more polarizable. Water with its permanent dipole is less likely to change shape due to an external electric field. Alkanes are the most polarizable molecules. Although alkenes and arenes are expected to have larger polarizability than alkanes because of their higher reactivity compared to alkanes, alkanes are in fact more polarizable. This results because of alkene's and arene's more electronegative sp carbons to

2208-417: The purified air he used for infrared experiments, John Tyndall discovered that bright light scattering off nanoscopic particulates was faintly blue-tinted. 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

2256-406: The sky. The human eye responds to this wavelength combination as if it were a combination of blue and white light. 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

2304-651: The temperature rises. 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: α scat = 8 π 3 3 λ 4 n 8 p 2 k T f β {\displaystyle \alpha _{\text{scat}}={\frac {8\pi ^{3}}{3\lambda ^{4}}}n^{8}p^{2}kT_{\text{f}}\beta } where n

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