5513:. For liquids the same observation can be made as for gases, for instance, the refractive index in alkanes increases nearly perfectly linear with the density. On the other hand, for carboxylic acids, the density decreases with increasing number of C-atoms within the homologeous series. The simple explanation of this finding is that it is not density, but the molar concentration of the chromophore that counts. In homologeous series, this is the excitation of the C-H-bonding. August Beer must have intuitively known that when he gave Hans H. Landolt in 1862 the tip to investigate the refractive index of compounds of homologeous series. While Landolt did not find this relationship, since, at this time dispersion theory was in its infancy, he had the idea of molar refractivity which can even be assigned to single atoms. Based on this concept, the refractive indices of organic materials can be calculated.
9369:
1334:
3436:
6803:
6651:
6395:
5082:
1514:
9405:
587:
6722:
4827:
74:
1490:
5442:
9417:
3856:
9381:
1283:
5077:{\displaystyle {\begin{aligned}Z&={\sqrt {\frac {\mu }{\varepsilon }}}={\sqrt {\frac {\mu _{\mathrm {0} }\mu _{\mathrm {r} }}{\varepsilon _{\mathrm {0} }\varepsilon _{\mathrm {r} }}}}={\sqrt {\frac {\mu _{\mathrm {0} }}{\varepsilon _{\mathrm {0} }}}}{\sqrt {\frac {\mu _{\mathrm {r} }}{\varepsilon _{\mathrm {r} }}}}\\&=Z_{0}{\sqrt {\frac {\mu _{\mathrm {r} }}{\varepsilon _{\mathrm {r} }}}}\\&=Z_{0}{\frac {\mu _{\mathrm {r} }}{n}}\end{aligned}}}
1478:
31:
6583:
3142:
9393:
6911:
6380:
3235:
651:
6788:. The gem is placed on a high refractive index prism and illuminated from below. A high refractive index contact liquid is used to achieve optical contact between the gem and the prism. At small incidence angles most of the light will be transmitted into the gem, but at high angles total internal reflection will occur in the prism. The critical angle is normally measured by looking through a telescope.
4703:
5957:
6162:
4543:
5768:
3110:
2358:
6983:. Since the refractive index is a fundamental physical property of a substance, it is often used to identify a particular substance, confirm its purity, or measure its concentration. The refractive index is used to measure solids, liquids, and gases. Most commonly it is used to measure the concentration of a solute in an
5432:
4416:
5987:
6885:
the illumination is split up into two beams that are given different polarizations, are phase shifted differently, and are shifted transversely with slightly different amounts. After the specimen, the two parts are made to interfere, giving an image of the derivative of the optical path length in the
6481:
independent of polarization. For other propagation directions the light will split into two linearly polarized beams. For light traveling perpendicularly to the optical axis the beams will have the same direction. This can be used to change the polarization direction of linearly polarized light or to
6822:
as most cellular structures do not attenuate appreciable quantities of light. Nevertheless, the variation in the materials that constitute these structures also corresponds to a variation in the refractive index. The following techniques convert such variation into measurable amplitude differences:
4534:
3420:
When light enters 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
2609:
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 the dielectric loss is also negligible, resulting in almost no absorption. However, at higher frequencies (such as visible
1391:
of all such contributions in 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
1403:
If the electrons emit a light wave which is 90° out of phase with the light wave shaking them, it will cause the total light wave to travel slower. This is the normal refraction of transparent materials like glass or water, and corresponds to a refractive index which is real and greater than
4804:
604:
was presumably the person who first used, and invented, the name "index of refraction", in 1807. At 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.
2037:
1171:", 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.
5460:. However, there does not exist an overall linear relationship between the refractive index and the density for all silicate and borosilicate glasses. A relatively high refractive index and low density can be obtained with glasses containing light metal oxides such as
2950:
6675:
to the surface. The second prism should have an index of refraction higher than that of the liquid, so that light only enters the prism at angles smaller than the critical angle for total reflection. This angle can then be measured either by looking through a
5760:
5243:
4698:{\displaystyle {\begin{aligned}n&={\sqrt {\frac {|{\underline {\varepsilon }}_{\mathrm {r} }|+\varepsilon _{\mathrm {r} }}{2}}},\\\kappa &={\sqrt {\frac {|{\underline {\varepsilon }}_{\mathrm {r} }|-\varepsilon _{\mathrm {r} }}{2}}}.\end{aligned}}}
1407:
If the electrons emit a light wave which is 270° out of phase with the light wave shaking them, it will cause the wave to travel faster. This is called "anomalous refraction", and is observed close to absorption lines (typically in infrared spectra), with
6670:
in the late 19th century. The same principles are still used today. In this instrument, a thin layer of the liquid to be measured is placed between two prisms. Light is shone through the liquid at incidence angles all the way up to 90°, i.e., light rays
5952:{\displaystyle {\begin{aligned}v_{\mathrm {g} }&=\mathrm {c} \!\left(n-\lambda _{0}{\frac {\mathrm {d} n}{\mathrm {d} \lambda _{0}}}\right)^{-1}\!,\\n_{\mathrm {g} }&=n-\lambda _{0}{\frac {\mathrm {d} n}{\mathrm {d} \lambda _{0}}},\end{aligned}}}
4292:
1379:.) As the electromagnetic fields oscillate in the wave, 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
4423:
1681:
747:
5672:
3604:
6614:
elements in the design of an optical system can greatly simplify the system, reducing the number of elements by as much as a third while maintaining overall performance. The crystalline lens of the human eye is an example of a
5764:
When the refractive index of a medium is known as a function of the vacuum wavelength (instead of the wavelength in the medium), the corresponding expressions for the group velocity and index are (for all values of dispersion)
3846:
1964:
334:), 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.
6890:. One of the beams is let through the sample before they are combined to interfere and give a direct image of the phase shifts. If the optical path length variations are more than a wavelength the image will contain fringes.
6364:
So far, we have assumed that refraction is given by linear equations involving a spatially constant, scalar refractive index. These assumptions can break down in different ways, to be described in the following subsections.
295:
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
6157:{\displaystyle {\begin{aligned}V&={\frac {\mathrm {c} }{n}}+{\frac {v\left(1-{\frac {1}{n^{2}}}\right)}{1+{\frac {v}{cn}}}}\\&\approx {\frac {\mathrm {c} }{n}}+v\left(1-{\frac {1}{n^{2}}}\right)\,.\end{aligned}}}
8170:
Lentes, Frank-Thomas; Clement, Marc K. Th.; Neuroth, Norbert; Hoffmann, Hans-Jürgen; Hayden, Yuiko T.; Hayden, Joseph S.; Kolberg, Uwe; Wolff, Silke (1998). "Optical
Properties". In Bach, Hans; Neuroth, Norbert (eds.).
3732:
4177:
5579:
2854:
4710:
6338:
8205:
3519:
3416:
8248:
5681:
5509:
is proportional to the density of the gas as long as the chemical composition does not change. This means that it is also proportional to the pressure and inversely proportional to the temperature for
2452:
844:
1699:
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
1446:
If the electrons emit a light wave which is 180° out of phase with the light wave shaking them, it will destructively interfere with the original light to reduce the total light intensity. This is
2353:{\displaystyle {\begin{aligned}\mathbf {E} (x,t)&=\operatorname {Re} \!\left\\&=\operatorname {Re} \!\left\\&=e^{-2\pi \kappa x/\lambda _{0}}\operatorname {Re} \!\left.\end{aligned}}}
5992:
5773:
5248:
4832:
4548:
4428:
2955:
2042:
1140:, 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
4109:
7595:
410:
4008:
1849:
500:
2943:
548:
3105:{\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}}}
5224:
1898:
4117:
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.
1577:
5180:
1183:, 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
668:
5609:
3537:
2594:
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
5427:{\displaystyle {\begin{aligned}R_{0}&=\left|{\frac {n_{1}-n_{2}}{n_{1}+n_{2}}}\right|^{2}\\&=\left|{\frac {Z_{2}-Z_{1}}{Z_{2}+Z_{1}}}\right|^{2}\,.\end{aligned}}}
3775:
1903:
6598:
If the refractive index of a medium is not constant but varies gradually with the position, the material is known as a gradient-index (GRIN) medium and is described by
1392:
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
8657:
1788:
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.
9024:
4411:{\displaystyle {\underline {\varepsilon }}_{\mathrm {r} }=\varepsilon _{\mathrm {r} }+i{\tilde {\varepsilon }}_{\mathrm {r} }={\underline {n}}^{2}=(n+i\kappa )^{2},}
8763:
609:, 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).
3634:
3525:. This occurs only when going to a less optically dense material, i.e., one with lower refractive index. To get total internal reflection the angles of incidence
4128:
5528:
2790:
1469:
For most materials at visible-light frequencies, the phase is somewhere between 90° and 180°, corresponding to a combination of both refraction and absorption.
1191:. 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 a refractive index
196:
3198:
1555:, 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
6842:
of the refractive index along the ray path. The phase cannot be measured directly at optical or higher frequencies, and therefore needs to be converted into
6261:
4529:{\displaystyle {\begin{aligned}\varepsilon _{\mathrm {r} }&=n^{2}-\kappa ^{2}\,,\\{\tilde {\varepsilon }}_{\mathrm {r} }&=2n\kappa \,,\end{aligned}}}
773:
that can be determined for a material by fitting the equation to measured refractive indices at known wavelengths. The coefficients are usually quoted for
6528:(a 3 by 3 matrix). In this case the propagation of light cannot simply be described by refractive indices except for polarizations along principal axes.
2755:
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
1148:
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
5499:
are examples of liquids that are more refractive, but less dense, than water, contrary to the general correlation between density and refractive index.
7599:
6995:
is the instrument used to measure the refractive index. For a solution of sugar, the refractive index can be used to determine the sugar content (see
1543:. As the refractive index varies with wavelength, so will the refraction angle as light goes from one material to another. Dispersion also causes the
7442:
6505:
can also often be made birefringent by introducing a preferred direction through, e.g., an external force or electric field. This effect is called
5678:
is the wavelength in the medium. In this case the group index can thus be written in terms of the wavelength dependence of the refractive index as
1457:
If the electrons emit a light wave which is in phase with the light wave shaking them, it will amplify the light wave. This is rare, but occurs in
3458:
3346:
4799:{\displaystyle |{\underline {\varepsilon }}_{\mathrm {r} }|={\sqrt {\varepsilon _{\mathrm {r} }^{2}+{\tilde {\varepsilon }}_{\mathrm {r} }^{2}}}}
2375:
9190:
8042:
1128:
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
791:
6855:
6807:
7621:
8615:
7111:. Such signals move with the group velocity, not with the phase velocity, and it can be shown that the group velocity is in fact less than
2641:, applicable to amorphous materials. Forouhi and Bloomer then applied the Kramers–Kronig relation to derive the corresponding equation for
1509:
of colors. The blue color is more deviated (refracted) than the red color because the refractive index of blue is higher than that of red.
1399:
Depending on the relative phase of the original driving wave and the waves radiated by the charge motion, there are several possibilities:
9240:
7490:
1785:
apart, which can be considered negligible for typical refractometers, but can cause confusion and lead to errors if accuracy is critical.
8996:
8561:
7418:
7374:
7340:
7107:. This does not, however, violate the law of relativity, which requires that only signals carrying information do not travel faster than
1144:
as 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.
6513:. A change in birefringence alters the polarization and thereby the fraction of light that is transmitted through the second polarizer.
4058:
2457:
259:
The refractive index may vary with wavelength. This causes white light to split into constituent colors when refracted. This is called
6472:. Light propagating in the direction of the optical axis will not be affected by the birefringence since the refractive index will be
6619:
lens with a refractive index varying from about 1.406 in the inner core to approximately 1.386 at the less dense cortex. Some common
1758:. Measurement accuracy of such typical commercial devices is in the order of 0.0002. Refractometers usually measure refractive index
8810:
8587:
358:
8872:"Ueber den Einfluss der atomistischen Zusammensetzung C, H und O-haltiger flüssiger Verbindungen auf die Fortpflanzung des Lichtes"
8007:
17:
3915:
1809:
1481:
Light of different colors has slightly different refractive indices in water and therefore shows up at different positions in the
467:
8421:
6566:. If the index varies linearly with the field (a nontrivial linear coefficient is only possible in materials that do not possess
8448:
8074:
2370:. Since intensity is proportional to the square of the electric field, intensity will depend on the depth into the material as
1751:
spectral lines are singlets and thus are suitable to perform a very precise measurements, such as spectral goniometric method.
1447:
276:
517:
323:. In this case, the speed of sound is used instead of that of light, and a reference medium other than vacuum must be chosen.
8753:
8724:
8697:
8536:
8387:
8188:
7977:
7786:
7642:
7240:
7207:
7179:
6421:
In the simplest form, uniaxial birefringence, there is only one special direction in the material. This axis is known as the
5228:
Thus refractive index in a non-magnetic media is the ratio of the vacuum wave impedance to the wave impedance of the medium.
620:
Young did not use a symbol for the index of refraction, in 1807. In the later years, others started using different symbols:
9158:
1567:
with wavelength. For visible light normal dispersion means that the refractive index is higher for blue light than for red.
1517:
The variation of refractive index with wavelength for various glasses. The shaded zone indicates the range of visible light.
9169:
8650:
8490:
8459:
3756:, and thus about 4% of the incident power is reflected. At other incidence angles the reflectivity will also depend on the
3617:
part. The reflection angle is equal to the incidence angle, and the amount of light that is reflected is determined by the
2603:
1797:
613:, who called it the "ratio of refraction", wrote it as a ratio with a fixed numerator, like "10000 to 7451.9" (for urine).
8787:
8479:
3421:
into a medium with lower refractive index, the light will instead be refracted away from the normal, towards the surface.
7044:
6881:
of the sample, so that high-spatial-frequency parts of the image can interfere with the low-frequency reference beam. In
1260:) allowing the radio wave to be refracted back toward earth, thus enabling long-distance radio communications. See also
8760:
6886:
direction of the difference in the transverse shift. In interferometry the illumination is split up into two beams by a
1869:
indicates the amount of attenuation when the electromagnetic wave propagates through the material. It is related to the
1297:
Recent research has also demonstrated the "existence" of materials with a negative refractive index, which can occur if
3772:) will be totally transmitted. Brewster's angle can be calculated from the two refractive indices of the interface as
1773:), which is actually a midpoint between two adjacent yellow spectral lines of sodium. Yellow spectral lines of helium (
1354:
1563:
with frequency. This is called "normal dispersion", in contrast to "anomalous dispersion", where the refractive index
238:
is the wavelength of that light in vacuum. This implies that vacuum has a refractive index of 1, and assumes that the
9437:
8276:
7818:
6958:
6932:
6171:
903:
7457:
6940:
1333:
5755:{\displaystyle n_{\mathrm {g} }={\frac {n}{1+{\frac {\lambda }{n}}{\frac {\mathrm {d} n}{\mathrm {d} \lambda }}}}.}
3168:
of the path light follows through a system, and the index of refraction of the medium through which it propagates,
9368:
8909:
Bor, Z.; Osvay, K.; Rácz, B.; Szabó, G. (1990). "Group refractive index measurement by
Michelson interferometer".
1706:
Manufacturers of optical glass in general define principal index of refraction at yellow spectral line of helium (
1439:, as discussed above). If the response is sufficiently strong and out-of-phase, the result is a negative value of
1384:
9075:
7009:
6662:. They typically measure some angle of refraction or the critical angle for total internal reflection. The first
5126:
4202:
3205:
2787:
with the alternative convention mentioned above). Far above the atomic resonance frequency delta can be given by
1256:), is less than unity, electromagnetic waves propagating through the plasma are bent "away from the normal" (see
141:
and angle of refraction, respectively, of a ray crossing the interface between two media with refractive indices
7298:
Hauksbee, Francis (1710). "A Description of the
Apparatus for Making Experiments on the Refractions of Fluids".
7014:
6987:. It can also be used as a useful tool to differentiate between different types of gemstone, due to the unique
6936:
6742:
3621:
of the surface. The reflectivity can be calculated from the refractive index and the incidence angle with the
2030:
being the vacuum wavelength; this can be inserted into the plane wave expression for a wave travelling in the
7039:
6398:
Birefringent materials can give rise to colors when placed between crossed polarizers. This is the basis for
1754:
In practical applications, measurements of refractive index are performed on various refractometers, such as
1149:
1125:
355:) is given by the ratio of speed of light in medium 1 to that in medium 2. This can be expressed as follows:
6602:. Light traveling through such a medium can be bent or focused, and this effect can be exploited to produce
5980:, when light is transmitted through a moving medium, its speed relative to an observer traveling with speed
7814:
7054:
7049:
6894:
6762:
3884:
2886:
multiplied by the atomic density, but more accurate calculation of the refractive index requires replacing
2626:
1322:
1277:
9215:
6897:
techniques to determine 2D or 3D spatial distribution of refractive index of samples in the X-ray regime.
5185:
1876:
1740:. The spectral data provided by glass manufacturers is also often more precise for these two wavelengths.
416:, then the refractive index of medium 2 is considered with respect to vacuum. It is simply represented as
9447:
6190:
6182:
3314:
138:
6509:, and can be used to reveal stresses in structures. The birefringent material is placed between crossed
2882:
is the electron density. One may assume the electron density is simply the number of electrons per atom
9359:
5145:
4051:
of the medium filling the space between the sample and the lens and the half collection angle of light
1570:
For optics in the visual range, the amount of dispersion of a lens material is often quantified by the
869:
645:
8600:
8069:
8002:
6851:
4807:
4217:
and electronics. Most naturally occurring materials are non-magnetic at optical frequencies, that is
3522:
3439:
3430:
3217:
2866:
2642:
2630:
1036:
164:
9342:
9186:
8306:
8032:
6784:, a different type of refractometer is used to measure the index of refraction and birefringence of
202:
of the radiation are reduced with respect to their vacuum values: the speed of light in a medium is
9409:
7232:
6921:
6554:. If the index varies quadratically with the field (linearly with the intensity), it is called the
1465:. It corresponds to an imaginary index of refraction, with the opposite sign to that of absorption.
601:
590:
304:
7361:[Determination of the Refraction and Color Scattering Power of Different Types of Glass].
7284:
7263:
6975:. It determines the focusing power of lenses, the dispersive power of prisms, the reflectivity of
5240:
between two media can thus be expressed both by the wave impedances and the refractive indices as
1359:
At the atomic scale, an electromagnetic wave's phase velocity is slowed in a material because the
9322:
9112:
Ciddor, P.E. (1996). "Refractive index of air: New equations for the visible and near infrared".
8689:
7656:
7034:
6976:
6925:
6819:
6770:
6422:
2897:
1973:
corresponds to absorption can be seen by inserting this refractive index into the expression for
1388:
1376:
1368:
1211:(exceptions close to some resonance frequencies). As an example, water has a refractive index of
8623:
8871:
8832:
8528:
8146:
7483:
6827:
6797:
6550:) may cause a medium's refractive index to vary as the light passes through it, giving rise to
4214:
3909:
3154:
1168:
8992:
8553:
7778:
7703:"Intrinsically core-shell plasmonic dielectric nanostructures with ultrahigh refractive index"
7398:
7358:
7334:
6425:
of the material. Light with linear polarization perpendicular to this axis will experience an
3435:
7354:
7024:
6847:
6624:
6599:
6563:
5113:
4189:
3213:
2611:
1345:
are used to study rocks. The method is based on the distinct refractive indices of different
1302:
9317:
7857:(1968). "The electrodynamics of substances with simultaneously negative values of ε and μ".
7770:
7224:
1676:{\displaystyle V={\frac {n_{\mathrm {yellow} }-1}{n_{\mathrm {blue} }-n_{\mathrm {red} }}}.}
9274:
9236:
9121:
9084:
9033:
8957:
8918:
8523:
8369:
8256:
8213:
7931:
7868:
7714:
7569:
7528:
7484:"The Index of Refraction of Some Soda-Lime-Silica Glasses as a Function of the Composition"
6451:. The birefringence of the material is the difference between these indices of refraction,
6407:
3757:
3614:
2367:
1552:
1287:
1180:
662:
272:
63:
8945:
4824:
The wave impedance of a plane electromagnetic wave in a non-conductive medium is given by
2651:. The same formalism was applied to crystalline materials by Forouhi and Bloomer in 1988.
1683:
For a more accurate description of the wavelength dependence of the refractive index, the
742:{\displaystyle n(\lambda )=A+{\frac {B}{\lambda ^{2}}}+{\frac {C}{\lambda ^{4}}}+\cdots ,}
8:
9442:
9312:
8802:
8583:
8406:
7997:
7558:"Index of refraction of sapphire between 24 and 1060°C for wavelengths of 633 and 799 nm"
7280:
Opticks: Or, A Treatise of the
Reflections, Refractions, Inflections and Colours of Light
7257:
7225:
6843:
6835:
6672:
5667:{\displaystyle v_{\mathrm {g} }=v-\lambda {\frac {\mathrm {d} v}{\mathrm {d} \lambda }},}
5603:
3761:
3161:
3150:
2752:
1522:
1498:
1462:
1310:
1196:
260:
172:
9278:
9125:
9088:
9037:
8961:
8922:
8260:
8217:
8096:
7935:
7872:
7718:
7573:
7532:
7278:
9292:
9051:
8294:
8282:
8229:
7947:
7884:
7743:
7702:
7688:
7648:
7315:
6972:
6874:
6734:
6663:
6567:
6246:
6186:
5450:
4031:
4023:
3769:
3599:{\displaystyle \theta _{\mathrm {c} }=\arcsin \!\left({\frac {n_{2}}{n_{1}}}\right)\!.}
2891:
2610:
light), dielectric loss may increase absorption significantly, reducing the material's
1755:
1684:
1338:
1282:
181:
9327:
8445:
8410:
8064:
7972:. Feynman Lectures on Physics. Vol. 1 (The New Millenium ed.). Basic Books.
7083:
being less than unity is that it implies that the phase velocity inside the material,
3171:
1806:. This can be conveniently taken into account by defining a complex refractive index,
1305:
have simultaneous negative values. This can be achieved with periodically constructed
9397:
9352:
9296:
9137:
8973:
8930:
8891:
8852:
8749:
8720:
8693:
8532:
8383:
8286:
8272:
8233:
8184:
7973:
7888:
7782:
7771:
7748:
7730:
7638:
7319:
7236:
7203:
7175:
6866:
6766:
6394:
6388:
5977:
4206:
3622:
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2478:
1261:
778:
168:
8212:. SPIE OPTO, 2014. Vol. 8992. San Francisco, California: SPIE. pp. 56–65.
7880:
7652:
6802:
9353:
The
Feynman Lectures on Physics Vol. II Ch. 32: Refractive Index of Dense Materials
9282:
9129:
9092:
9041:
8965:
8926:
8883:
8844:
8779:
8375:
8264:
8221:
8176:
7939:
7922:
7917:
7876:
7738:
7722:
7630:
7629:. IEEE Nuclear Science Symposium Conference Record. Vol. 2. pp. 816–818.
7577:
7536:
7410:
7359:"Bestimmung des Brechungs und Farbenzerstreuungs Vermogens verschiedener Glasarten"
7307:
6984:
6551:
6537:
3864:
3841:{\displaystyle \theta _{\mathsf {B}}=\arctan \left({\frac {n_{2}}{n_{1}}}\right)~.}
3626:
2691:
from such measured quantities will involve developing a theoretical expression for
1959:{\displaystyle \alpha _{\text{abs}}(\omega )={\frac {2\omega \kappa (\omega )}{c}}}
1451:
1257:
1253:
1200:
610:
563:
284:
9155:
7951:
7674:
5456:
In general, it is assumed that the refractive index of a glass increases with its
3241:
of light at the interface between two media of different refractive indices, with
1687:
can be used. It is an empirical formula that works well in describing dispersion.
1420:
less than 1, which causes the refractive index to be also less than unity and the
9421:
9346:
9173:
9166:
9162:
9071:"An evaluation of the expression of the atmospheric refractivity for GPS signals"
8767:
8714:
8494:
8487:
8483:
8463:
8456:
8452:
8344:
8320:
7859:
7854:
7436:
7059:
7029:
6774:
6738:
6506:
6399:
5606:
is small, the group velocity can be linked to the phase velocity by the relation
5471:
1432:
1047:
9336:
Refractive index database featuring online plotting and parameterisation of data
8206:"Measuring the Refractive Index with Precision Goniometers: A Comparative Study"
7675:"Polycarbodiimide having high index of refraction and production method thereof"
7634:
9385:
9373:
8745:
8681:
8622:. Department of Physics and Astronomy. Georgia State University. Archived from
8476:
7541:
7516:
7394:
6878:
6859:
6571:
6543:
6517:
6251:
6178:
5599:
5591:
5477:
5446:
4819:
4210:
4044:
3340:
3318:
3256:
2537:(light travels forever without loss). In special situations, especially in the
1974:
1858:
1532:
1494:
1425:
1421:
1372:
1360:
1314:
1184:
1089:
955:
614:
559:
458:
440:
280:
264:
86:
59:
8379:
8180:
7903:
7414:
6516:
In the more general case of trirefringent materials described by the field of
3291:
When light moves from one medium to another, it changes direction, i.e. it is
1248:
An example of a plasma with an index of refraction less than unity is Earth's
9431:
8977:
8895:
8887:
8856:
8848:
8247:
Rupp, Fabian; Jedamzik, Ralf; Bartelmess, Lothar; Petzold, Uwe (2021-09-12).
7734:
7432:
6992:
6980:
6887:
6831:
6811:
6681:
6659:
6645:
6641:
6607:
6603:
6559:
6411:
6374:
5510:
5461:
4114:
3876:
3860:
3201:
1966:
These values depend upon the frequency of the light used in the measurement.
1700:
1548:
1380:
1306:
1121:
1057:
551:
7943:
6650:
6238:; the multiplication factors are used because the refractive index for air,
3727:{\displaystyle R_{0}=\left|{\frac {n_{1}-n_{2}}{n_{1}+n_{2}}}\right|^{2}\!.}
9141:
9046:
9019:
8249:"The modern way of refractive index measurement of optical glass at SCHOTT"
8037:
7752:
7726:
7581:
7311:
7019:
6174:
issue with two different values having different physical interpretations.
5483:
4172:{\displaystyle n={\sqrt {\varepsilon _{\mathrm {r} }\mu _{\mathrm {r} }}},}
3872:
3618:
2674:
1544:
1440:
1417:
1342:
1298:
1237:
1025:
606:
586:
160:
35:
7843:. The Advisory Group for Aerospace Research and Development. pp. 1–7.
7806:
7701:
Yue, Zengji; Cai, Boyuan; Wang, Lan; Wang, Xiaolin; Gu, Min (2016-03-01).
7200:
Soft X-rays and extreme ultraviolet radiation: principles and applications
5574:{\displaystyle n_{\mathrm {g} }={\frac {\mathrm {c} }{v_{\mathrm {g} }}},}
2849:{\displaystyle \delta ={\frac {r_{0}\lambda ^{2}n_{\mathrm {e} }}{2\pi }}}
1513:
73:
9133:
9097:
9070:
8969:
7677:. US Patent Office. US patent 2004/0158021 A1 – via Google Patents.
6850:
with a reference beam. In the visual spectrum this is done using
Zernike
6746:
6688:
of the liquid can then be calculated from the maximum transmission angle
6555:
6255:
3209:
3146:
2538:
1986:
1803:
1723:
1571:
1188:
1068:
770:
575:
331:
292:
288:
9330:
Free database of refractive index and absorption coefficient information
1383:, as the charges may move out of phase with the force driving them (see
617:
wrote it as a ratio with a fixed denominator, like 1.3358 to 1 (water).
8268:
8225:
7596:"Forensic Science Communications, Glass Refractive Index Determination"
6988:
6971:
The refractive index is an important property of the components of any
6870:
6834:
of the light wave exiting the sample. The phase is proportional to the
6750:
6667:
6510:
6415:
6353:
6333:{\displaystyle A={\frac {M}{\rho }}\cdot {\frac {n^{2}-1}{n^{2}+2}}\ ,}
4047:. The numerical aperture in turn is determined by the refractive index
4027:
3855:
3292:
3238:
3229:
1978:
1413:
1393:
1291:
1249:
1167:
and has a refractive index of about 4. A type of new materials termed "
1145:
1137:
1109:
782:
312:
199:
82:
81:
The refractive index determines how much the path of light is bent, or
39:
9380:
9287:
9262:
6865:
Zernike phase-contrast microscopy introduces a phase shift to the low
6586:
A gradient-index lens with a parabolic variation of refractive index (
4289:(the latter called the "extinction coefficient"), follow the relation
3287:; that is, the ray in the higher-index medium is closer to the normal.
2662:, are typically measured from quantities that depend on them, such as
661:
Refractive index also varies with wavelength of the light as given by
9055:
8518:
6882:
6826:
To measure the spatial variation of the refractive index in a sample
6785:
6730:
6677:
6494:
6483:
6359:
5492:
3905:
1528:
1318:
1207:. In the X-ray regime the refractive indices are lower than but very
1160:
998:
239:
8121:
7557:
7363:
Denkschriften der Königlichen
Akademie der Wissenschaften zu München
6910:
6725:
A handheld refractometer used to measure the sugar content of fruits
6482:
convert between linear, circular, and elliptical polarizations with
1477:
159:. The refractive indices also determine the amount of light that is
8514:
7841:
High
Frequency Radio Communications with Emphasis on Polar Problems
6839:
6781:
5521:
Sometimes, a "group velocity refractive index", usually called the
1802:
When light passes through a medium, some part of it will always be
1443:
and imaginary index of refraction, as observed in metals or plasma.
1364:
1156:
1079:
940:
571:
346:
of an optical medium 2 with respect to another reference medium 1 (
30:
9392:
7259:
A course of lectures on natural philosophy and the mechanical arts
6258:
of a substance and can be calculated from the refractive index as
3141:
2481:(the distance after which the intensity is reduced by a factor of
1694:
1527:
The refractive index of materials varies with the wavelength (and
1501:
causes different colors to refract at different angles, splitting
788:
Usually, it is sufficient to use a two-term form of the equation:
9349:
Thin film and bulk index of refraction and photonics calculations
8041:. Department of Physics and Astronomy, Georgia State University.
7906:. US Patent Office. US Patent 7629941 – via Google Patents.
6594:). The lens focuses light in the same way as a conventional lens.
6498:
6490:
6384:
6345:
5496:
5457:
3200:
This is an important concept in optics because it determines the
1536:
1506:
1482:
1363:
creates a disturbance in the charges of each atom (primarily the
1346:
1265:
1141:
1129:
1099:
988:
654:
268:
8833:"Ueber die Brechungsexponenten flüssiger homologer Verbindungen"
6818:
Unstained biological structures appear mostly transparent under
6721:
2625:, parts of the complex refractive index are related through the
1489:
9333:
9211:
9020:"The refraction and dispersion of air for the visible spectrum"
6658:
The refractive index of liquids or solids can be measured with
6620:
6525:
5476:, while the opposite trend is observed with glasses containing
4213:; while the relative permittivity and permeability are used in
1133:
970:
925:
887:
413:
163:
when reaching the interface, as well as the critical angle for
47:
5103:
are the absolute permeability and permittivity of the medium,
8246:
6838:
the light ray has traversed, and thus gives a measure of the
6758:
6547:
6502:
6242:
deviates from unity by at most a few parts per ten thousand.
5445:
The relation between the refractive index and the density of
5441:
4244:. In this particular case, the complex relative permittivity
3234:
2748:
2542:
1540:
1502:
1458:
1409:
1387:). The light wave traveling in the medium is the macroscopic
1321:
and other new phenomena to be actively developed by means of
1290:
array arranged to produce a negative index of refraction for
1204:
1008:
978:
650:
320:
308:
67:
8251:. In Völkel, Reinhard; Geyl, Roland; Otaduy, Deitze (eds.).
8169:
7904:"Electromagnetic compression apparatus, methods and systems"
6582:
3867:
is determined by the shape and refractive index of the lens.
3514:{\displaystyle {\frac {n_{1}}{n_{2}}}\sin \theta _{1}>1,}
3411:{\displaystyle n_{1}\sin \theta _{1}=n_{2}\sin \theta _{2}.}
1691:
are often quoted instead of the refractive index in tables.
9313:
NIST calculator for determining the refractive index of air
8784:
Statistical
Calculation and Development of Glass Properties
7963:
7961:
7619:
6996:
6754:
854:
are determined specifically for this form of the equation.
555:
550:
The phase velocity is the speed at which the crests or the
327:
316:
8716:
Photonics, Volume 2: Nanophotonic
Structures and Materials
8411:"Solid State Physics Part II Optical Properties of Solids"
8374:. Schott Series on Glass and Glass Ceramics. p. 267.
8367:
8026:
8024:
6830:
methods are used. These methods measure the variations in
6684:
placed in the focal plane of a lens. The refractive index
6379:
6177:
The refractive index of a substance can be related to its
2447:{\displaystyle I(x)=I_{0}e^{-4\pi \kappa x/\lambda _{0}}.}
9025:
Philosophical Transactions of the Royal Society of London
8809:. National Institute of Standards and Technology (NIST).
8175:. Schott Series on Glass and Glass Ceramics. p. 30.
7515:
Sultanova, N.; Kasarova, S.; Nikolov, I. (October 2009).
7300:
Philosophical Transactions of the Royal Society of London
5971:
4125:
The refractive index of electromagnetic radiation equals
4120:
3521:
the light cannot be transmitted and will instead undergo
1710:) and alternatively at a green spectral line of mercury (
1015:
910:
899:
567:
8204:
Krey, Stefan; Off, Dennis; Ruprecht, Aiko (2014-03-08).
7958:
7902:
Pendry, J. B.; Schurig, D.; Smith, D. R. (Dec 8, 2009).
7514:
6166:
The momentum of photons in a medium of refractive index
839:{\displaystyle n(\lambda )=A+{\frac {B}{\lambda ^{2}}},}
303:
The concept of refractive index applies across the full
8401:
8399:
8021:
7283:. William Innys at the West-End of St. Paul's. p.
6410:
and propagation direction of the light. This is called
6406:
In some materials, the refractive index depends on the
3768:-polarized light (light with the electric field in the
3216:, light rays can be characterized as those curves that
1412:
in ordinary materials, and with radio waves in Earth's
256:) of the wave is not affected by the refractive index.
198:, can be seen as the factor by which the speed and the
9189:. Humboldt State University, Richard A. Paselk. 1998.
6623:
are caused by a spatially varying refractive index of
2523:
are dependent on the frequency. In most circumstances
9357:
9339:
9069:
Aparicio, Josep M.; Laroche, Stéphane (2 June 2011).
8210:
Proc. SPIE 8992, Photonic Instrumentation Engineering
6438:
while light polarized in parallel will experience an
6264:
5990:
5771:
5684:
5612:
5531:
5246:
5188:
5148:
4830:
4713:
4546:
4426:
4295:
4131:
4061:
3918:
3778:
3637:
3540:
3461:
3349:
2953:
2900:
2793:
2378:
2040:
1985:-direction. This can be done by relating the complex
1906:
1879:
1812:
1580:
1159:
light refractive indices can be considerably higher.
794:
671:
520:
470:
361:
300:
must specify the wavelength used in the measurement.
184:
8586:. Newton BBS / Argonne National Laboratory. US DOE.
8396:
7222:
6387:
crystal laid upon a paper with some letters showing
1539:
to divide white light into its constituent spectral
439:
of an optical medium is defined as the ratio of the
7768:
2715:. By fitting the theoretical model to the measured
1252:. Since the refractive index of the ionosphere (a
7991:
7989:
7901:
7764:
7762:
7489:. National Institute of Standards and Technology.
7367:Journal of the Royal Academy of Sciences in Munich
6360:Nonscalar, nonlinear, or nonhomogeneous refraction
6332:
6156:
5951:
5754:
5666:
5573:
5426:
5218:
5174:
5132:In non-magnetic media (that is, in materials with
5076:
4798:
4697:
4528:
4410:
4171:
4104:{\displaystyle A_{\mathrm {Num} }=n\sin \theta ~.}
4103:
4002:
3840:
3726:
3598:
3513:
3410:
3295:. If it moves from a medium with refractive index
3192:
3153:through the thin soap film in a phenomenon called
3104:
2937:
2848:
2629:. In 1986, A.R. Forouhi and I. Bloomer deduced an
2552:, corresponding to an amplification of the light.
2446:
2352:
1958:
1892:
1843:
1675:
838:
741:
542:
494:
404:
190:
8944:Milonni, Peter W.; Boyd, Robert W. (2010-12-31).
8908:
7691:in the Photonics Handbook, accessed on 2014-09-10
6546:of high intensity light (such as the output of a
5868:
5800:
3908:in air is given by the simplified version of the
3760:of the incoming light. At a certain angle called
3720:
3613:Apart from the transmitted light there is also a
3592:
3559:
2654:The refractive index and extinction coefficient,
2366:gives an exponential decay, as expected from the
2289:
2149:
2075:
1531:) of light. This is called dispersion and causes
212:, and similarly the wavelength in that medium is
85:, when entering a material. This is described by
9429:
8801:Stone, Jack A.; Zimmerman, Jay H. (2011-12-28).
8780:"Calculation of the Refractive Index of Glasses"
7920:(2007). "Optical negative-index metamaterials".
7399:"On the structure of doubly refracting crystals"
3131:
9068:
8253:Optical Fabrication, Testing, and Metrology VII
8203:
7986:
7759:
6630:
6250:, on the other hand, is a measure of the total
1695:Principal refractive index wavelength ambiguity
1174:
562:, the speed at which the pulse of light or the
8800:
8680:
8527:(7th expanded ed.). CUP Archive. p.
7700:
7623:Development of Silica Aerogel with Any Density
7353:
7197:
6791:
5598:, which is always defined with respect to the
1551:to be wavelength dependent. This is a type of
405:{\displaystyle n_{21}={\frac {v_{1}}{v_{2}}}.}
8599:Incorporates Public Domain material from the
8208:. In Soskind, Yakov G.; Olson, Craig (eds.).
8119:
7672:
7555:
7169:
6856:differential interference contrast microscopy
6808:differential interference contrast microscopy
4205:. The refractive index is used for optics in
3164:(OPL) is the product of the geometric length
1163:is transparent in the wavelength region from
665:. The most general form of this equation is
9167:Encyclopedia of Laser Physics and Technology
9017:
8488:Encyclopedia of Laser Physics and Technology
8457:Encyclopedia of Laser Physics and Technology
7847:
7379:
4003:{\displaystyle {\frac {1}{f}}=(n-1)\left\ ,}
3424:
1844:{\displaystyle {\underline {n}}=n+i\kappa .}
1271:
495:{\displaystyle n={\frac {\mathrm {c} }{v}}.}
8943:
8644:
8642:
8640:
8509:
8507:
8505:
8503:
8405:
8368:Bach, Hans; Neuroth, Norbert, eds. (1998).
7910:
7562:Journal of the Optical Society of America A
7517:"Dispersion Properties of Optical Polymers"
6939:. Unsourced material may be challenged and
1791:
657:have a very high refractive index of 2.417.
9260:
8946:"Momentum of Light in a Dielectric Medium"
8094:
7202:. Cambridge University Press. p. 60.
1857:is the refractive index and indicates the
1375:creates a disturbance proportional to the
1328:
1234:for X-ray radiation at a photon energy of
9286:
9187:"The Evolution of the Abbe Refractometer"
9096:
9045:
9028:. A, Mathematical and Physical Sciences.
8255:. Vol. 11873. SPIE. pp. 15–22.
7742:
7598:. FBI Laboratory Services. Archived from
7556:Tapping, J.; Reilly, M. L. (1 May 1986).
7540:
7481:
7347:
7336:Philosophical and mathematical dictionary
7193:
7191:
6959:Learn how and when to remove this message
6146:
5594:. This value should not be confused with
5416:
5212:
4518:
4473:
8648:
8637:
8513:
8500:
7853:
7455:
7431:
7425:
7393:
7297:
7165:
7163:
7161:
7159:
7157:
7155:
7153:
7151:
7103:, is larger than the velocity of light,
6801:
6729:This type of device is commonly used in
6720:
6649:
6581:
6393:
6378:
5440:
4017:
3854:
3434:
3233:
3212:of light as it propagates. According to
3140:
1512:
1488:
1476:
1332:
1281:
649:
585:
543:{\displaystyle n\propto {\frac {1}{v}}.}
72:
29:
8869:
8830:
8712:
8674:
8581:
7967:
7916:
7800:
7798:
7482:Faick, C. A.; Finn, A. N. (July 1931).
7387:
7291:
7149:
7147:
7145:
7143:
7141:
7139:
7137:
7135:
7133:
7131:
5984:in the same direction as the light is:
3534:must be larger than the critical angle
2742:
2707:in terms of a valid physical model for
1385:sinusoidally driven harmonic oscillator
578:has been common as a reference medium.
558:moves, which may be different from the
14:
9430:
9111:
8739:
8713:Andrews, David L. (24 February 2015).
8575:
8144:
7769:Als-Nielsen, J.; McMorrow, D. (2011).
7496:from the original on December 30, 2016
7332:
7276:
7216:
7188:
6718:is the refractive index of the prism.
6616:
6611:
5972:Velocity, momentum, and polarizability
4121:Relative permittivity and permeability
3879:is determined by its refractive index
3785:
3442:can be seen at the air-water boundary.
3136:
1981:electromagnetic wave traveling in the
1039:(acrylic, plexiglas, lucite, perspex)
8990:
8719:. John Wiley & Sons. p. 54.
8551:
8345:"Abbe Multi-Wavelength Refractometer"
8062:
7995:
7970:Mainly Mechanics, Radiation, and Heat
7804:
7673:Sadayori, Naoki; Hotta, Yuji (2004).
7326:
7270:
7255:
5488:as seen in the diagram at the right.
4420:and their components are related by:
1559:with increasing wavelength, and thus
8999:from the original on 10 January 2015
8321:"Abbe Refractometer| ATAGO CO., LTD"
8030:
7838:
7795:
7128:
7079:One consequence of the real part of
6937:adding citations to reliable sources
6904:
6666:sold commercially were developed by
6654:The principle of many refractometers
6635:
5219:{\displaystyle n={Z_{0} \over Z}\,.}
3280:is less than the angle of incidence
2604:Mathematical descriptions of opacity
1893:{\displaystyle \alpha _{\text{abs}}}
1798:Mathematical descriptions of opacity
1448:light absorption in opaque materials
7588:
7381:Exponent des Brechungsverhältnisses
7045:Optical properties of water and ice
6733:laboratories for identification of
4273:, and the complex refractive index
868:. For references, see the extended
279:materials can be described using a
24:
9212:"Refractometers and refractometry"
8582:Swenson, Jim (November 10, 2009).
6991:each individual stone displays. A
6979:, and the light-guiding nature of
6098:
6008:
5925:
5915:
5882:
5837:
5827:
5796:
5782:
5736:
5726:
5691:
5651:
5641:
5619:
5560:
5550:
5538:
5059:
5022:
5010:
4972:
4960:
4908:
4882:
4783:
4754:
4732:
4675:
4655:
4603:
4583:
4496:
4437:
4351:
4324:
4309:
4158:
4146:
4074:
4071:
4068:
3547:
2829:
1661:
1658:
1655:
1640:
1637:
1634:
1631:
1611:
1608:
1605:
1602:
1599:
1596:
480:
25:
9459:
9306:
9261:Fitzgerald, Richard (July 2000).
9018:Barrell, H.; Sears, J.E. (1939).
8590:from the original on May 28, 2010
7689:Common Infrared Optical Materials
6610:, and other devices. Introducing
5175:{\displaystyle Z={Z_{0} \over n}}
4813:
4014:is the focal length of the lens.
1152:can have values as high as 1.76.
639:
263:. This effect can be observed in
66:that gives the indication of the
9415:
9403:
9391:
9379:
9367:
8950:Advances in Optics and Photonics
8790:from the original on 2007-10-15.
8613:
8418:Course 6.732 Solid State Physics
7807:"X-Ray interactions with matter"
7773:Elements of Modern X-ray Physics
7620:Tabata, M.; et al. (2005).
7445:from the original on 2015-11-24.
7421:from the original on 2017-02-22.
7377:from the original on 2017-02-22.
7343:from the original on 2017-02-22.
6909:
6577:
6493:are naturally birefringent, but
6368:
4281:, with real and imaginary parts
4255:, with real and imaginary parts
3904:of its surfaces. The power of a
2637:as a function of photon energy,
2297:
2157:
2083:
2046:
1994:to the complex refractive index
1726:is defined for both and denoted
1317:) offers the possibility of the
566:of the wave moves. Historically
275:in lenses. Light propagation in
70:bending ability of that medium.
9263:"Phase-Sensitive X-Ray Imaging"
9254:
9243:from the original on 2011-09-10
9229:
9218:from the original on 2011-10-20
9204:
9193:from the original on 2011-06-12
9179:
9148:
9105:
9076:Journal of Geophysical Research
9062:
9011:
8984:
8937:
8902:
8863:
8824:
8813:from the original on 2014-01-11
8794:
8772:
8733:
8706:
8663:from the original on 2015-04-02
8607:
8564:from the original on 2015-06-28
8545:
8469:
8438:
8427:from the original on 2015-07-24
8371:The Properties of Optical Glass
8361:
8337:
8313:
8240:
8197:
8173:The Properties of Optical Glass
8163:
8138:
8113:
8088:
8077:from the original on 2015-03-19
8056:
8045:from the original on 2014-09-24
8010:from the original on 2015-06-29
7895:
7881:10.1070/PU2003v046n07ABEH001614
7832:
7821:from the original on 2011-08-27
7694:
7681:
7666:
7613:
7549:
7508:
7475:
7449:
7073:
7010:Calculation of glass properties
6900:
6531:
6196:
3608:
3259:is lower in the second medium (
2673:, or ellipsometric parameters,
2555:An alternative convention uses
1371:of the medium. (Similarly, the
1187:of light, which does not carry
858:Selected refractive indices at
8584:"Refractive Index of Minerals"
7249:
5516:
5095:is the vacuum wave impedance,
4775:
4739:
4715:
4662:
4638:
4590:
4566:
4488:
4396:
4380:
4343:
4226:is very close to 1, therefore
4055:according to Carlsson (2007):
3944:
3932:
3455:fulfilling Snell's law, i.e.,
3019:
3002:
2388:
2382:
2333:
2315:
2229:
2199:
2184:
2175:
2126:
2101:
2062:
2050:
1947:
1941:
1923:
1917:
1355:Ewald–Oseen extinction theorem
1150:high-refractive-index polymers
804:
798:
681:
675:
283:-valued refractive index. The
13:
1:
8807:Engineering metrology toolbox
7687:Tosi, Jeffrey L., article on
7223:Kinsler, Lawrence E. (2000).
7122:
7040:Laser Schlieren deflectometry
6763:inline process refractometers
6558:and causes phenomena such as
6201:In atmospheric applications,
5968:is the wavelength in vacuum.
3304:to one with refractive index
3223:
3132:Relations to other quantities
2873:is the X-ray wavelength, and
1765:, defined for sodium doublet
1472:
510:is inversely proportional to
412:If the reference medium 1 is
337:
8931:10.1016/0030-4018(90)90104-2
8870:Landolt, H. (January 1864).
8831:Landolt, H. (January 1862).
8803:"Index of refraction of air"
8742:Optical Properties of Solids
7968:Feynman, Richard P. (2011).
7815:Lawrence Berkeley Laboratory
7066:
7055:Prism-coupling refractometry
7050:Phase-contrast X-ray imaging
6895:phase-contrast X-ray imaging
6631:Refractive index measurement
4030:is mainly determined by the
1278:Negative index metamaterials
1175:Refractive index below unity
315:. It can also be applied to
7:
9328:Filmetrics' online database
8554:"Total Internal Reflection"
7811:The Center for X-Ray Optics
7635:10.1109/NSSMIC.2005.1596380
7458:"Refractive Index Database"
7002:
6888:partially reflective mirror
6792:Refractive index variations
6216:, often rescaled as either
6189:of its constituents by the
3273:), the angle of refraction
2938:{\displaystyle f=Z+f'+if''}
2731:using regression analysis,
2545:, it is also possible that
1861:, while the imaginary part
1136:, with a wavelength of 589
10:
9464:
9214:. Refractometer.pl. 2011.
8740:Wooten, Frederick (1972).
8151:Hoya Group Optics Division
8097:"Interactive Abbe Diagram"
7542:10.12693/APhysPolA.116.585
7015:Clausius–Mossotti relation
6795:
6639:
6535:
6372:
5436:
4817:
3428:
3227:
3120:typically of the order of
1795:
1520:
1424:of light greater than the
1352:
1275:
1199:, for absorbing media, in
870:List of refractive indices
646:List of refractive indices
643:
581:
9154:R. Paschotta, article on
8686:Electricity and Magnetism
8601:U.S. Department of Energy
8558:RP Photonics Encyclopedia
8475:R. Paschotta, article on
8444:R. Paschotta, article on
8380:10.1007/978-3-642-57769-7
8181:10.1007/978-3-642-57769-7
8070:RP Photonics Encyclopedia
8003:RP Photonics Encyclopedia
7415:10.1080/14786441508638398
7227:Fundamentals of Acoustics
6852:phase-contrast microscopy
6664:laboratory refractometers
3850:
3736:For common glass in air,
3523:total internal reflection
3440:Total internal reflection
3431:Total internal reflection
3425:Total internal reflection
3220:the optical path length.
3204:of the light and governs
2867:classical electron radius
1272:Negative refractive index
1108:
1098:
1088:
1078:
1067:
1056:
1046:
1035:
1024:
1014:
1007:
997:
987:
977:
969:
954:
939:
924:
909:
898:
886:
879:
876:
753:is the refractive index,
434:absolute refractive index
427:absolute refractive index
344:relative refractive index
165:total internal reflection
77:Refraction of a light ray
9438:Dimensionless quantities
9239:. The Gemology Project.
9176:, accessed on 2014-09-09
8888:10.1002/andp.18641991206
8849:10.1002/andp.18621931102
8684:; Bleaney, B.I. (1976).
8649:Carlsson, Kjell (2007).
8497:, accessed on 2014-09-08
8466:, accessed on 2014-09-08
7333:Hutton, Charles (1795).
6590:) with radial distance (
2627:Kramers–Kronig relations
1792:Complex refractive index
1426:speed of light in vacuum
1195:This can occur close to
904:0 °C and 1 atm
464:of light in the medium,
305:electromagnetic spectrum
18:Complex refractive index
8690:Oxford University Press
8349:Nova-Tech International
7944:10.1038/nphoton.2006.49
7521:Acta Physica Polonica A
7198:Attwood, David (1999).
7035:Index-matching material
6820:bright-field microscopy
6771:pharmaceutical industry
6191:Gladstone–Dale relation
6183:Lorentz–Lorenz equation
3339:can be calculated from
3330:, the refraction angle
2683:. The determination of
2530:(light is absorbed) or
1377:magnetic susceptibility
1369:electric susceptibility
1329:Microscopic explanation
846:where the coefficients
757:is the wavelength, and
9047:10.1098/rsta.1939.0004
8616:"Lens-makers' formula"
8031:Nave, Carl R. (2000).
7998:"Chromatic Dispersion"
7860:Soviet Physics Uspekhi
7727:10.1126/sciadv.1501536
7582:10.1364/JOSAA.3.000610
7438:On the Theory of Light
7403:Philosophical Magazine
7384:is index of refraction
7380:
7355:von Fraunhofer, Joseph
7312:10.1098/rstl.1710.0015
7277:Newton, Isaac (1730).
7262:. J. Johnson. p.
7256:Young, Thomas (1807).
7231:. John Wiley. p.
7170:Hecht, Eugene (2002).
6873:with a phase-shifting
6828:phase-contrast imaging
6815:
6798:Phase-contrast imaging
6726:
6655:
6595:
6570:), it is known as the
6403:
6391:
6334:
6158:
5953:
5756:
5668:
5575:
5453:
5428:
5220:
5176:
5078:
4800:
4699:
4530:
4412:
4173:
4105:
4004:
3868:
3842:
3728:
3600:
3515:
3443:
3412:
3288:
3194:
3158:
3155:thin-film interference
3149:are determined by the
3106:
2939:
2850:
2614:to these frequencies.
2458:absorption coefficient
2448:
2354:
1960:
1894:
1871:absorption coefficient
1867:extinction coefficient
1845:
1689:Sellmeier coefficients
1677:
1518:
1510:
1486:
1450:and corresponds to an
1416:. It corresponds to a
1367:) proportional to the
1350:
1294:
1169:topological insulators
840:
743:
658:
598:
544:
496:
406:
287:part then handles the
192:
178:The refractive index,
78:
43:
8993:"Refractivity of Air"
8911:Optics Communications
7809:. Optical constants.
7777:. Wiley-VCH. p.
6805:
6724:
6653:
6600:gradient index optics
6585:
6564:self-phase modulation
6397:
6382:
6335:
6159:
5954:
5757:
5669:
5576:
5444:
5429:
5221:
5177:
5127:relative permeability
5114:relative permittivity
5079:
4801:
4700:
4531:
4413:
4203:relative permeability
4190:relative permittivity
4174:
4106:
4018:Microscope resolution
4005:
3858:
3843:
3729:
3601:
3516:
3446:If there is no angle
3438:
3413:
3237:
3195:
3144:
3107:
2940:
2851:
2449:
2355:
1961:
1895:
1846:
1678:
1516:
1492:
1480:
1336:
1313:(i.e., a reversal of
1285:
1197:resonance frequencies
841:
744:
653:
636:gradually prevailed.
589:
545:
497:
407:
193:
76:
33:
9334:RefractiveIndex.INFO
9318:Dielectric materials
9134:10.1364/ao.35.001566
9098:10.1029/2010JD015214
8991:Young, A.T. (2011).
8970:10.1364/AOP.2.000519
8524:Principles of Optics
8147:"Optical Properties"
8122:"Optical Properties"
8063:Paschotta, Rüdiger.
7996:Paschotta, Rüdiger.
7462:refractiveindex.info
7433:Herschel, John F. W.
6933:improve this section
6893:There exist several
6680:, or with a digital
6262:
6187:molar refractivities
5988:
5769:
5682:
5610:
5529:
5451:borosilicate glasses
5244:
5186:
5146:
4828:
4711:
4544:
4424:
4293:
4129:
4059:
3916:
3776:
3635:
3538:
3459:
3347:
3172:
2951:
2898:
2791:
2743:X-ray and extreme UV
2668:, or transmittance,
2376:
2038:
1904:
1877:
1853:Here, the real part
1810:
1722:lines respectively.
1578:
1553:chromatic aberration
1288:split-ring resonator
1181:theory of relativity
792:
669:
518:
468:
359:
273:chromatic aberration
182:
64:dimensionless number
42:through a glass slab
9279:2000PhT....53g..23F
9126:1996ApOpt..35.1566C
9089:2011JGRD..11611104A
9038:1939RSPTA.238....1B
8962:2010AdOP....2..519M
8923:1990OptCo..78..109B
8261:2021SPIE11873E..08R
8218:2014SPIE.8992E..0DK
8120:Ohara Corporation.
8065:"Sellmeier formula"
7936:2007NaPho...1...41S
7873:1968SvPhU..10..509V
7839:Lied, Finn (1967).
7719:2016SciA....2E1536Y
7574:1986JOSAA...3..610T
7533:2009AcPPA.116..585S
7369:] (in German).
6836:optical path length
6765:are used in, e.g.,
6556:optical Kerr effect
6522:dielectric constant
5491:Many oils (such as
4793:
4764:
4215:Maxwell's equations
3910:Lensmaker's formula
3162:Optical path length
3151:optical path length
3137:Optical path length
2753:extreme ultraviolet
1523:Dispersion (optics)
1463:stimulated emission
1435:is still less than
1389:superposition (sum)
1311:negative refraction
873:
595:index of refraction
167:, their intensity (
9448:Optical quantities
9345:2013-09-07 at the
9172:2015-08-13 at the
9161:2015-07-03 at the
8876:Annalen der Physik
8837:Annalen der Physik
8766:2011-10-03 at the
8688:(Third ed.).
8493:2015-08-13 at the
8482:2015-06-28 at the
8462:2015-08-13 at the
8451:2015-03-22 at the
8407:Dresselhaus, M. S.
8269:10.1117/12.2597023
8226:10.1117/12.2041760
7174:. Addison-Wesley.
7025:Fermat's principle
6973:optical instrument
6869:components of the
6816:
6727:
6656:
6596:
6568:inversion symmetry
6497:materials such as
6404:
6392:
6330:
6247:Molar refractivity
6154:
6152:
5949:
5947:
5752:
5664:
5571:
5454:
5424:
5422:
5216:
5172:
5112:is the material's
5074:
5072:
4796:
4768:
4748:
4728:
4695:
4693:
4651:
4579:
4526:
4524:
4408:
4369:
4305:
4188:is the material's
4169:
4101:
4032:numerical aperture
4026:of a good optical
4000:
3885:radii of curvature
3869:
3838:
3770:plane of incidence
3724:
3596:
3511:
3444:
3408:
3289:
3214:Fermat's principle
3159:
3102:
3100:
2935:
2892:atomic form factor
2846:
2444:
2350:
2348:
2112:
1956:
1890:
1841:
1821:
1756:Abbe refractometer
1685:Sellmeier equation
1673:
1519:
1511:
1487:
1351:
1339:optical mineralogy
1295:
857:
836:
739:
659:
599:
570:at a standardized
540:
492:
425:and is called the
402:
319:phenomena such as
188:
139:angle of incidence
79:
44:
27:Property in optics
9410:Underwater diving
9288:10.1063/1.1292471
8755:978-0-12-763450-0
8744:. New York City:
8726:978-1-118-22551-6
8699:978-0-19-851141-0
8538:978-0-521-78449-8
8446:optical thickness
8389:978-3-642-63349-2
8190:978-3-642-63349-2
7979:978-0-465-02493-3
7805:Gullikson, Eric.
7788:978-0-470-97395-0
7644:978-0-7803-9221-2
7456:Malitson (1965).
7242:978-0-471-84789-2
7209:978-0-521-02997-1
7181:978-0-321-18878-6
6969:
6968:
6961:
6867:spatial frequency
6743:Handheld variants
6636:Homogeneous media
6442:refractive index
6429:refractive index
6389:double refraction
6326:
6322:
6279:
6170:is a complex and
6139:
6105:
6083:
6080:
6052:
6015:
5978:Fizeau experiment
5940:
5852:
5747:
5744:
5720:
5659:
5566:
5404:
5325:
5231:The reflectivity
5210:
5170:
5068:
5029:
5028:
4979:
4978:
4949:
4948:
4916:
4915:
4855:
4854:
4794:
4778:
4721:
4686:
4685:
4644:
4614:
4613:
4572:
4491:
4362:
4346:
4298:
4230:is approximately
4207:Fresnel equations
4164:
4097:
3996:
3987:
3967:
3927:
3834:
3826:
3708:
3623:Fresnel equations
3586:
3484:
3177:
3095:
3078:
3029:
3000:
2890:with the complex
2844:
2646:as a function of
2479:penetration depth
2362:Here we see that
2105:
1954:
1914:
1887:
1814:
1668:
1454:refractive index.
1262:Radio Propagation
1179:According to the
1118:
1117:
831:
779:vacuum wavelength
728:
708:
663:Cauchy's equation
535:
487:
397:
191:{\displaystyle n}
169:Fresnel equations
16:(Redirected from
9455:
9420:
9419:
9418:
9408:
9407:
9406:
9396:
9395:
9384:
9383:
9372:
9371:
9363:
9301:
9300:
9290:
9258:
9252:
9251:
9249:
9248:
9233:
9227:
9226:
9224:
9223:
9208:
9202:
9201:
9199:
9198:
9183:
9177:
9152:
9146:
9145:
9120:(9): 1566–1573.
9109:
9103:
9102:
9100:
9066:
9060:
9059:
9049:
9015:
9009:
9008:
9006:
9004:
8988:
8982:
8981:
8941:
8935:
8934:
8906:
8900:
8899:
8867:
8861:
8860:
8828:
8822:
8821:
8819:
8818:
8798:
8792:
8791:
8776:
8770:
8759:
8737:
8731:
8730:
8710:
8704:
8703:
8678:
8672:
8671:
8669:
8668:
8662:
8655:
8651:Light microscopy
8646:
8635:
8634:
8632:
8631:
8611:
8605:
8604:
8596:
8595:
8579:
8573:
8572:
8570:
8569:
8549:
8543:
8542:
8511:
8498:
8473:
8467:
8442:
8436:
8435:
8433:
8432:
8426:
8415:
8403:
8394:
8393:
8365:
8359:
8358:
8356:
8355:
8341:
8335:
8334:
8332:
8331:
8317:
8311:
8310:
8304:
8300:
8298:
8290:
8244:
8238:
8237:
8201:
8195:
8194:
8167:
8161:
8160:
8158:
8157:
8142:
8136:
8135:
8133:
8132:
8117:
8111:
8110:
8108:
8107:
8095:Schott Company.
8092:
8086:
8085:
8083:
8082:
8060:
8054:
8053:
8051:
8050:
8028:
8019:
8018:
8016:
8015:
7993:
7984:
7983:
7965:
7956:
7955:
7923:Nature Photonics
7914:
7908:
7907:
7899:
7893:
7892:
7851:
7845:
7844:
7836:
7830:
7829:
7827:
7826:
7802:
7793:
7792:
7776:
7766:
7757:
7756:
7746:
7707:Science Advances
7698:
7692:
7685:
7679:
7678:
7670:
7664:
7663:
7661:
7655:. Archived from
7628:
7617:
7611:
7610:
7608:
7607:
7592:
7586:
7585:
7553:
7547:
7546:
7544:
7512:
7506:
7505:
7503:
7501:
7495:
7488:
7479:
7473:
7472:
7470:
7468:
7453:
7447:
7446:
7429:
7423:
7422:
7391:
7385:
7383:
7378:
7351:
7345:
7344:
7330:
7324:
7323:
7306:(325–336): 207.
7295:
7289:
7288:
7274:
7268:
7267:
7253:
7247:
7246:
7230:
7220:
7214:
7213:
7195:
7186:
7185:
7167:
7116:
7114:
7110:
7106:
7102:
7100:
7099:
7098:
7094:
7091:
7090:
7082:
7077:
6985:aqueous solution
6964:
6957:
6953:
6950:
6944:
6913:
6905:
6884:
6717:
6708:
6691:
6687:
6618:
6613:
6593:
6589:
6552:nonlinear optics
6538:Nonlinear optics
6480:
6471:
6450:
6437:
6351:
6343:
6339:
6337:
6336:
6331:
6324:
6323:
6321:
6314:
6313:
6303:
6296:
6295:
6285:
6280:
6272:
6241:
6237:
6226:
6215:
6169:
6163:
6161:
6160:
6155:
6153:
6145:
6141:
6140:
6138:
6137:
6125:
6106:
6101:
6096:
6088:
6084:
6082:
6081:
6079:
6068:
6059:
6058:
6054:
6053:
6051:
6050:
6038:
6021:
6016:
6011:
6006:
5983:
5976:As shown in the
5967:
5958:
5956:
5955:
5950:
5948:
5941:
5939:
5938:
5937:
5928:
5922:
5918:
5912:
5910:
5909:
5887:
5886:
5885:
5867:
5866:
5858:
5854:
5853:
5851:
5850:
5849:
5840:
5834:
5830:
5824:
5822:
5821:
5799:
5787:
5786:
5785:
5761:
5759:
5758:
5753:
5748:
5746:
5745:
5743:
5739:
5733:
5729:
5723:
5721:
5713:
5701:
5696:
5695:
5694:
5677:
5673:
5671:
5670:
5665:
5660:
5658:
5654:
5648:
5644:
5638:
5624:
5623:
5622:
5597:
5589:
5580:
5578:
5577:
5572:
5567:
5565:
5564:
5563:
5553:
5548:
5543:
5542:
5541:
5508:
5486:
5480:
5474:
5468:
5433:
5431:
5430:
5425:
5423:
5415:
5414:
5409:
5405:
5403:
5402:
5401:
5389:
5388:
5378:
5377:
5376:
5364:
5363:
5353:
5340:
5336:
5335:
5330:
5326:
5324:
5323:
5322:
5310:
5309:
5299:
5298:
5297:
5285:
5284:
5274:
5260:
5259:
5239:
5225:
5223:
5222:
5217:
5211:
5206:
5205:
5196:
5181:
5179:
5178:
5173:
5171:
5166:
5165:
5156:
5141:
5124:
5111:
5102:
5098:
5094:
5083:
5081:
5080:
5075:
5073:
5069:
5064:
5063:
5062:
5052:
5050:
5049:
5034:
5030:
5027:
5026:
5025:
5015:
5014:
5013:
5003:
5002:
5000:
4999:
4984:
4980:
4977:
4976:
4975:
4965:
4964:
4963:
4953:
4952:
4950:
4947:
4946:
4945:
4935:
4934:
4933:
4923:
4922:
4917:
4914:
4913:
4912:
4911:
4901:
4900:
4899:
4888:
4887:
4886:
4885:
4875:
4874:
4873:
4862:
4861:
4856:
4847:
4846:
4805:
4803:
4802:
4797:
4795:
4792:
4787:
4786:
4780:
4779:
4771:
4763:
4758:
4757:
4747:
4742:
4737:
4736:
4735:
4729:
4718:
4704:
4702:
4701:
4696:
4694:
4687:
4681:
4680:
4679:
4678:
4665:
4660:
4659:
4658:
4652:
4641:
4635:
4634:
4615:
4609:
4608:
4607:
4606:
4593:
4588:
4587:
4586:
4580:
4569:
4563:
4562:
4535:
4533:
4532:
4527:
4525:
4501:
4500:
4499:
4493:
4492:
4484:
4472:
4471:
4459:
4458:
4442:
4441:
4440:
4417:
4415:
4414:
4409:
4404:
4403:
4376:
4375:
4370:
4356:
4355:
4354:
4348:
4347:
4339:
4329:
4328:
4327:
4314:
4313:
4312:
4306:
4288:
4284:
4280:
4279:
4272:
4263:
4254:
4250:
4243:
4242:
4241:
4229:
4225:
4200:
4187:
4178:
4176:
4175:
4170:
4165:
4163:
4162:
4161:
4151:
4150:
4149:
4139:
4113:For this reason
4110:
4108:
4107:
4102:
4095:
4079:
4078:
4077:
4054:
4050:
4042:
4013:
4009:
4007:
4006:
4001:
3994:
3993:
3989:
3988:
3986:
3985:
3973:
3968:
3966:
3965:
3953:
3928:
3920:
3903:
3894:
3882:
3865:magnifying glass
3847:
3845:
3844:
3839:
3832:
3831:
3827:
3825:
3824:
3815:
3814:
3805:
3790:
3789:
3788:
3762:Brewster's angle
3755:
3745:
3733:
3731:
3730:
3725:
3719:
3718:
3713:
3709:
3707:
3706:
3705:
3693:
3692:
3682:
3681:
3680:
3668:
3667:
3657:
3647:
3646:
3627:normal incidence
3605:
3603:
3602:
3597:
3591:
3587:
3585:
3584:
3575:
3574:
3565:
3552:
3551:
3550:
3533:
3520:
3518:
3517:
3512:
3501:
3500:
3485:
3483:
3482:
3473:
3472:
3463:
3454:
3417:
3415:
3414:
3409:
3404:
3403:
3388:
3387:
3375:
3374:
3359:
3358:
3338:
3329:
3312:
3303:
3199:
3197:
3196:
3193:{\text{OPL}}=nd.
3191:
3178:
3175:
3167:
3145:The colors of a
3127:
3123:
3119:
3115:
3111:
3109:
3108:
3103:
3101:
3097:
3096:
3093:
3087:
3079:
3077:
3069:
3068:
3067:
3058:
3057:
3047:
3031:
3030:
3027:
3018:
3001:
2999:
2991:
2990:
2989:
2980:
2979:
2969:
2947:It follows that
2946:
2944:
2942:
2941:
2936:
2934:
2920:
2889:
2885:
2881:
2872:
2864:
2855:
2853:
2852:
2847:
2845:
2843:
2835:
2834:
2833:
2832:
2822:
2821:
2812:
2811:
2801:
2786:
2777:
2770:
2761:
2739:can be deduced.
2738:
2734:
2730:
2726:
2722:
2718:
2714:
2710:
2706:
2702:
2698:
2694:
2690:
2686:
2681:
2677:
2671:
2667:
2661:
2657:
2649:
2645:
2640:
2636:
2624:
2621:, and imaginary
2620:
2601:
2597:
2593:
2586:
2577:
2570:
2561:
2551:
2536:
2529:
2522:
2518:
2511:
2487:
2476:
2453:
2451:
2450:
2445:
2440:
2439:
2438:
2437:
2428:
2403:
2402:
2368:Beer–Lambert law
2365:
2359:
2357:
2356:
2351:
2349:
2342:
2338:
2337:
2336:
2306:
2305:
2300:
2285:
2284:
2283:
2282:
2273:
2242:
2238:
2234:
2233:
2232:
2219:
2218:
2209:
2166:
2165:
2160:
2139:
2135:
2131:
2130:
2129:
2113:
2092:
2091:
2086:
2049:
2033:
2029:
2020:
2012:
2006:
1999:
1998:
1993:
1992:
1984:
1972:
1965:
1963:
1962:
1957:
1955:
1950:
1930:
1916:
1915:
1912:
1899:
1897:
1896:
1891:
1889:
1888:
1885:
1864:
1856:
1850:
1848:
1847:
1842:
1822:
1784:
1780:
1776:
1772:
1768:
1764:
1750:
1746:
1739:
1732:
1721:
1717:
1713:
1709:
1682:
1680:
1679:
1674:
1669:
1667:
1666:
1665:
1664:
1645:
1644:
1643:
1623:
1616:
1615:
1614:
1588:
1493:In a triangular
1438:
1430:
1309:. The resulting
1258:Geometric optics
1244:
1240:
1233:
1232:
1230:
1223:
1221:
1220:
1217:
1210:
1194:
1166:
965:
964:
950:
949:
935:
934:
920:
919:
894:
882:
874:
867:
866:
862:
856:
853:
849:
845:
843:
842:
837:
832:
830:
829:
817:
776:
768:
764:
760:
756:
752:
748:
746:
745:
740:
729:
727:
726:
714:
709:
707:
706:
694:
635:
631:
627:
623:
593:coined the term
549:
547:
546:
541:
536:
528:
513:
509:
505:
501:
499:
498:
493:
488:
483:
478:
463:
456:
455:
453:
450:
424:
411:
409:
408:
403:
398:
396:
395:
386:
385:
376:
371:
370:
354:
299:
255:
237:
228:
211:
197:
195:
194:
189:
173:Brewster's angle
158:
149:
136:
127:
118:
56:refraction index
52:refractive index
21:
9463:
9462:
9458:
9457:
9456:
9454:
9453:
9452:
9428:
9427:
9426:
9416:
9414:
9404:
9402:
9390:
9378:
9366:
9358:
9347:Wayback Machine
9309:
9304:
9259:
9255:
9246:
9244:
9237:"Refractometer"
9235:
9234:
9230:
9221:
9219:
9210:
9209:
9205:
9196:
9194:
9185:
9184:
9180:
9174:Wayback Machine
9163:Wayback Machine
9153:
9149:
9110:
9106:
9083:(D11): D11104.
9067:
9063:
9016:
9012:
9002:
9000:
8989:
8985:
8942:
8938:
8907:
8903:
8882:(12): 595–628.
8868:
8864:
8843:(11): 353–385.
8829:
8825:
8816:
8814:
8799:
8795:
8778:
8777:
8773:
8768:Wayback Machine
8756:
8738:
8734:
8727:
8711:
8707:
8700:
8679:
8675:
8666:
8664:
8660:
8653:
8647:
8638:
8629:
8627:
8612:
8608:
8593:
8591:
8580:
8576:
8567:
8565:
8550:
8546:
8539:
8512:
8501:
8495:Wayback Machine
8484:Wayback Machine
8474:
8470:
8464:Wayback Machine
8453:Wayback Machine
8443:
8439:
8430:
8428:
8424:
8413:
8404:
8397:
8390:
8366:
8362:
8353:
8351:
8343:
8342:
8338:
8329:
8327:
8319:
8318:
8314:
8302:
8301:
8292:
8291:
8279:
8245:
8241:
8202:
8198:
8191:
8168:
8164:
8155:
8153:
8143:
8139:
8130:
8128:
8118:
8114:
8105:
8103:
8093:
8089:
8080:
8078:
8061:
8057:
8048:
8046:
8029:
8022:
8013:
8011:
7994:
7987:
7980:
7966:
7959:
7915:
7911:
7900:
7896:
7855:Veselago, V. G.
7852:
7848:
7837:
7833:
7824:
7822:
7803:
7796:
7789:
7767:
7760:
7713:(3): e1501536.
7699:
7695:
7686:
7682:
7671:
7667:
7659:
7645:
7626:
7618:
7614:
7605:
7603:
7594:
7593:
7589:
7554:
7550:
7513:
7509:
7499:
7497:
7493:
7486:
7480:
7476:
7466:
7464:
7454:
7450:
7441:. p. 368.
7430:
7426:
7395:Brewster, David
7392:
7388:
7352:
7348:
7339:. p. 299.
7331:
7327:
7296:
7292:
7275:
7271:
7254:
7250:
7243:
7221:
7217:
7210:
7196:
7189:
7182:
7168:
7129:
7125:
7120:
7119:
7112:
7108:
7104:
7096:
7095:
7092:
7088:
7087:
7086:
7084:
7080:
7078:
7074:
7069:
7064:
7060:Velocity factor
7030:Index ellipsoid
7005:
6965:
6954:
6948:
6945:
6930:
6914:
6903:
6800:
6794:
6775:process control
6739:quality control
6716:
6710:
6703:
6693:
6689:
6685:
6648:
6640:Main articles:
6638:
6633:
6591:
6587:
6580:
6540:
6534:
6507:photoelasticity
6479:
6473:
6470:
6463:
6452:
6449:
6443:
6436:
6430:
6400:photoelasticity
6377:
6371:
6362:
6349:
6341:
6309:
6305:
6304:
6291:
6287:
6286:
6284:
6271:
6263:
6260:
6259:
6239:
6228:
6217:
6206:
6199:
6167:
6151:
6150:
6133:
6129:
6124:
6117:
6113:
6097:
6095:
6086:
6085:
6072:
6067:
6060:
6046:
6042:
6037:
6030:
6026:
6022:
6020:
6007:
6005:
5998:
5991:
5989:
5986:
5985:
5981:
5974:
5966:
5960:
5946:
5945:
5933:
5929:
5924:
5923:
5914:
5913:
5911:
5905:
5901:
5888:
5881:
5880:
5876:
5873:
5872:
5859:
5845:
5841:
5836:
5835:
5826:
5825:
5823:
5817:
5813:
5806:
5802:
5801:
5795:
5788:
5781:
5780:
5776:
5772:
5770:
5767:
5766:
5735:
5734:
5725:
5724:
5722:
5712:
5705:
5700:
5690:
5689:
5685:
5683:
5680:
5679:
5675:
5650:
5649:
5640:
5639:
5637:
5618:
5617:
5613:
5611:
5608:
5607:
5595:
5588:
5582:
5559:
5558:
5554:
5549:
5547:
5537:
5536:
5532:
5530:
5527:
5526:
5519:
5503:
5484:
5478:
5472:
5466:
5462:
5439:
5421:
5420:
5410:
5397:
5393:
5384:
5380:
5379:
5372:
5368:
5359:
5355:
5354:
5352:
5348:
5347:
5338:
5337:
5331:
5318:
5314:
5305:
5301:
5300:
5293:
5289:
5280:
5276:
5275:
5273:
5269:
5268:
5261:
5255:
5251:
5247:
5245:
5242:
5241:
5238:
5232:
5201:
5197:
5195:
5187:
5184:
5183:
5161:
5157:
5155:
5147:
5144:
5143:
5139:
5133:
5123:
5117:
5110:
5104:
5100:
5096:
5093:
5087:
5071:
5070:
5058:
5057:
5053:
5051:
5045:
5041:
5032:
5031:
5021:
5020:
5016:
5009:
5008:
5004:
5001:
4995:
4991:
4982:
4981:
4971:
4970:
4966:
4959:
4958:
4954:
4951:
4941:
4940:
4936:
4929:
4928:
4924:
4921:
4907:
4906:
4902:
4895:
4894:
4890:
4889:
4881:
4880:
4876:
4869:
4868:
4864:
4863:
4860:
4845:
4838:
4831:
4829:
4826:
4825:
4822:
4816:
4808:complex modulus
4788:
4782:
4781:
4770:
4769:
4759:
4753:
4752:
4746:
4738:
4731:
4730:
4720:
4719:
4714:
4712:
4709:
4708:
4692:
4691:
4674:
4673:
4669:
4661:
4654:
4653:
4643:
4642:
4637:
4636:
4633:
4626:
4620:
4619:
4602:
4601:
4597:
4589:
4582:
4581:
4571:
4570:
4565:
4564:
4561:
4554:
4547:
4545:
4542:
4541:
4523:
4522:
4502:
4495:
4494:
4483:
4482:
4481:
4478:
4477:
4467:
4463:
4454:
4450:
4443:
4436:
4435:
4431:
4427:
4425:
4422:
4421:
4399:
4395:
4371:
4361:
4360:
4350:
4349:
4338:
4337:
4336:
4323:
4322:
4318:
4308:
4307:
4297:
4296:
4294:
4291:
4290:
4286:
4282:
4275:
4274:
4271:
4265:
4262:
4256:
4253:
4246:
4245:
4240:
4234:
4232:
4231:
4227:
4224:
4218:
4199:
4193:
4186:
4180:
4157:
4156:
4152:
4145:
4144:
4140:
4138:
4130:
4127:
4126:
4123:
4067:
4066:
4062:
4060:
4057:
4056:
4052:
4048:
4041:
4035:
4020:
4011:
3981:
3977:
3972:
3961:
3957:
3952:
3951:
3947:
3919:
3917:
3914:
3913:
3902:
3896:
3893:
3887:
3880:
3853:
3820:
3816:
3810:
3806:
3804:
3800:
3784:
3783:
3779:
3777:
3774:
3773:
3753:
3747:
3743:
3737:
3714:
3701:
3697:
3688:
3684:
3683:
3676:
3672:
3663:
3659:
3658:
3656:
3652:
3651:
3642:
3638:
3636:
3633:
3632:
3611:
3580:
3576:
3570:
3566:
3564:
3560:
3546:
3545:
3541:
3539:
3536:
3535:
3532:
3526:
3496:
3492:
3478:
3474:
3468:
3464:
3462:
3460:
3457:
3456:
3453:
3447:
3433:
3427:
3399:
3395:
3383:
3379:
3370:
3366:
3354:
3350:
3348:
3345:
3344:
3337:
3331:
3328:
3322:
3315:incidence angle
3311:
3305:
3302:
3296:
3286:
3279:
3272:
3265:
3254:
3247:
3232:
3226:
3174:
3173:
3170:
3169:
3165:
3139:
3134:
3125:
3121:
3117:
3113:
3099:
3098:
3092:
3088:
3080:
3070:
3063:
3059:
3053:
3049:
3048:
3046:
3039:
3033:
3032:
3026:
3022:
3011:
2992:
2985:
2981:
2975:
2971:
2970:
2968:
2961:
2954:
2952:
2949:
2948:
2927:
2913:
2899:
2896:
2895:
2894:
2887:
2883:
2880:
2874:
2870:
2863:
2857:
2836:
2828:
2827:
2823:
2817:
2813:
2807:
2803:
2802:
2800:
2792:
2789:
2788:
2773:
2772:
2757:
2756:
2745:
2736:
2732:
2728:
2724:
2720:
2716:
2712:
2708:
2704:
2700:
2696:
2692:
2688:
2684:
2679:
2675:
2669:
2665:
2659:
2655:
2647:
2643:
2638:
2634:
2622:
2618:
2599:
2595:
2588:
2573:
2572:
2557:
2556:
2546:
2531:
2524:
2520:
2516:
2506:
2495:
2489:
2482:
2475:
2461:
2433:
2429:
2424:
2408:
2404:
2398:
2394:
2377:
2374:
2373:
2363:
2347:
2346:
2311:
2307:
2301:
2296:
2295:
2294:
2290:
2278:
2274:
2269:
2253:
2249:
2240:
2239:
2214:
2210:
2205:
2171:
2167:
2161:
2156:
2155:
2154:
2150:
2137:
2136:
2104:
2097:
2093:
2087:
2082:
2081:
2080:
2076:
2065:
2045:
2041:
2039:
2036:
2035:
2034:-direction as:
2031:
2028:
2022:
2019:
2008:
2002:
2001:
1996:
1995:
1990:
1989:
1982:
1970:
1931:
1929:
1911:
1907:
1905:
1902:
1901:
1884:
1880:
1878:
1875:
1874:
1862:
1854:
1813:
1811:
1808:
1807:
1800:
1794:
1782:
1778:
1774:
1770:
1766:
1763:
1759:
1748:
1744:
1738:
1734:
1731:
1727:
1719:
1715:
1711:
1707:
1697:
1654:
1653:
1649:
1630:
1629:
1625:
1624:
1595:
1594:
1590:
1589:
1587:
1579:
1576:
1575:
1525:
1475:
1436:
1433:signal velocity
1431:(note that the
1428:
1357:
1331:
1280:
1274:
1242:
1235:
1228:
1226:
1224:
1218:
1215:
1213:
1212:
1208:
1192:
1177:
1165:2 to 14 μm
1164:
962:
960:
947:
945:
932:
930:
917:
915:
892:
880:
864:
860:
859:
851:
847:
825:
821:
816:
793:
790:
789:
774:
766:
762:
758:
754:
750:
722:
718:
713:
702:
698:
693:
670:
667:
666:
648:
642:
633:
629:
625:
621:
584:
527:
519:
516:
515:
511:
507:
503:
479:
477:
469:
466:
465:
461:
451:
448:
446:
444:
423:
417:
391:
387:
381:
377:
375:
366:
362:
360:
357:
356:
353:
347:
340:
297:
243:
236:
230:
223:
213:
203:
183:
180:
179:
157:
151:
148:
142:
135:
129:
126:
120:
117:
110:
103:
96:
90:
89:of refraction,
38:of light being
28:
23:
22:
15:
12:
11:
5:
9461:
9451:
9450:
9445:
9440:
9425:
9424:
9412:
9400:
9388:
9376:
9356:
9355:
9350:
9337:
9331:
9325:
9320:
9315:
9308:
9307:External links
9305:
9303:
9302:
9253:
9228:
9203:
9178:
9147:
9114:Applied Optics
9104:
9061:
9010:
8983:
8936:
8917:(2): 109–112.
8901:
8862:
8823:
8793:
8771:
8754:
8748:. p. 49.
8746:Academic Press
8732:
8725:
8705:
8698:
8673:
8636:
8614:Nave, Carl R.
8606:
8574:
8552:Paschotta, R.
8544:
8537:
8499:
8468:
8437:
8395:
8388:
8360:
8336:
8312:
8303:|journal=
8277:
8239:
8196:
8189:
8162:
8137:
8112:
8087:
8055:
8020:
7985:
7978:
7957:
7918:Shalaev, V. M.
7909:
7894:
7867:(4): 509–514.
7846:
7831:
7794:
7787:
7758:
7693:
7680:
7665:
7662:on 2013-05-18.
7643:
7612:
7587:
7548:
7527:(4): 585–587.
7507:
7474:
7448:
7424:
7386:
7346:
7325:
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7017:
7012:
7006:
7004:
7001:
6967:
6966:
6949:September 2014
6917:
6915:
6908:
6902:
6899:
6860:interferometry
6796:Main article:
6793:
6790:
6714:
6701:
6660:refractometers
6637:
6634:
6632:
6629:
6608:optical fibers
6579:
6576:
6572:Pockels effect
6544:electric field
6536:Main article:
6533:
6530:
6518:crystal optics
6477:
6468:
6461:
6447:
6434:
6373:Main article:
6370:
6367:
6361:
6358:
6329:
6320:
6317:
6312:
6308:
6302:
6299:
6294:
6290:
6283:
6278:
6275:
6270:
6267:
6252:polarizability
6205:is defined as
6198:
6195:
6179:polarizability
6149:
6144:
6136:
6132:
6128:
6123:
6120:
6116:
6112:
6109:
6104:
6100:
6094:
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5973:
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5897:
5894:
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5889:
5884:
5879:
5875:
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5871:
5865:
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5857:
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5839:
5833:
5829:
5820:
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5812:
5809:
5805:
5798:
5794:
5791:
5789:
5784:
5779:
5775:
5774:
5751:
5742:
5738:
5732:
5728:
5719:
5716:
5711:
5708:
5704:
5699:
5693:
5688:
5663:
5657:
5653:
5647:
5643:
5636:
5633:
5630:
5627:
5621:
5616:
5600:phase velocity
5592:group velocity
5586:
5570:
5562:
5557:
5552:
5546:
5540:
5535:
5518:
5515:
5464:
5438:
5435:
5419:
5413:
5408:
5400:
5396:
5392:
5387:
5383:
5375:
5371:
5367:
5362:
5358:
5351:
5346:
5343:
5341:
5339:
5334:
5329:
5321:
5317:
5313:
5308:
5304:
5296:
5292:
5288:
5283:
5279:
5272:
5267:
5264:
5262:
5258:
5254:
5250:
5249:
5236:
5215:
5209:
5204:
5200:
5194:
5191:
5169:
5164:
5160:
5154:
5151:
5137:
5121:
5108:
5091:
5067:
5061:
5056:
5048:
5044:
5040:
5037:
5035:
5033:
5024:
5019:
5012:
5007:
4998:
4994:
4990:
4987:
4985:
4983:
4974:
4969:
4962:
4957:
4944:
4939:
4932:
4927:
4920:
4910:
4905:
4898:
4893:
4884:
4879:
4872:
4867:
4859:
4853:
4850:
4844:
4841:
4839:
4837:
4834:
4833:
4820:Wave impedance
4815:
4814:Wave impedance
4812:
4791:
4785:
4777:
4774:
4767:
4762:
4756:
4751:
4745:
4741:
4734:
4727:
4724:
4717:
4690:
4684:
4677:
4672:
4668:
4664:
4657:
4650:
4647:
4640:
4632:
4629:
4627:
4625:
4622:
4621:
4618:
4612:
4605:
4600:
4596:
4592:
4585:
4578:
4575:
4568:
4560:
4557:
4555:
4553:
4550:
4549:
4521:
4517:
4514:
4511:
4508:
4505:
4503:
4498:
4490:
4487:
4480:
4479:
4476:
4470:
4466:
4462:
4457:
4453:
4449:
4446:
4444:
4439:
4434:
4430:
4429:
4407:
4402:
4398:
4394:
4391:
4388:
4385:
4382:
4379:
4374:
4368:
4365:
4359:
4353:
4345:
4342:
4335:
4332:
4326:
4321:
4317:
4311:
4304:
4301:
4269:
4260:
4251:
4238:
4222:
4197:
4184:
4168:
4160:
4155:
4148:
4143:
4137:
4134:
4122:
4119:
4100:
4094:
4091:
4088:
4085:
4082:
4076:
4073:
4070:
4065:
4045:objective lens
4039:
4019:
4016:
3999:
3992:
3984:
3980:
3976:
3971:
3964:
3960:
3956:
3950:
3946:
3943:
3940:
3937:
3934:
3931:
3926:
3923:
3900:
3891:
3852:
3849:
3837:
3830:
3823:
3819:
3813:
3809:
3803:
3799:
3796:
3793:
3787:
3782:
3751:
3741:
3723:
3717:
3712:
3704:
3700:
3696:
3691:
3687:
3679:
3675:
3671:
3666:
3662:
3655:
3650:
3645:
3641:
3610:
3607:
3595:
3590:
3583:
3579:
3573:
3569:
3563:
3558:
3555:
3549:
3544:
3530:
3510:
3507:
3504:
3499:
3495:
3491:
3488:
3481:
3477:
3471:
3467:
3451:
3429:Main article:
3426:
3423:
3407:
3402:
3398:
3394:
3391:
3386:
3382:
3378:
3373:
3369:
3365:
3362:
3357:
3353:
3335:
3326:
3319:surface normal
3309:
3300:
3284:
3277:
3270:
3263:
3257:phase velocity
3252:
3245:
3228:Main article:
3225:
3222:
3190:
3187:
3184:
3181:
3138:
3135:
3133:
3130:
3091:
3086:
3083:
3076:
3073:
3066:
3062:
3056:
3052:
3045:
3042:
3040:
3038:
3035:
3034:
3025:
3021:
3017:
3014:
3010:
3007:
3004:
2998:
2995:
2988:
2984:
2978:
2974:
2967:
2964:
2962:
2960:
2957:
2956:
2933:
2930:
2926:
2923:
2919:
2916:
2912:
2909:
2906:
2903:
2878:
2861:
2842:
2839:
2831:
2826:
2820:
2816:
2810:
2806:
2799:
2796:
2744:
2741:
2504:
2493:
2473:
2443:
2436:
2432:
2427:
2423:
2420:
2417:
2414:
2411:
2407:
2401:
2397:
2393:
2390:
2387:
2384:
2381:
2345:
2341:
2335:
2332:
2329:
2326:
2323:
2320:
2317:
2314:
2310:
2304:
2299:
2293:
2288:
2281:
2277:
2272:
2268:
2265:
2262:
2259:
2256:
2252:
2248:
2245:
2243:
2241:
2237:
2231:
2228:
2225:
2222:
2217:
2213:
2208:
2204:
2201:
2198:
2195:
2192:
2189:
2186:
2183:
2180:
2177:
2174:
2170:
2164:
2159:
2153:
2148:
2145:
2142:
2140:
2138:
2134:
2128:
2125:
2122:
2119:
2116:
2111:
2108:
2103:
2100:
2096:
2090:
2085:
2079:
2074:
2071:
2068:
2066:
2064:
2061:
2058:
2055:
2052:
2048:
2044:
2043:
2026:
2017:
1975:electric field
1953:
1949:
1946:
1943:
1940:
1937:
1934:
1928:
1925:
1922:
1919:
1910:
1883:
1865:is called the
1859:phase velocity
1840:
1837:
1834:
1831:
1828:
1825:
1820:
1817:
1793:
1790:
1777:) and sodium (
1771:589.29 nm
1761:
1736:
1729:
1712:546.07 nm
1708:587.56 nm
1701:emission lines
1696:
1693:
1672:
1663:
1660:
1657:
1652:
1648:
1642:
1639:
1636:
1633:
1628:
1622:
1619:
1613:
1610:
1607:
1604:
1601:
1598:
1593:
1586:
1583:
1566:
1562:
1558:
1521:Main article:
1474:
1471:
1467:
1466:
1455:
1444:
1422:phase velocity
1405:
1373:magnetic field
1361:electric field
1353:Main article:
1330:
1327:
1273:
1270:
1185:phase velocity
1176:
1173:
1116:
1115:
1112:
1106:
1105:
1102:
1096:
1095:
1092:
1090:Cubic zirconia
1086:
1085:
1082:
1076:
1075:
1072:
1065:
1064:
1061:
1054:
1053:
1050:
1044:
1043:
1040:
1033:
1032:
1029:
1022:
1021:
1018:
1012:
1011:
1005:
1004:
1001:
995:
994:
991:
985:
984:
981:
975:
974:
973:at 20 °C
967:
966:
958:
956:Carbon dioxide
952:
951:
943:
937:
936:
928:
922:
921:
913:
907:
906:
896:
895:
890:
884:
883:
878:
835:
828:
824:
820:
815:
812:
809:
806:
803:
800:
797:
738:
735:
732:
725:
721:
717:
712:
705:
701:
697:
692:
689:
686:
683:
680:
677:
674:
641:
640:Typical values
638:
583:
580:
560:group velocity
539:
534:
531:
526:
523:
491:
486:
482:
476:
473:
459:phase velocity
441:speed of light
421:
401:
394:
390:
384:
380:
374:
369:
365:
351:
339:
336:
234:
221:
187:
155:
146:
133:
124:
115:
108:
101:
94:
60:optical medium
26:
9:
6:
4:
3:
2:
9460:
9449:
9446:
9444:
9441:
9439:
9436:
9435:
9433:
9423:
9413:
9411:
9401:
9399:
9394:
9389:
9387:
9382:
9377:
9375:
9370:
9365:
9364:
9361:
9354:
9351:
9348:
9344:
9341:
9338:
9335:
9332:
9329:
9326:
9324:
9323:Science World
9321:
9319:
9316:
9314:
9311:
9310:
9298:
9294:
9289:
9284:
9280:
9276:
9272:
9268:
9267:Physics Today
9264:
9257:
9242:
9238:
9232:
9217:
9213:
9207:
9192:
9188:
9182:
9175:
9171:
9168:
9164:
9160:
9157:
9156:birefringence
9151:
9143:
9139:
9135:
9131:
9127:
9123:
9119:
9115:
9108:
9099:
9094:
9090:
9086:
9082:
9078:
9077:
9072:
9065:
9057:
9053:
9048:
9043:
9039:
9035:
9032:(786): 1–64.
9031:
9027:
9026:
9021:
9014:
8998:
8994:
8987:
8979:
8975:
8971:
8967:
8963:
8959:
8955:
8951:
8947:
8940:
8932:
8928:
8924:
8920:
8916:
8912:
8905:
8897:
8893:
8889:
8885:
8881:
8877:
8873:
8866:
8858:
8854:
8850:
8846:
8842:
8838:
8834:
8827:
8812:
8808:
8804:
8797:
8789:
8785:
8781:
8775:
8769:
8765:
8762:
8757:
8751:
8747:
8743:
8736:
8728:
8722:
8718:
8717:
8709:
8701:
8695:
8691:
8687:
8683:
8677:
8659:
8652:
8645:
8643:
8641:
8626:on 2014-09-26
8625:
8621:
8617:
8610:
8603:
8602:
8589:
8585:
8578:
8563:
8559:
8555:
8548:
8540:
8534:
8530:
8526:
8525:
8520:
8516:
8510:
8508:
8506:
8504:
8496:
8492:
8489:
8485:
8481:
8478:
8472:
8465:
8461:
8458:
8454:
8450:
8447:
8441:
8423:
8419:
8412:
8408:
8402:
8400:
8391:
8385:
8381:
8377:
8373:
8372:
8364:
8350:
8346:
8340:
8326:
8325:www.atago.net
8322:
8316:
8308:
8296:
8288:
8284:
8280:
8278:9781510645905
8274:
8270:
8266:
8262:
8258:
8254:
8250:
8243:
8235:
8231:
8227:
8223:
8219:
8215:
8211:
8207:
8200:
8192:
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8182:
8178:
8174:
8166:
8152:
8148:
8141:
8127:
8126:Oharacorp.com
8123:
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8034:
8027:
8025:
8009:
8005:
8004:
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7992:
7990:
7981:
7975:
7971:
7964:
7962:
7953:
7949:
7945:
7941:
7937:
7933:
7929:
7925:
7924:
7919:
7913:
7905:
7898:
7890:
7886:
7882:
7878:
7874:
7870:
7866:
7862:
7861:
7856:
7850:
7842:
7835:
7820:
7816:
7812:
7808:
7801:
7799:
7790:
7784:
7780:
7775:
7774:
7765:
7763:
7754:
7750:
7745:
7740:
7736:
7732:
7728:
7724:
7720:
7716:
7712:
7708:
7704:
7697:
7690:
7684:
7676:
7669:
7658:
7654:
7650:
7646:
7640:
7636:
7632:
7625:
7624:
7616:
7602:on 2014-09-10
7601:
7597:
7591:
7583:
7579:
7575:
7571:
7567:
7563:
7559:
7552:
7543:
7538:
7534:
7530:
7526:
7522:
7518:
7511:
7492:
7485:
7478:
7463:
7459:
7452:
7444:
7440:
7439:
7434:
7428:
7420:
7416:
7412:
7408:
7404:
7400:
7396:
7390:
7382:
7376:
7372:
7368:
7364:
7360:
7356:
7350:
7342:
7338:
7337:
7329:
7321:
7317:
7313:
7309:
7305:
7301:
7294:
7286:
7282:
7281:
7273:
7265:
7261:
7260:
7252:
7244:
7238:
7234:
7229:
7228:
7219:
7211:
7205:
7201:
7194:
7192:
7183:
7177:
7173:
7166:
7164:
7162:
7160:
7158:
7156:
7154:
7152:
7150:
7148:
7146:
7144:
7142:
7140:
7138:
7136:
7134:
7132:
7127:
7076:
7072:
7061:
7058:
7056:
7053:
7051:
7048:
7046:
7043:
7041:
7038:
7036:
7033:
7031:
7028:
7026:
7023:
7021:
7018:
7016:
7013:
7011:
7008:
7007:
7000:
6998:
6994:
6993:refractometer
6990:
6986:
6982:
6981:optical fiber
6978:
6977:lens coatings
6974:
6963:
6960:
6952:
6942:
6938:
6934:
6928:
6927:
6923:
6918:This section
6916:
6912:
6907:
6906:
6898:
6896:
6891:
6889:
6880:
6879:Fourier plane
6876:
6872:
6868:
6863:
6861:
6857:
6853:
6849:
6845:
6841:
6837:
6833:
6829:
6824:
6821:
6813:
6812:budding yeast
6809:
6804:
6799:
6789:
6787:
6783:
6778:
6776:
6772:
6768:
6764:
6760:
6756:
6755:sugar content
6753:to determine
6752:
6748:
6744:
6740:
6736:
6732:
6723:
6719:
6713:
6707:
6700:
6696:
6683:
6682:photodetector
6679:
6674:
6669:
6665:
6661:
6652:
6647:
6646:Refractometer
6643:
6642:Refractometry
6628:
6626:
6622:
6609:
6605:
6601:
6584:
6578:Inhomogeneity
6575:
6573:
6569:
6565:
6561:
6560:self-focusing
6557:
6553:
6549:
6545:
6539:
6529:
6527:
6523:
6519:
6514:
6512:
6508:
6504:
6500:
6496:
6492:
6487:
6485:
6476:
6467:
6460:
6456:
6446:
6441:
6440:extraordinary
6433:
6428:
6424:
6419:
6417:
6413:
6412:birefringence
6409:
6401:
6396:
6390:
6386:
6381:
6376:
6375:Birefringence
6369:Birefringence
6366:
6357:
6355:
6347:
6327:
6318:
6315:
6310:
6306:
6300:
6297:
6292:
6288:
6281:
6276:
6273:
6268:
6265:
6257:
6253:
6249:
6248:
6243:
6235:
6231:
6224:
6220:
6213:
6209:
6204:
6194:
6192:
6188:
6184:
6180:
6175:
6173:
6172:controversial
6164:
6147:
6142:
6134:
6130:
6126:
6121:
6118:
6114:
6110:
6107:
6102:
6092:
6090:
6076:
6073:
6069:
6064:
6061:
6055:
6047:
6043:
6039:
6034:
6031:
6027:
6023:
6017:
6012:
6002:
6000:
5995:
5979:
5969:
5963:
5942:
5934:
5930:
5919:
5906:
5902:
5898:
5895:
5892:
5890:
5877:
5869:
5863:
5860:
5855:
5846:
5842:
5831:
5818:
5814:
5810:
5807:
5803:
5792:
5790:
5777:
5762:
5749:
5740:
5730:
5717:
5714:
5709:
5706:
5702:
5697:
5686:
5661:
5655:
5645:
5634:
5631:
5628:
5625:
5614:
5605:
5601:
5593:
5585:
5568:
5555:
5544:
5533:
5524:
5514:
5512:
5506:
5500:
5498:
5494:
5489:
5487:
5481:
5475:
5469:
5459:
5452:
5448:
5443:
5434:
5417:
5411:
5406:
5398:
5394:
5390:
5385:
5381:
5373:
5369:
5365:
5360:
5356:
5349:
5344:
5342:
5332:
5327:
5319:
5315:
5311:
5306:
5302:
5294:
5290:
5286:
5281:
5277:
5270:
5265:
5263:
5256:
5252:
5235:
5229:
5226:
5213:
5207:
5202:
5198:
5192:
5189:
5167:
5162:
5158:
5152:
5149:
5136:
5130:
5128:
5120:
5115:
5107:
5090:
5084:
5065:
5054:
5046:
5042:
5038:
5036:
5017:
5005:
4996:
4992:
4988:
4986:
4967:
4955:
4942:
4937:
4930:
4925:
4918:
4903:
4896:
4891:
4877:
4870:
4865:
4857:
4851:
4848:
4842:
4840:
4835:
4821:
4811:
4809:
4789:
4772:
4765:
4760:
4749:
4743:
4725:
4722:
4705:
4688:
4682:
4670:
4666:
4648:
4645:
4630:
4628:
4623:
4616:
4610:
4598:
4594:
4576:
4573:
4558:
4556:
4551:
4539:
4536:
4519:
4515:
4512:
4509:
4506:
4504:
4485:
4474:
4468:
4464:
4460:
4455:
4451:
4447:
4445:
4432:
4418:
4405:
4400:
4392:
4389:
4386:
4383:
4377:
4372:
4366:
4363:
4357:
4340:
4333:
4330:
4319:
4315:
4302:
4299:
4278:
4268:
4259:
4249:
4237:
4221:
4216:
4212:
4208:
4204:
4196:
4191:
4183:
4166:
4153:
4141:
4135:
4132:
4118:
4116:
4115:oil immersion
4111:
4098:
4092:
4089:
4086:
4083:
4080:
4063:
4046:
4038:
4033:
4029:
4025:
4015:
3997:
3990:
3982:
3978:
3974:
3969:
3962:
3958:
3954:
3948:
3941:
3938:
3935:
3929:
3924:
3921:
3911:
3907:
3899:
3890:
3886:
3878:
3874:
3866:
3862:
3857:
3848:
3835:
3828:
3821:
3817:
3811:
3807:
3801:
3797:
3794:
3791:
3780:
3771:
3767:
3763:
3759:
3750:
3740:
3734:
3721:
3715:
3710:
3702:
3698:
3694:
3689:
3685:
3677:
3673:
3669:
3664:
3660:
3653:
3648:
3643:
3639:
3630:
3628:
3624:
3620:
3616:
3606:
3593:
3588:
3581:
3577:
3571:
3567:
3561:
3556:
3553:
3542:
3529:
3524:
3508:
3505:
3502:
3497:
3493:
3489:
3486:
3479:
3475:
3469:
3465:
3450:
3441:
3437:
3432:
3422:
3418:
3405:
3400:
3396:
3392:
3389:
3384:
3380:
3376:
3371:
3367:
3363:
3360:
3355:
3351:
3342:
3334:
3325:
3320:
3316:
3308:
3299:
3294:
3283:
3276:
3269:
3262:
3258:
3251:
3244:
3240:
3236:
3231:
3221:
3219:
3215:
3211:
3207:
3203:
3188:
3185:
3182:
3179:
3163:
3156:
3152:
3148:
3143:
3129:
3089:
3084:
3081:
3074:
3071:
3064:
3060:
3054:
3050:
3043:
3041:
3036:
3023:
3015:
3012:
3008:
3005:
2996:
2993:
2986:
2982:
2976:
2972:
2965:
2963:
2958:
2931:
2928:
2924:
2921:
2917:
2914:
2910:
2907:
2904:
2901:
2893:
2877:
2868:
2860:
2840:
2837:
2824:
2818:
2814:
2808:
2804:
2797:
2794:
2785:
2781:
2776:
2769:
2765:
2760:
2754:
2750:
2740:
2682:
2672:
2664:reflectance,
2652:
2650:
2632:
2628:
2615:
2613:
2607:
2605:
2591:
2585:
2581:
2576:
2569:
2565:
2560:
2553:
2549:
2544:
2540:
2534:
2527:
2513:
2510:
2503:
2499:
2492:
2486:
2480:
2472:
2468:
2464:
2459:
2456:and thus the
2454:
2441:
2434:
2430:
2425:
2421:
2418:
2415:
2412:
2409:
2405:
2399:
2395:
2391:
2385:
2379:
2371:
2369:
2360:
2343:
2339:
2330:
2327:
2324:
2321:
2318:
2312:
2308:
2302:
2291:
2286:
2279:
2275:
2270:
2266:
2263:
2260:
2257:
2254:
2250:
2246:
2244:
2235:
2226:
2223:
2220:
2215:
2211:
2206:
2202:
2196:
2193:
2190:
2187:
2181:
2178:
2172:
2168:
2162:
2151:
2146:
2143:
2141:
2132:
2123:
2120:
2117:
2114:
2109:
2106:
2098:
2094:
2088:
2077:
2072:
2069:
2067:
2059:
2056:
2053:
2025:
2016:
2011:
2005:
1988:
1980:
1976:
1967:
1951:
1944:
1938:
1935:
1932:
1926:
1920:
1908:
1881:
1872:
1868:
1860:
1851:
1838:
1835:
1832:
1829:
1826:
1823:
1818:
1815:
1805:
1799:
1789:
1786:
1757:
1752:
1741:
1725:
1704:
1702:
1692:
1690:
1686:
1670:
1650:
1646:
1626:
1620:
1617:
1591:
1584:
1581:
1573:
1568:
1564:
1560:
1556:
1554:
1550:
1546:
1542:
1538:
1534:
1530:
1524:
1515:
1508:
1504:
1500:
1496:
1491:
1484:
1479:
1470:
1464:
1460:
1456:
1453:
1449:
1445:
1442:
1434:
1427:
1423:
1419:
1415:
1411:
1406:
1402:
1401:
1400:
1397:
1395:
1390:
1386:
1382:
1378:
1374:
1370:
1366:
1362:
1356:
1348:
1344:
1343:thin sections
1340:
1335:
1326:
1324:
1323:metamaterials
1320:
1316:
1312:
1308:
1307:metamaterials
1304:
1300:
1293:
1289:
1284:
1279:
1269:
1267:
1263:
1259:
1255:
1251:
1246:
1245:wavelength).
1239:
1206:
1202:
1198:
1190:
1186:
1182:
1172:
1170:
1162:
1158:
1153:
1151:
1147:
1143:
1139:
1135:
1131:
1127:
1123:
1122:visible light
1113:
1111:
1107:
1103:
1101:
1097:
1093:
1091:
1087:
1083:
1081:
1077:
1073:
1070:
1066:
1062:
1059:
1058:Polycarbonate
1055:
1051:
1049:
1045:
1041:
1038:
1034:
1030:
1027:
1023:
1019:
1017:
1013:
1010:
1006:
1002:
1000:
996:
992:
990:
986:
982:
980:
976:
972:
968:
959:
957:
953:
944:
942:
938:
929:
927:
923:
914:
912:
908:
905:
901:
897:
891:
889:
885:
875:
871:
855:
833:
826:
822:
818:
813:
810:
807:
801:
795:
786:
784:
780:
772:
769:, etc., are
736:
733:
730:
723:
719:
715:
710:
703:
699:
695:
690:
687:
684:
678:
672:
664:
656:
652:
647:
637:
632:. The symbol
618:
616:
612:
608:
603:
596:
592:
588:
579:
577:
573:
569:
565:
561:
557:
553:
537:
532:
529:
524:
521:
506:is constant,
489:
484:
474:
471:
460:
442:
438:
435:
430:
429:of medium 2.
428:
420:
415:
399:
392:
388:
382:
378:
372:
367:
363:
350:
345:
335:
333:
329:
324:
322:
318:
314:
310:
306:
301:
294:
290:
286:
282:
278:
274:
270:
266:
262:
257:
254:
250:
246:
241:
233:
227:
220:
216:
210:
206:
201:
185:
176:
174:
170:
166:
162:
154:
145:
140:
132:
123:
114:
107:
100:
93:
88:
84:
75:
71:
69:
65:
61:
57:
53:
49:
41:
37:
32:
19:
9270:
9266:
9256:
9245:. Retrieved
9231:
9220:. Retrieved
9206:
9195:. Retrieved
9181:
9150:
9117:
9113:
9107:
9080:
9074:
9064:
9029:
9023:
9013:
9001:. Retrieved
8986:
8953:
8949:
8939:
8914:
8910:
8904:
8879:
8875:
8865:
8840:
8836:
8826:
8815:. Retrieved
8806:
8796:
8783:
8774:
8761:(online pdf)
8741:
8735:
8715:
8708:
8685:
8676:
8665:. Retrieved
8628:. Retrieved
8624:the original
8620:HyperPhysics
8619:
8609:
8598:
8592:. Retrieved
8577:
8566:. Retrieved
8557:
8547:
8522:
8471:
8440:
8429:. Retrieved
8417:
8370:
8363:
8352:. Retrieved
8348:
8339:
8328:. Retrieved
8324:
8315:
8252:
8242:
8209:
8199:
8172:
8165:
8154:. Retrieved
8150:
8145:Hoya Group.
8140:
8129:. Retrieved
8125:
8115:
8104:. Retrieved
8100:
8090:
8079:. Retrieved
8068:
8058:
8047:. Retrieved
8038:HyperPhysics
8036:
8033:"Dispersion"
8012:. Retrieved
8001:
7969:
7930:(1): 41–48.
7927:
7921:
7912:
7897:
7864:
7858:
7849:
7840:
7834:
7823:. Retrieved
7810:
7772:
7710:
7706:
7696:
7683:
7668:
7657:the original
7622:
7615:
7604:. Retrieved
7600:the original
7590:
7565:
7561:
7551:
7524:
7520:
7510:
7498:. Retrieved
7477:
7465:. Retrieved
7461:
7451:
7437:
7427:
7409:(202): 126.
7406:
7402:
7389:
7370:
7366:
7362:
7349:
7335:
7328:
7303:
7299:
7293:
7279:
7272:
7258:
7251:
7226:
7218:
7199:
7171:
7075:
7020:Ellipsometry
6970:
6955:
6946:
6931:Please help
6919:
6901:Applications
6892:
6864:
6848:interference
6825:
6817:
6779:
6745:are used in
6728:
6711:
6705:
6698:
6694:
6657:
6597:
6541:
6532:Nonlinearity
6524:is a rank-2
6521:
6515:
6488:
6474:
6465:
6458:
6454:
6444:
6439:
6431:
6426:
6423:optical axis
6420:
6408:polarization
6405:
6363:
6245:
6244:
6233:
6229:
6222:
6218:
6211:
6207:
6203:refractivity
6202:
6200:
6197:Refractivity
6176:
6165:
5975:
5961:
5763:
5583:
5525:is defined:
5522:
5520:
5504:
5501:
5490:
5455:
5233:
5230:
5227:
5134:
5131:
5118:
5105:
5088:
5085:
4823:
4706:
4540:
4537:
4419:
4276:
4266:
4257:
4247:
4235:
4219:
4194:
4181:
4124:
4112:
4036:
4021:
3897:
3888:
3873:focal length
3870:
3765:
3758:polarization
3748:
3738:
3735:
3631:
3625:, which for
3619:reflectivity
3612:
3609:Reflectivity
3527:
3448:
3445:
3419:
3332:
3323:
3306:
3297:
3290:
3281:
3274:
3267:
3260:
3255:. Since the
3249:
3242:
3206:interference
3160:
2875:
2858:
2783:
2779:
2774:
2767:
2763:
2758:
2746:
2653:
2616:
2612:transparency
2608:
2589:
2587:, but where
2583:
2579:
2574:
2567:
2563:
2558:
2554:
2547:
2532:
2525:
2514:
2508:
2501:
2497:
2490:
2484:
2470:
2466:
2462:
2455:
2372:
2361:
2023:
2014:
2009:
2003:
1968:
1870:
1866:
1852:
1801:
1787:
1783:1.73 nm
1753:
1742:
1705:
1698:
1688:
1569:
1545:focal length
1526:
1468:
1441:permittivity
1418:permittivity
1398:
1358:
1303:permeability
1299:permittivity
1296:
1247:
1243:0.04 nm
1178:
1154:
1119:
1048:Window glass
1026:Fused silica
787:
771:coefficients
660:
619:
602:Thomas Young
600:
594:
591:Thomas Young
436:
433:
431:
426:
418:
348:
343:
341:
325:
302:
291:, while the
258:
252:
248:
244:
231:
225:
218:
214:
208:
204:
177:
152:
143:
130:
121:
112:
105:
98:
91:
80:
55:
51:
45:
8682:Bleaney, B.
7500:11 December
6761:juice, and
6751:wine makers
6747:agriculture
6542:The strong
6414:or optical
5602:. When the
5523:group index
5517:Group index
5511:ideal gases
4211:Snell's law
3629:reduces to
3341:Snell's law
3210:diffraction
3147:soap bubble
2633:describing
2571:instead of
2539:gain medium
1987:wave number
1900:, through:
1724:Abbe number
1572:Abbe number
1503:white light
1381:phase delay
1315:Snell's law
1189:information
1126:transparent
1069:Flint glass
865:589 nm
783:micrometres
576:temperature
443:in vacuum,
332:eye glasses
313:radio waves
289:attenuation
87:Snell's law
9443:Refraction
9432:Categories
9398:Technology
9247:2011-09-03
9222:2011-09-03
9197:2011-09-03
8956:(4): 519.
8817:2014-01-11
8667:2015-01-02
8656:(Report).
8630:2014-09-08
8594:2010-07-28
8568:2015-08-16
8519:Wolf, Emil
8477:refraction
8431:2015-01-05
8354:2022-08-15
8330:2022-08-15
8156:2023-08-13
8131:2022-08-15
8106:2023-08-13
8101:Schott.com
8081:2014-09-08
8049:2023-08-13
8014:2023-08-13
7825:2011-08-30
7606:2014-09-08
7568:(5): 610.
7123:References
6989:chatoyance
6858:(DIC), or
6749:by, e.g.,
6735:substances
6668:Ernst Abbe
6511:polarizers
6484:waveplates
6416:anisotropy
6354:molar mass
6185:or to the
5604:dispersion
4818:See also:
4028:microscope
4024:resolution
3313:, with an
3239:Refraction
3230:Refraction
3224:Refraction
2477:, and the
1796:See also:
1714:), called
1499:dispersion
1473:Dispersion
1414:ionosphere
1394:scattering
1292:microwaves
1276:See also:
1250:ionosphere
1209:close to 1
1203:, and for
1146:Moissanite
1138:nanometers
1110:Moissanite
1071:(typical)
644:See also:
457:, and the
338:Definition
261:dispersion
200:wavelength
9297:121322301
9273:(7): 23.
8978:1943-8206
8896:0003-3804
8857:0003-3804
8515:Born, Max
8305:ignored (
8295:cite book
8287:240561530
8234:120544352
7889:250862458
7735:2375-2548
7320:186208526
7067:Footnotes
6920:does not
6844:intensity
6810:image of
6786:gemstones
6678:telescope
6495:isotropic
6298:−
6282:⋅
6277:ρ
6181:with the
6122:−
6093:≈
6035:−
5931:λ
5903:λ
5899:−
5861:−
5843:λ
5815:λ
5811:−
5741:λ
5715:λ
5656:λ
5635:λ
5632:−
5502:For air,
5493:olive oil
5366:−
5287:−
5055:μ
5018:ε
5006:μ
4968:ε
4956:μ
4938:ε
4926:μ
4904:ε
4892:ε
4878:μ
4866:μ
4852:ε
4849:μ
4776:~
4773:ε
4750:ε
4726:_
4723:ε
4671:ε
4667:−
4649:_
4646:ε
4624:κ
4599:ε
4577:_
4574:ε
4516:κ
4489:~
4486:ε
4465:κ
4461:−
4433:ε
4393:κ
4367:_
4344:~
4341:ε
4320:ε
4303:_
4300:ε
4154:μ
4142:ε
4093:θ
4090:
4043:) of its
3970:−
3939:−
3906:thin lens
3798:
3781:θ
3670:−
3615:reflected
3543:θ
3494:θ
3490:
3397:θ
3393:
3368:θ
3364:
3293:refracted
3075:π
3061:λ
3037:β
2997:π
2983:λ
2959:δ
2841:π
2815:λ
2795:δ
2617:The real
2431:λ
2419:κ
2416:π
2410:−
2328:ω
2325:−
2276:λ
2264:κ
2261:π
2255:−
2224:ω
2221:−
2212:λ
2197:κ
2182:π
2121:ω
2118:−
2110:_
1945:ω
1939:κ
1936:ω
1921:ω
1909:α
1882:α
1836:κ
1819:_
1647:−
1618:−
1565:increases
1529:frequency
1452:imaginary
1365:electrons
1319:superlens
1161:Germanium
1060:(Lexan™)
1028:(quartz)
999:Olive oil
877:Material
823:λ
802:λ
734:⋯
720:λ
700:λ
679:λ
525:∝
454: m/s
330:(such as
285:imaginary
277:absorbing
271:, and as
240:frequency
161:reflected
83:refracted
40:refracted
9422:Minerals
9343:Archived
9241:Archived
9216:Archived
9191:Archived
9170:Archived
9159:Archived
9142:21085275
8997:Archived
8811:Archived
8788:Archived
8764:Archived
8658:Archived
8588:Archived
8562:Archived
8521:(1999).
8491:Archived
8480:Archived
8460:Archived
8449:Archived
8422:Archived
8409:(1999).
8075:Archived
8043:Archived
8008:Archived
7819:Archived
7753:27051869
7653:18187536
7491:Archived
7467:June 20,
7443:Archived
7435:(1828).
7419:Archived
7397:(1815).
7375:Archived
7357:(1817).
7341:Archived
7003:See also
6840:integral
6782:gemology
6767:chemical
6737:and for
6731:chemical
6709:, where
6673:parallel
6499:plastics
6491:crystals
6427:ordinary
5447:silicate
3883:and the
3218:optimize
3085:″
3016:′
2932:″
2918:′
2631:equation
2000:through
1804:absorbed
1561:increase
1557:decrease
1537:rainbows
1347:minerals
1236:30
1193:below 1.
1157:infrared
1080:Sapphire
941:Hydrogen
655:Diamonds
611:Hauksbee
597:in 1807.
572:pressure
564:envelope
269:rainbows
229:, where
137:are the
119:, where
58:) of an
9386:Science
9374:Physics
9360:Portals
9275:Bibcode
9165:in the
9122:Bibcode
9085:Bibcode
9034:Bibcode
9003:31 July
8958:Bibcode
8919:Bibcode
8486:in the
8455:in the
8420:. MIT.
8257:Bibcode
8214:Bibcode
7932:Bibcode
7869:Bibcode
7744:4820380
7715:Bibcode
7570:Bibcode
7529:Bibcode
7373:: 208.
7101:
7085:
6941:removed
6926:sources
6877:in the
6875:annulus
6621:mirages
6606:, some
6385:calcite
6352:is the
6346:density
6344:is the
5590:is the
5497:ethanol
5458:density
5437:Density
5125:is its
4806:is the
4233:√
4201:is its
3317:to the
2865:is the
2598:versus
2021:, with
1507:rainbow
1505:into a
1483:rainbow
1461:due to
1266:Skywave
1201:plasmas
1142:aerogel
1100:Diamond
989:Ethanol
971:Liquids
777:as the
582:History
554:of the
307:, from
281:complex
9340:LUXPOP
9295:
9140:
9054:
8976:
8894:
8855:
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8723:
8696:
8535:
8386:
8285:
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8232:
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7976:
7952:170678
7950:
7887:
7785:
7751:
7741:
7733:
7651:
7641:
7318:
7239:
7206:
7178:
7172:Optics
6604:lenses
6526:tensor
6520:, the
6348:, and
6340:where
6325:
6232:= 10 (
6221:= 10 (
5959:where
5674:where
5581:where
5495:) and
5116:, and
5086:where
4707:where
4192:, and
4179:where
4096:
4010:where
3995:
3851:Lenses
3833:
3795:arctan
3557:arcsin
2856:where
2778:= 1 −
2762:= 1 −
2602:. See
2592:> 0
2550:< 0
2543:lasers
2528:> 0
1781:) are
1743:Both,
1549:lenses
1541:colors
1533:prisms
1459:lasers
1410:X-rays
1254:plasma
1205:X-rays
1134:sodium
1130:D-line
1104:2.417
1009:Solids
983:1.333
926:Helium
888:Vacuum
749:where
628:, and
615:Hutton
607:Newton
502:Since
414:vacuum
328:lenses
309:X-rays
265:prisms
171:) and
50:, the
48:optics
9293:S2CID
9056:91351
9052:JSTOR
8661:(PDF)
8654:(PDF)
8425:(PDF)
8414:(PDF)
8283:S2CID
8230:S2CID
7948:S2CID
7885:S2CID
7660:(PDF)
7649:S2CID
7627:(PDF)
7494:(PDF)
7487:(PDF)
7365:[
7316:S2CID
6871:image
6832:phase
6814:cells
6759:grape
6548:laser
6503:glass
6489:Many
6254:of a
4538:and:
3875:of a
3863:of a
3861:power
3754:= 1.5
3266:<
3248:>
3202:phase
3112:with
2749:X-ray
2723:, or
2699:, or
2515:Both
2488:) is
1979:plane
1977:of a
1969:That
1495:prism
1214:0.999
1124:most
1114:2.65
1094:2.15
1084:1.77
1074:1.69
1063:1.58
1052:1.52
1042:1.49
1031:1.46
1020:1.31
1003:1.47
993:1.36
979:Water
961:1.000
946:1.000
931:1.000
916:1.000
900:Gases
552:phase
321:sound
68:light
62:is a
9138:PMID
9005:2014
8974:ISSN
8892:ISSN
8853:ISSN
8750:ISBN
8721:ISBN
8694:ISBN
8533:ISBN
8384:ISBN
8307:help
8273:ISBN
8185:ISBN
7974:ISBN
7783:ISBN
7749:PMID
7731:ISSN
7639:ISBN
7502:2016
7469:2018
7237:ISBN
7204:ISBN
7176:ISBN
6997:Brix
6924:any
6922:cite
6773:for
6769:and
6704:sin
6644:and
6617:GRIN
6612:GRIN
6562:and
6501:and
6256:mole
6236:– 1)
6225:– 1)
5482:and
5470:and
5449:and
5182:and
5099:and
4285:and
4264:and
4209:and
4022:The
3895:and
3877:lens
3871:The
3859:The
3746:and
3503:>
3208:and
3124:and
3116:and
3094:atom
3028:atom
2771:(or
2751:and
2747:For
2735:and
2727:and
2711:and
2703:and
2687:and
2678:and
2658:and
2519:and
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2007:= 2π
1747:and
1733:and
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1301:and
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1225:1 −
1155:For
1120:For
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850:and
574:and
556:wave
445:c =
432:The
342:The
326:For
317:wave
293:real
267:and
207:= c/
150:and
128:and
111:sin
97:sin
54:(or
9283:doi
9130:doi
9093:doi
9081:116
9042:doi
9030:238
8966:doi
8927:doi
8884:doi
8880:199
8845:doi
8841:193
8376:doi
8265:doi
8222:doi
8177:doi
7940:doi
7877:doi
7739:PMC
7723:doi
7631:doi
7578:doi
7537:doi
7525:116
7411:doi
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7264:413
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1886:abs
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1016:Ice
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4258:ε
4252:r
4248:ε
4239:r
4236:ε
4228:n
4223:r
4220:μ
4198:r
4195:μ
4185:r
4182:ε
4167:,
4159:r
4147:r
4136:=
4133:n
4099:.
4084:n
4081:=
4075:m
4072:u
4069:N
4064:A
4053:θ
4049:n
4037:A
4034:(
4012:f
3998:,
3991:]
3983:2
3979:R
3975:1
3963:1
3959:R
3955:1
3949:[
3945:)
3942:1
3936:n
3933:(
3930:=
3925:f
3922:1
3901:2
3898:R
3892:1
3889:R
3881:n
3836:.
3829:)
3822:1
3818:n
3812:2
3808:n
3802:(
3792:=
3786:B
3766:p
3752:2
3749:n
3742:1
3739:n
3722:.
3716:2
3711:|
3703:2
3699:n
3695:+
3690:1
3686:n
3678:2
3674:n
3665:1
3661:n
3654:|
3649:=
3644:0
3640:R
3594:.
3589:)
3582:1
3578:n
3572:2
3568:n
3562:(
3554:=
3548:c
3531:1
3528:θ
3509:,
3506:1
3498:1
3480:2
3476:n
3470:1
3466:n
3452:2
3449:θ
3406:.
3401:2
3385:2
3381:n
3377:=
3372:1
3356:1
3352:n
3336:2
3333:θ
3327:1
3324:θ
3310:2
3307:n
3301:1
3298:n
3285:1
3282:θ
3278:2
3275:θ
3271:1
3268:v
3264:2
3261:v
3253:1
3250:n
3246:2
3243:n
3189:.
3186:d
3183:n
3180:=
3166:d
3157:.
3118:β
3114:δ
3090:n
3082:f
3072:2
3065:2
3055:0
3051:r
3044:=
3024:n
3020:)
3013:f
3009:+
3006:Z
3003:(
2994:2
2987:2
2977:0
2973:r
2966:=
2945:.
2929:f
2925:i
2922:+
2915:f
2911:+
2908:Z
2905:=
2902:f
2888:Z
2884:Z
2879:e
2876:n
2871:λ
2862:0
2859:r
2838:2
2830:e
2825:n
2819:2
2809:0
2805:r
2798:=
2780:δ
2775:n
2764:δ
2759:n
2737:κ
2733:n
2729:δ
2725:ψ
2721:T
2717:R
2713:κ
2709:n
2705:δ
2701:ψ
2697:T
2693:R
2689:κ
2685:n
2680:δ
2676:ψ
2670:T
2666:R
2660:κ
2656:n
2648:E
2644:n
2639:E
2635:κ
2623:κ
2619:n
2590:κ
2580:n
2575:n
2564:n
2559:n
2548:κ
2533:κ
2526:κ
2521:κ
2517:n
2509:κ
2505:0
2502:λ
2498:α
2494:p
2491:δ
2485:e
2474:0
2471:λ
2469:/
2467:κ
2463:α
2442:.
2435:0
2426:/
2422:x
2413:4
2406:e
2400:0
2396:I
2392:=
2389:)
2386:x
2383:(
2380:I
2364:κ
2344:.
2340:]
2334:)
2331:t
2322:x
2319:k
2316:(
2313:i
2309:e
2303:0
2298:E
2292:[
2280:0
2271:/
2267:x
2258:2
2251:e
2247:=
2236:]
2230:)
2227:t
2216:0
2207:/
2203:x
2200:)
2194:i
2191:+
2188:n
2185:(
2179:2
2176:(
2173:i
2169:e
2163:0
2158:E
2152:[
2144:=
2133:]
2127:)
2124:t
2115:x
2107:k
2102:(
2099:i
2095:e
2089:0
2084:E
2078:[
2070:=
2063:)
2060:t
2057:,
2054:x
2051:(
2047:E
2032:x
2027:0
2024:λ
2018:0
2015:λ
2013:/
2010:n
2004:k
1997:n
1991:k
1983:x
1971:κ
1952:c
1948:)
1942:(
1933:2
1927:=
1924:)
1918:(
1863:κ
1855:n
1839:.
1833:i
1830:+
1827:n
1824:=
1816:n
1779:D
1775:d
1769:(
1767:D
1762:D
1760:n
1749:e
1745:d
1737:e
1735:V
1730:d
1728:V
1720:e
1716:d
1671:.
1662:d
1659:e
1656:r
1651:n
1641:e
1638:u
1635:l
1632:b
1627:n
1621:1
1612:w
1609:o
1606:l
1603:l
1600:e
1597:y
1592:n
1585:=
1582:V
1485:.
1437:c
1429:c
1349:.
1241:(
1229:×
1222:=
893:1
881:n
861:λ
852:B
848:A
834:,
827:2
819:B
814:+
811:A
808:=
805:)
799:(
796:n
775:λ
767:C
763:B
759:A
755:λ
751:n
737:,
731:+
724:4
716:C
711:+
704:2
696:B
691:+
688:A
685:=
682:)
676:(
673:n
634:n
630:µ
626:m
622:n
538:.
533:v
530:1
522:n
512:v
508:n
504:c
490:.
485:v
481:c
475:=
472:n
462:v
437:n
422:2
419:n
400:.
393:2
389:v
383:1
379:v
373:=
364:n
349:n
298:n
253:λ
251:/
249:v
245:f
242:(
235:0
232:λ
226:n
224:/
222:0
219:λ
215:λ
209:n
205:v
186:n
156:2
153:n
147:1
144:n
134:2
131:θ
125:1
122:θ
116:2
113:θ
109:2
106:n
102:1
99:θ
95:1
92:n
20:)
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