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69-518: Because it was deposited throughout a wide area at a known time, the Mazama Ash is an important marker bed for paleoclimatology , paleoecology , and archaeology , as well as for Quaternary geology and stratigraphic correlation. The ash particles and gasses from the Mazama eruption would have caused climate cooling for a period of several years after the eruption. Throughout the northern Great Plains ,

138-558: A lens is determined by its refractive index n and the radii of curvature R 1 and R 2 of its surfaces. The power of a thin lens in air is given by the simplified version of the Lensmaker's formula : 1 f = ( n − 1 ) [ 1 R 1 − 1 R 2 ]   , {\displaystyle {\frac {1}{f}}=(n-1)\left[{\frac {1}{R_{1}}}-{\frac {1}{R_{2}}}\right]\ ,} where f

207-527: A dating tool in archaeology , since the dates of eruptions are generally well-established. One particular bolide impact 66 million years ago, which formed the Chicxulub crater , produced an iridium anomaly that occurs in a thin, global layer of clay marking the Cretaceous–Paleogene boundary . Iridium layers are associated with bolide impacts and are not unique, but when occurring in conjunction with

276-649: A function of photon energy, E , applicable to amorphous materials. Forouhi and Bloomer then applied the Kramers–Kronig relation to derive the corresponding equation for n as a function of E . The same formalism was applied to crystalline materials by Forouhi and Bloomer in 1988. The refractive index and extinction coefficient, n and κ , are typically measured from quantities that depend on them, such as reflectance, R , or transmittance, T , or ellipsometric parameters, ψ and δ . The determination of n and κ from such measured quantities will involve developing

345-401: A geologically short period of time have created key beds in the form of peat beds, coal beds, shell beds, marine bands , black shales in cyclothems , and oil shales . A well-known example of a key bed is the global layer of iridium -rich impact ejecta that marks the Cretaceous–Paleogene boundary (K–T boundary). Palynology , the study of fossil pollens and spores, routinely works out

414-606: A green spectral line of mercury ( 546.07 nm ), called d and e lines respectively. Abbe number is defined for both and denoted V d and V e . The spectral data provided by glass manufacturers is also often more precise for these two wavelengths. Both, d and e spectral lines are singlets and thus are suitable to perform a very precise measurements, such as spectral goniometric method. In practical applications, measurements of refractive index are performed on various refractometers, such as Abbe refractometer . Measurement accuracy of such typical commercial devices

483-532: A hiatus in human occupation of the ash-affected area there of perhaps 200 years. The particles and gasses released during the Mazama eruption caused climate cooling. Studies of the Greenland ice core suggest that the eruption produced a substantial stratospheric aerosol loading spread over a period about 6 years. This may have produced a temperature depression of about 0.6 to 0.7 °C at mid to high northern latitudes for 1 to 3 years. The release of chlorine during

552-412: A material with higher refractive index, the angle of refraction will be smaller than the angle of incidence and the light will be refracted towards the normal of the surface. The higher the refractive index, the closer to the normal direction the light will travel. When passing into a medium with lower refractive index, the light will instead be refracted away from the normal, towards the surface. If there

621-697: A more accurate description of the wavelength dependence of the refractive index, the Sellmeier equation can be used. It is an empirical formula that works well in describing dispersion. Sellmeier coefficients are often quoted instead of the refractive index in tables. Because of dispersion, it is usually important to specify the vacuum wavelength of light for which a refractive index is measured. Typically, measurements are done at various well-defined spectral emission lines . Manufacturers of optical glass in general define principal index of refraction at yellow spectral line of helium ( 587.56 nm ) and alternatively at

690-462: A plasma with an index of refraction less than unity is Earth's ionosphere . Since the refractive index of the ionosphere (a plasma ), is less than unity, electromagnetic waves propagating through the plasma are bent "away from the normal" (see Geometric optics ) allowing the radio wave to be refracted back toward earth, thus enabling long-distance radio communications. See also Radio Propagation and Skywave . Recent research has also demonstrated

759-468: A ratio with a fixed numerator, like "10000 to 7451.9" (for urine). Hutton wrote it as a ratio with a fixed denominator, like 1.3358 to 1 (water). Young did not use a symbol for the index of refraction, in 1807. In the later years, others started using different symbols: n , m , and µ . The symbol n gradually prevailed. Refractive index also varies with wavelength of the light as given by Cauchy's equation . The most general form of this equation

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828-499: A refractive index below 1. This can occur close to resonance frequencies , for absorbing media, in plasmas , and for X-rays . In the X-ray regime the refractive indices are lower than but very close to 1 (exceptions close to some resonance frequencies). As an example, water has a refractive index of 0.999 999 74 = 1 − 2.6 × 10 for X-ray radiation at a photon energy of 30  keV ( 0.04 nm wavelength). An example of

897-488: A theoretical expression for R or T , or ψ and δ in terms of a valid physical model for n and κ . By fitting the theoretical model to the measured R or T , or ψ and δ using regression analysis, n and κ can be deduced. For X-ray and extreme ultraviolet radiation the complex refractive index deviates only slightly from unity and usually has a real part smaller than 1. It is therefore normally written as n = 1 − δ + iβ (or n = 1 − δ − iβ with

966-653: A very large geographic area. As a result, a key bed is useful for correlating sequences of sedimentary rocks over a large area. Typically, key beds were created as the result of either instantaneous events or (geologically speaking) very short episodes of the widespread deposition of a specific types of sediment . As the result, key beds often can be used for both mapping and correlating sedimentary rocks and dating them. Volcanic ash beds ( tonsteins and bentonite beds) and impact spherule beds, and specific mega turbidites are types of key beds created by instantaneous events. The widespread accumulation of distinctive sediments over

1035-416: Is n ( λ ) = A + B λ 2 + C λ 4 + ⋯ , {\displaystyle n(\lambda )=A+{\frac {B}{\lambda ^{2}}}+{\frac {C}{\lambda ^{4}}}+\cdots ,} where n is the refractive index, λ is the wavelength, and A , B , C , etc., are coefficients that can be determined for a material by fitting

1104-399: Is α = 4π κ / λ 0 , and the penetration depth (the distance after which the intensity is reduced by a factor of 1/ e ) is δ p = 1/ α = λ 0 /4π κ . Both n and κ are dependent on the frequency. In most circumstances κ > 0 (light is absorbed) or κ = 0 (light travels forever without loss). In special situations, especially in the gain medium of lasers , it

1173-629: Is also possible that κ < 0 , corresponding to an amplification of the light. An alternative convention uses n = n + iκ instead of n = n − iκ , but where κ > 0 still corresponds to loss. Therefore, these two conventions are inconsistent and should not be confused. The difference is related to defining sinusoidal time dependence as Re[exp(− iωt )] versus Re[exp(+ iωt )] . See Mathematical descriptions of opacity . Dielectric loss and non-zero DC conductivity in materials cause absorption. Good dielectric materials such as glass have extremely low DC conductivity, and at low frequencies

1242-699: Is called "normal dispersion", in contrast to "anomalous dispersion", where the refractive index increases with wavelength. For visible light normal dispersion means that the refractive index is higher for blue light than for red. For optics in the visual range, the amount of dispersion of a lens material is often quantified by the Abbe number : V = n y e l l o w − 1 n b l u e − n r e d . {\displaystyle V={\frac {n_{\mathrm {yellow} }-1}{n_{\mathrm {blue} }-n_{\mathrm {red} }}}.} For

1311-545: Is called the absolute refractive index of medium 2. The absolute refractive index n of an optical medium is defined as the ratio of the speed of light in vacuum, c = 299 792 458  m/s , and the phase velocity v of light in the medium, n = c v . {\displaystyle n={\frac {\mathrm {c} }{v}}.} Since c is constant, n is inversely proportional to v : n ∝ 1 v . {\displaystyle n\propto {\frac {1}{v}}.} The phase velocity

1380-434: Is commonly used to obtain high resolution in microscopy. In this technique the objective is dipped into a drop of high refractive index immersion oil on the sample under study. The refractive index of electromagnetic radiation equals n = ε r μ r , {\displaystyle n={\sqrt {\varepsilon _{\mathrm {r} }\mu _{\mathrm {r} }}},} where ε r

1449-485: Is critical. All three typical principle refractive indices definitions can be found depending on application and region, so a proper subscript should be used to avoid ambiguity. When light passes through a medium, some part of it will always be absorbed . This can be conveniently taken into account by defining a complex refractive index, n _ = n + i κ . {\displaystyle {\underline {n}}=n+i\kappa .} Here,

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1518-406: Is given by the ratio of speed of light in medium 1 to that in medium 2. This can be expressed as follows: n 21 = v 1 v 2 . {\displaystyle n_{21}={\frac {v_{1}}{v_{2}}}.} If the reference medium 1 is vacuum , then the refractive index of medium 2 is considered with respect to vacuum. It is simply represented as n 2 and

1587-419: Is in the order of 0.0002. Refractometers usually measure refractive index n D , defined for sodium doublet D ( 589.29 nm ), which is actually a midpoint between two adjacent yellow spectral lines of sodium. Yellow spectral lines of helium ( d ) and sodium ( D ) are 1.73 nm apart, which can be considered negligible for typical refractometers, but can cause confusion and lead to errors if accuracy

1656-467: Is no angle θ 2 fulfilling Snell's law, i.e., n 1 n 2 sin ⁡ θ 1 > 1 , {\displaystyle {\frac {n_{1}}{n_{2}}}\sin \theta _{1}>1,} the light cannot be transmitted and will instead undergo total internal reflection . This occurs only when going to a less optically dense material, i.e., one with lower refractive index. To get total internal reflection

1725-966: Is the electron density. One may assume the electron density is simply the number of electrons per atom Z multiplied by the atomic density, but more accurate calculation of the refractive index requires replacing Z with the complex atomic form factor f = Z + f ′ + i f ″ {\displaystyle f=Z+f'+if''} . It follows that δ = r 0 λ 2 2 π ( Z + f ′ ) n atom β = r 0 λ 2 2 π f ″ n atom {\displaystyle {\begin{aligned}\delta &={\frac {r_{0}\lambda ^{2}}{2\pi }}(Z+f')n_{\text{atom}}\\\beta &={\frac {r_{0}\lambda ^{2}}{2\pi }}f''n_{\text{atom}}\end{aligned}}} with δ and β typically of

1794-579: Is the focal length of the lens. The resolution of a good optical microscope is mainly determined by the numerical aperture ( A Num ) of its objective lens . The numerical aperture in turn is determined by the refractive index n of the medium filling the space between the sample and the lens and the half collection angle of light θ according to Carlsson (2007): A N u m = n sin ⁡ θ   . {\displaystyle A_{\mathrm {Num} }=n\sin \theta ~.} For this reason oil immersion

1863-499: Is the material's relative permittivity , and μ r is its relative permeability . The refractive index is used for optics in Fresnel equations and Snell's law ; while the relative permittivity and permeability are used in Maxwell's equations and electronics. Most naturally occurring materials are non-magnetic at optical frequencies, that is μ r is very close to 1, therefore n

1932-417: Is the speed at which the crests or the phase of the wave moves, which may be different from the group velocity , the speed at which the pulse of light or the envelope of the wave moves. Historically air at a standardized pressure and temperature has been common as a reference medium. Thomas Young was presumably the person who first used, and invented, the name "index of refraction", in 1807. At

2001-450: Is transparent in the wavelength region from 2 to 14 μm and has a refractive index of about 4. A type of new materials termed " topological insulators ", was recently found which have high refractive index of up to 6 in the near to mid infrared frequency range. Moreover, topological insulators are transparent when they have nanoscale thickness. These properties are potentially important for applications in infrared optics. According to

2070-470: The Beer–Lambert law . Since intensity is proportional to the square of the electric field, intensity will depend on the depth into the material as I ( x ) = I 0 e − 4 π κ x / λ 0 . {\displaystyle I(x)=I_{0}e^{-4\pi \kappa x/\lambda _{0}}.} and thus the absorption coefficient

2139-672: The Pacific Northwest , as well as by other methods such as identification of ash from within an ice core from the Greenland Ice Sheet Project , from sediment cores from the Lake Superior basin, and by radiocarbon dating of wood charred by ashflows. The Mazama ash spread over an area of at least 900,000 km (350,000 sq mi) in the northern Great Plains, where it is most commonly preserved within peat , alluvial , lacustrine , and aeolian sediments . In

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2208-483: The angle of incidence and angle of refraction, respectively, of a ray crossing the interface between two media with refractive indices n 1 and n 2 . The refractive indices also determine the amount of light that is reflected when reaching the interface, as well as the critical angle for total internal reflection , their intensity ( Fresnel equations ) and Brewster's angle . The refractive index, n {\displaystyle n} , can be seen as

2277-507: The attenuation , while the real part accounts for refraction. For most materials the refractive index changes with wavelength by several percent across the visible spectrum. Consequently, refractive indices for materials reported using a single value for n must specify the wavelength used in the measurement. The concept of refractive index applies across the full electromagnetic spectrum , from X-rays to radio waves . It can also be applied to wave phenomena such as sound . In this case,

2346-411: The refractive index (or refraction index ) of an optical medium is the ratio of the apparent speed of light in the air or vacuum to the speed in the medium. The refractive index determines how much the path of light is bent, or refracted , when entering a material. This is described by Snell's law of refraction, n 1 sin θ 1 = n 2 sin θ 2 , where θ 1 and θ 2 are

2415-405: The theory of relativity , no information can travel faster than the speed of light in vacuum, but this does not mean that the refractive index cannot be less than 1. The refractive index measures the phase velocity of light, which does not carry information . The phase velocity is the speed at which the crests of the wave move and can be faster than the speed of light in vacuum, and thereby give

2484-418: The "existence" of materials with a negative refractive index, which can occur if permittivity and permeability have simultaneous negative values. This can be achieved with periodically constructed metamaterials . The resulting negative refraction (i.e., a reversal of Snell's law ) offers the possibility of the superlens and other new phenomena to be actively developed by means of metamaterials . At

2553-750: The Hospital Hill Series in the Witwatersrand Basin , include a fine-grained ferruginous quartzite which is particularly magnetic. From the same series a ripple marked quartzite and a speckled bed are used as marker horizons. On a much smaller time scale, marker horizons may be created by sedimentologists and limnologists in order to measure deposition and erosion rates in a marsh or pond environment. The materials used for such an artificial horizon are chosen for their visibility and stability and may be brick dust, grog , sand, kaolin, glitter or feldspar clay. Refractive index In optics ,

2622-483: The Mazama Ash would have covered the landscape in a blanket up to 15 cm (6 in) thick, coating vegetation and clogging watercourses throughout the ashfall area. This would have caused an immediate scarcity of resources for the native people and wildlife, necessitating the movement of people out of the main ashfall area. Available archeological evidence from a site in the Cypress Hills of southern Alberta suggests

2691-531: The U.S., it is present in portions of the U.S. states of California , Oregon , Washington , Idaho , Montana , Nevada , Wyoming and Utah . It is also present in the Greenland ice sheet, and in marine sediments off the coast of Oregon , Washington , and southernmost British Columbia . In Canada , deposits of Mazama Ash several centimeters thick are commonly present in southern areas of British Columbia , Alberta , and Saskatchewan . In southern Alberta, about 1000 kilometers (about 600 miles) northeast of

2760-418: The alternative convention mentioned above). Far above the atomic resonance frequency delta can be given by δ = r 0 λ 2 n e 2 π {\displaystyle \delta ={\frac {r_{0}\lambda ^{2}n_{\mathrm {e} }}{2\pi }}} where r 0 is the classical electron radius , λ is the X-ray wavelength, and n e

2829-596: The amount of light that is reflected is determined by the reflectivity of the surface. The reflectivity can be calculated from the refractive index and the incidence angle with the Fresnel equations , which for normal incidence reduces to R 0 = | n 1 − n 2 n 1 + n 2 | 2 . {\displaystyle R_{0}=\left|{\frac {n_{1}-n_{2}}{n_{1}+n_{2}}}\right|^{2}\!.} For common glass in air, n 1 = 1 and n 2 = 1.5 , and thus about 4% of

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2898-423: The angles of incidence θ 1 must be larger than the critical angle θ c = arcsin ( n 2 n 1 ) . {\displaystyle \theta _{\mathrm {c} }=\arcsin \!\left({\frac {n_{2}}{n_{1}}}\right)\!.} Apart from the transmitted light there is also a reflected part. The reflection angle is equal to the incidence angle, and

2967-460: The ash would have darkened the sky and a layer of ash at least several centimeters thick would have blanketed much of the landscape, causing severe disruptions for the native people and wildlife. The climactic eruption of Mount Mazama during which the Mazama Ash was ejected occurred approximately 6790 ± 15 C yrs BP , or 7640 ± 20 calibrated years Before Present (5677 ± 150 B.C.E.) , based on analysis of multiple ash and tephra sources throughout

3036-406: The atomic scale, an electromagnetic wave's phase velocity is slowed in a material because the electric field creates a disturbance in the charges of each atom (primarily the electrons ) proportional to the electric susceptibility of the medium. (Similarly, the magnetic field creates a disturbance proportional to the magnetic susceptibility .) As the electromagnetic fields oscillate in the wave,

3105-428: The charges in the material will be "shaken" back and forth at the same frequency. The charges thus radiate their own electromagnetic wave that is at the same frequency, but usually with a phase delay , as the charges may move out of phase with the force driving them (see sinusoidally driven harmonic oscillator ). The light wave traveling in the medium is the macroscopic superposition (sum) of all such contributions in

3174-448: The clear exception. Aerogel is a very low density solid that can be produced with refractive index in the range from 1.002 to 1.265. Moissanite lies at the other end of the range with a refractive index as high as 2.65. Most plastics have refractive indices in the range from 1.3 to 1.7, but some high-refractive-index polymers can have values as high as 1.76. For infrared light refractive indices can be considerably higher. Germanium

3243-407: The correlation of strata , and used in conjunction with fossil floral and faunal assemblages and paleomagnetism , permit the mapping of land masses and bodies of water throughout the history of the earth. They usually consist of a relatively thin layer of sedimentary rock that is readily recognized on the basis of either its distinct physical characteristics or fossil content and can be mapped over

3312-504: The dielectric loss is also negligible, resulting in almost no absorption. However, at higher frequencies (such as visible light), dielectric loss may increase absorption significantly, reducing the material's transparency to these frequencies. The real n , and imaginary κ , parts of the complex refractive index are related through the Kramers–Kronig relations . In 1986, A.R. Forouhi and I. Bloomer deduced an equation describing κ as

3381-468: The equation to measured refractive indices at known wavelengths. The coefficients are usually quoted for λ as the vacuum wavelength in micrometres . Usually, it is sufficient to use a two-term form of the equation: n ( λ ) = A + B λ 2 , {\displaystyle n(\lambda )=A+{\frac {B}{\lambda ^{2}}},} where the coefficients A and B are determined specifically for this form of

3450-464: The equation. For visible light most transparent media have refractive indices between 1 and 2. A few examples are given in the adjacent table. These values are measured at the yellow doublet D-line of sodium , with a wavelength of 589 nanometers , as is conventionally done. Gases at atmospheric pressure have refractive indices close to 1 because of their low density. Almost all solids and liquids have refractive indices above 1.3, with aerogel as

3519-473: The eruption may also have led to substantial depletion of stratospheric ozone . Marker horizon Marker horizons (also referred to as chronohorizons , key beds or marker beds ) are stratigraphic units of the same age and of such distinctive composition and appearance, that, despite their presence in separate geographic locations, there is no doubt about their being of equivalent age ( isochronous ) and of common origin. Such clear markers facilitate

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3588-535: The eruption site, the Mazama Ash is typically found as a white band located several metres below the present ground surface. Shards of volcanic glass from the Mazama Ash have also been identified in the sediments of Lake Superior and in a bog in Newfoundland . Mazama Ash is the most widely distributed tephra layer from the late Quaternary in the United States and southwestern Canada, extending to eight states to

3657-472: The extinction of specialised tropical planktic foraminifera and the appearance of the first Danian species, signal a reliable marker horizon for the Cretaceous–Paleogene boundary. Fossil faunal and floral assemblages , both marine and terrestrial, make for distinctive marker horizons. Some marker units are distinctive by virtue of their magnetic qualities. The Water Tower Slates, forming part of

3726-402: The factor by which the speed and the wavelength of the radiation are reduced with respect to their vacuum values: the speed of light in a medium is v = c/ n , and similarly the wavelength in that medium is λ = λ 0 / n , where λ 0 is the wavelength of that light in vacuum. This implies that vacuum has a refractive index of 1, and assumes that the frequency ( f = v / λ ) of

3795-445: The frequency of the light used in the measurement. That κ corresponds to absorption can be seen by inserting this refractive index into the expression for electric field of a plane electromagnetic wave traveling in the x -direction. This can be done by relating the complex wave number k to the complex refractive index n through k = 2π n / λ 0 , with λ 0 being the vacuum wavelength; this can be inserted into

3864-644: The incident power is reflected. At other incidence angles the reflectivity will also depend on the polarization of the incoming light. At a certain angle called Brewster's angle , p -polarized light (light with the electric field in the plane of incidence ) will be totally transmitted. Brewster's angle can be calculated from the two refractive indices of the interface as θ B = arctan ⁡ ( n 2 n 1 )   . {\displaystyle \theta _{\mathsf {B}}=\arctan \left({\frac {n_{2}}{n_{1}}}\right)~.} The focal length of

3933-465: The material: the original wave plus the waves radiated by all the moving charges. This wave is typically a wave with the same frequency but shorter wavelength than the original, leading to a slowing of the wave's phase velocity. Most of the radiation from oscillating material charges will modify the incoming wave, changing its velocity. However, some net energy will be radiated in other directions or even at other frequencies (see scattering ). Depending on

4002-596: The optical path length. When light moves from one medium to another, it changes direction, i.e. it is refracted . If it moves from a medium with refractive index n 1 to one with refractive index n 2 , with an incidence angle to the surface normal of θ 1 , the refraction angle θ 2 can be calculated from Snell's law : n 1 sin ⁡ θ 1 = n 2 sin ⁡ θ 2 . {\displaystyle n_{1}\sin \theta _{1}=n_{2}\sin \theta _{2}.} When light enters

4071-540: The order of 10 and 10 . Optical path length (OPL) is the product of the geometric length d of the path light follows through a system, and the index of refraction of the medium through which it propagates, OPL = n d . {\text{OPL}}=nd. This is an important concept in optics because it determines the phase of the light and governs interference and diffraction of light as it propagates. According to Fermat's principle , light rays can be characterized as those curves that optimize

4140-1189: The plane wave expression for a wave travelling in the x -direction as: E ( x , t ) = Re [ E 0 e i ( k _ x − ω t ) ] = Re [ E 0 e i ( 2 π ( n + i κ ) x / λ 0 − ω t ) ] = e − 2 π κ x / λ 0 Re [ E 0 e i ( k x − ω t ) ] . {\displaystyle {\begin{aligned}\mathbf {E} (x,t)&=\operatorname {Re} \!\left[\mathbf {E} _{0}e^{i({\underline {k}}x-\omega t)}\right]\\&=\operatorname {Re} \!\left[\mathbf {E} _{0}e^{i(2\pi (n+i\kappa )x/\lambda _{0}-\omega t)}\right]\\&=e^{-2\pi \kappa x/\lambda _{0}}\operatorname {Re} \!\left[\mathbf {E} _{0}e^{i(kx-\omega t)}\right].\end{aligned}}} Here we see that κ gives an exponential decay, as expected from

4209-653: The real part n is the refractive index and indicates the phase velocity , while the imaginary part κ is called the extinction coefficient indicates the amount of attenuation when the electromagnetic wave propagates through the material. It is related to the absorption coefficient , α abs {\displaystyle \alpha _{\text{abs}}} , through: α abs ( ω ) = 2 ω κ ( ω ) c {\displaystyle \alpha _{\text{abs}}(\omega )={\frac {2\omega \kappa (\omega )}{c}}} These values depend upon

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4278-482: The refractive index varies with wavelength, so will the refraction angle as light goes from one material to another. Dispersion also causes the focal length of lenses to be wavelength dependent. This is a type of chromatic aberration , which often needs to be corrected for in imaging systems. In regions of the spectrum where the material does not absorb light, the refractive index tends to decrease with increasing wavelength, and thus increase with frequency. This

4347-506: The relative phase of the original driving wave and the waves radiated by the charge motion, there are several possibilities: For most materials at visible-light frequencies, the phase is somewhere between 90° and 180°, corresponding to a combination of both refraction and absorption. The refractive index of materials varies with the wavelength (and frequency ) of light. This is called dispersion and causes prisms and rainbows to divide white light into its constituent spectral colors . As

4416-420: The same time he changed this value of refractive power into a single number, instead of the traditional ratio of two numbers. The ratio had the disadvantage of different appearances. Newton , who called it the "proportion of the sines of incidence and refraction", wrote it as a ratio of two numbers, like "529 to 396" (or "nearly 4 to 3"; for water). Hauksbee , who called it the "ratio of refraction", wrote it as

4485-487: The speed of sound is used instead of that of light, and a reference medium other than vacuum must be chosen. For lenses (such as eye glasses ), a lens made from a high refractive index material will be thinner, and hence lighter, than a conventional lens with a lower refractive index. Such lenses are generally more expensive to manufacture than conventional ones. The relative refractive index of an optical medium 2 with respect to another reference medium 1 ( n 21 )

4554-465: The stratigraphy of rocks by comparing pollen and spore assemblages with those of well-known layers—a tool frequently used by petroleum exploration companies in the search for new fields. The fossilised teeth or elements of conodonts are an equally useful tool. The ejecta from volcanoes and bolide impacts create useful markers, as different volcanic eruptions and impacts produce beds with distinctive compositions. Marker horizons of tephra are used as

4623-489: The unique chemistry of those constituents. This can be determined by electron microprobe analysis, by the refractive index of the volcanic glass, and by neutron activation analysis and similar techniques. Radiocarbon dating of associated carbon-bearing material may also aid identification of the Mazama Ash. It forms orange colored deposits. Comparison with the effects of the Mount St. Helens eruption of 1980 indicates that

4692-435: The wave is not affected by the refractive index. The refractive index may vary with wavelength. This causes white light to split into constituent colors when refracted. This is called dispersion . This effect can be observed in prisms and rainbows , and as chromatic aberration in lenses. Light propagation in absorbing materials can be described using a complex -valued refractive index. The imaginary part then handles

4761-891: The west and three Canadian provinces. Like the Glacier Peak Ash deposits, Mazama Ash is well preserved in the Pacific Northwest. It is distinguishable from the lump pumice deposits ejected from the Glacier Peak volcano, which contain more phenocrysts . Mazama Ash also has more soda , yttrium , ytterbium , and zirconium , and less silica and lime than eruptive products from Glacier Peak, and it forms finer deposits than Glacier Peak Ash. The Mazama ash includes plagioclase , hypersthene , magnetite , hornblende , clinopyroxene , and volcanic glass . It can be distinguished from other volcanic ash deposits, such as those from eruptions of Glacier Peak , Mount St. Helens and Mount Rainier , by

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