Refractive index - Knowledge

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

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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

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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:

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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

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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

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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

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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

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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

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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

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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.

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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.).

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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

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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

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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

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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

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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

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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

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are examples of liquids that are more refractive, but less dense, than water, contrary to the general correlation between density and refractive index.

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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

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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

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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.

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Depending on the relative phase of the original driving wave and the waves radiated by the charge motion, there are several possibilities:

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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: 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

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Thus refractive index in a non-magnetic media is the ratio of the vacuum wave impedance to the wave impedance of the medium.

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Young did not use a symbol for the index of refraction, in 1807. In the later years, others started using different symbols:

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with wavelength. For visible light normal dispersion means that the refractive index is higher for blue light than for red.

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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.

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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 17: 8760: 6886:

direction of the difference in the transverse shift. In interferometry the illumination is split up into two beams by a

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indicates the amount of attenuation when the electromagnetic wave propagates through the material. It is related to the

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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

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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,

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Bor, Z.; Osvay, K.; Rácz, B.; Szabó, G. (1990). "Group refractive index measurement by Michelson interferometer".

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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

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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

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being the vacuum wavelength; this can be inserted into the plane wave expression for a wave travelling in the

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Birefringent materials can give rise to colors when placed between crossed polarizers. This is the basis for

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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

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of the medium filling the space between the sample and the lens and the half collection angle of light

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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

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At the atomic scale, an electromagnetic wave's phase velocity is slowed in a material because the

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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: 2663: 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

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of light at the interface between two media of different refractive indices, with

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can be used. It is an empirical formula that works well in describing dispersion.

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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

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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

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When light moves from one medium to another, it changes direction, i.e. it is

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An example of a plasma with an index of refraction less than unity is Earth's

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Rupp, Fabian; Jedamzik, Ralf; Bartelmess, Lothar; Petzold, Uwe (2021-09-12).

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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 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 ( 18:Index of refraction 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: 7290: 7269: 7248: 7241: 7215: 7208: 7187: 7180: 7126: 7124: 7121: 7118: 7117: 7071: 7070: 7068: 7065: 7063: 7062: 7057: 7052: 7047: 7042: 7037: 7032: 7027: 7022: 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: 6091: 6089: 6087: 6078: 6075: 6071: 6066: 6063: 6057: 6049: 6045: 6041: 6036: 6033: 6029: 6025: 6019: 6014: 6010: 6004: 6001: 5999: 5997: 5994: 5993: 5973: 5970: 5964: 5944: 5936: 5932: 5927: 5921: 5917: 5908: 5904: 5900: 5897: 5894: 5891: 5889: 5884: 5879: 5875: 5874: 5871: 5865: 5862: 5857: 5848: 5844: 5839: 5833: 5829: 5820: 5816: 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: 8186: 8182: 8178: 8174: 8166: 8152: 8148: 8141: 8127: 8126:Oharacorp.com 8123: 8116: 8102: 8098: 8091: 8076: 8072: 8071: 8066: 8059: 8044: 8040: 8039: 8034: 8027: 8025: 8009: 8005: 8004: 7999: 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: 8752: 8723: 8696: 8535: 8386: 8285: 8275: 8232: 8187: 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:. 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