Aray of light beingrefracted through a glass slabRefraction of a light ray
Inoptics, therefractive index (orrefraction index) of anoptical medium is theratio of the apparent speed of light in the air or vacuum to the speed in the medium. The refractive index determines how much the path oflight is bent, orrefracted, when entering a material. This is described bySnell's law of refraction,n1 sinθ1 =n2 sinθ2, whereθ1 andθ2 are theangle of incidence and angle of refraction, respectively, of a ray crossing the interface between two media with refractive indicesn1 andn2. The refractive indices also determine the amount of light that isreflected when reaching the interface, as well as the critical angle fortotal internal reflection, their intensity (Fresnel equations) andBrewster's angle.[1]
The refractive index,, can be seen as the factor by which the speed and thewavelength of the radiation are reduced with respect to their vacuum values: the speed of light in a medium isv = c/n, and similarly the wavelength in that medium isλ =λ0/n, whereλ0 is the wavelength of that light in vacuum. This implies that vacuum has a refractive index of 1, and assumes that thefrequency (f =v/λ) of the wave is not affected by the refractive index.
The refractive index may vary with wavelength. This causes white light to split into constituent colors when refracted. This is calleddispersion. This effect can be observed inprisms andrainbows, and aschromatic aberration in lenses. Light propagation inabsorbing materials can be described using acomplex-valued refractive index.[2] Theimaginary part then handles theattenuation, while thereal 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 forn must specify the wavelength used in the measurement.
The concept of refractive index applies across the fullelectromagnetic spectrum, fromX-rays toradio waves. It can also be applied towave phenomena such assound. In this case, thespeed of sound is used instead of that of light, and a reference medium other than vacuum must be chosen.[3] Refraction also occurs in oceans when light passes into thehalocline where salinity has impacted the density of the water column.
Forlenses (such aseye glasses), a lens made from a high refractive index material will be thinner, and hence lighter, than a conventional lens with a lower refractive index. Such lenses are generally more expensive to manufacture than conventional ones.
Therelative refractive index of an optical medium 2 with respect to another reference medium 1 (n21) is given by the ratio of speed of light in medium 1 to that in medium 2. This can be expressed as follows:If the reference medium 1 isvacuum, then the refractive index of medium 2 is considered with respect to vacuum. It is simply represented asn2 and is called theabsolute refractive index of medium 2.
Theabsolute refractive indexn of an optical medium is defined as the ratio of thespeed of light in vacuum,c =299792458 m/s, and thephase velocityv of light in the medium,Sincec is constant,n is inversely proportional tov:The phase velocity is the speed at which the crests or thephase of thewave moves, which may be different from thegroup velocity, the speed at which the pulse of light or theenvelope of the wave moves.[1] Historicallyair at a standardizedpressure andtemperature has been common as a reference medium.
Thomas Young coined the termindex of refraction in 1807.
Thomas Young was presumably the person who first used, and invented, the name "index of refraction", in 1807.[4]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.Newton, who called it the "proportion of the sines of incidence and refraction", wrote it as a ratio of two numbers, like "529 to 396" (or "nearly 4 to 3"; for water).[5]Hauksbee, who called it the "ratio of refraction", wrote it as a ratio with a fixed numerator, like "10000 to 7451.9" (for urine).[6]Hutton wrote it as a ratio with a fixed denominator, like 1.3358 to 1 (water).[7]
Young did not use a symbol for the index of refraction, in 1807. In the later years, others started using different symbols:n,m, andµ.[8][9][10] The symboln gradually prevailed.
Diamonds have a very high refractive index of 2.417.
Refractive index also varies with wavelength of the light as given byCauchy's equation. The most general form of this equation iswheren is the refractive index,λ is the wavelength, andA,B,C, etc., arecoefficients that can be determined for a material by fitting the equation to measured refractive indices at known wavelengths. The coefficients are usually quoted forλ as thevacuum wavelength inmicrometres.
Usually, it is sufficient to use a two-term form of the equation:where the coefficientsA andB are determined specifically for this form of the equation.
Forvisible light mosttransparent media have refractive indices between 1 and 2. A few examples are given in the adjacent table. These values are measured at the yellow doubletD-line ofsodium, with a wavelength of 589nanometers, as is conventionally done.[15] 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, withaerogel 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.[16]Moissanite lies at the other end of the range with a refractive index as high as 2.65. Most plastics have refractive indices in the range from 1.3 to 1.7, but somehigh-refractive-index polymers can have values as high as 1.76.[17]
Forinfrared light refractive indices can be considerably higher.Germanium is transparent in the wavelength region from2 to 14 μm and has a refractive index of about 4.[18] A type of new materials termed "topological insulators", was recently found which have high refractive index of up to 6 in the near to mid infrared frequency range. Moreover, topological insulators are transparent when they have nanoscale thickness. These properties are potentially important for applications in infrared optics.[19]
According to thetheory of relativity, no information can travel faster than the speed of light in vacuum, but this does not mean that the refractive index cannot be less than 1. The refractive index measures thephase velocity of light, which does not carryinformation.[20][a] 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 indexbelow 1. This can occur close toresonance frequencies, for absorbing media, inplasmas, and forX-rays. In the X-ray regime the refractive indices are lower than but veryclose to 1 (exceptions close to some resonance frequencies).[21]As an example, water has a refractive index of0.99999974 =1 −2.6×10−7 for X-ray radiation at a photon energy of30 keV (0.04 nm wavelength).[21]
An example of a plasma with an index of refraction less than unity is Earth'sionosphere. Since the refractive index of the ionosphere (aplasma), is less than unity, electromagnetic waves propagating through the plasma are bent "away from the normal" (seeGeometric optics) allowing the radio wave to be refracted back toward earth, thus enabling long-distance radio communications. See alsoRadio Propagation andSkywave.[22]
Recent research has also demonstrated the "existence" of materials with a negative refractive index, which can occur ifpermittivity andpermeability have simultaneous negative values.[23] This can be achieved with periodically constructedmetamaterials. The resultingnegative refraction (i.e., a reversal ofSnell's law) offers the possibility of thesuperlens and other new phenomena to be actively developed by means ofmetamaterials.[24][25]
At the atomic scale, an electromagnetic wave's phase velocity is slowed in a material because theelectric field creates a disturbance in the charges of each atom (primarily theelectrons) proportional to theelectric susceptibility of the medium. (Similarly, themagnetic field creates a disturbance proportional to themagnetic susceptibility.) As the electromagnetic fields oscillate in the wave, the charges in the material will be "shaken" back and forth at the same frequency.[1]: 67 The charges thus radiate their own electromagnetic wave that is at the same frequency, but usually with aphase delay, as the charges may move out of phase with the force driving them (seesinusoidally driven harmonic oscillator). The light wave traveling in the medium is the macroscopicsuperposition (sum) 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 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 (seescattering).
Depending on the relative phase of the original driving wave and the waves radiated by the charge motion, there are several possibilities:
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 1.[26][page needed]
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), withX-rays in ordinary materials, and with radio waves in Earth'sionosphere. It corresponds to apermittivity less than 1, which causes the refractive index to be also less than unity and thephase velocity of light greater than thespeed of light in vacuumc (note that thesignal velocity is still less thanc, as discussed above). If the response is sufficiently strong and out-of-phase, the result is a negative value ofpermittivity and imaginary index of refraction, as observed in metals or plasma.[26][page needed]
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 islight absorption in opaque materials and corresponds to animaginary refractive index.
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 inlasers due tostimulated emission. It corresponds to an imaginary index of refraction, with the opposite sign to that of absorption.
For most materials at visible-light frequencies, the phase is somewhere between 90° and 180°, corresponding to a combination of both refraction and absorption.
Light of different colors has slightly different refractive indices in water and therefore shows up at different positions in therainbow.In a triangularprism,dispersion causes different colors to refract at different angles, splittingwhite light into arainbow 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.The variation of refractive index with wavelength for various glasses. The shaded zone indicates the range of visible light.
The refractive index of materials varies with the wavelength (andfrequency) of light.[27] This is called dispersion and causesprisms andrainbows to divide white light into its constituent spectralcolors.[28] As the refractive index varies with wavelength, so will the refraction angle as light goes from one material to another. Dispersion also causes thefocal length oflenses to be wavelength dependent. This is a type ofchromatic aberration, which often needs to be corrected for in imaging systems. In regions of the spectrum where the material does not absorb light, the refractive index tends todecrease with increasing wavelength, and thusincrease with frequency. This is called "normal dispersion", in contrast to "anomalous dispersion", where the refractive indexincreases with wavelength.[27] For visible light normal dispersion means that the refractive index is higher for blue light than for red.
For optics in the visual range, the amount of dispersion of a lens material is often quantified by theAbbe number:[28]For a more accurate description of the wavelength dependence of the refractive index, theSellmeier equation can be used.[29] It is an empirical formula that works well in describing dispersion.Sellmeier coefficients are often quoted instead of the refractive index in tables.
Because of dispersion, it is usually important to specify the vacuum wavelength of light for which a refractive index is measured. Typically, measurements are done at various well-defined spectralemission lines.
Manufacturers of optical glass in general define principal index of refraction at yellow spectral line of helium (587.56 nm) and alternatively at a green spectral line of mercury (546.07 nm), calledd ande lines respectively.Abbe number is defined for both and denotedVd andVe. The spectral data provided by glass manufacturers is also often more precise for these two wavelengths.[30][31][32][33]
Both,d ande spectral lines are singlets and thus are suitable to perform a very precise measurements, such as spectral goniometric method.[34][35]
In practical applications, measurements of refractive index are performed on various refractometers, such asAbbe refractometer. Measurement accuracy of such typical commercial devices is in the order of 0.0002.[36][37] Refractometers usually measure refractive indexnD, defined for sodium doubletD (589.29 nm), which is actually a midpoint between two adjacent yellow spectral lines of sodium. Yellow spectral lines of helium (d) and sodium (D) are1.73 nm apart, which can be considered negligible for typical refractometers, but can cause confusion and lead to errors if accuracy is critical.
All three typical principle refractive indices definitions can be found depending on application and region,[38] so a proper subscript should be used to avoid ambiguity.
When light passes through a medium, some part of it will always beabsorbed. This can be conveniently taken into account by defining a complex refractive index,
The real and imaginary part of this refractive index are not independent, and are connected through theKramers–Kronig relations, i.e. the complex refractive index is alinear response function, ensuring causality.[39] Here, the real partn is the refractive index and indicates thephase velocity, while the imaginary partκ is called theextinction coefficient[40]: 36 indicates the amount of attenuation when the electromagnetic wave propagates through the material.[1]: 128 It is related to theabsorption coefficient,, through:[40]: 41 These values depend upon the frequency of the light used in the measurement.
Thatκ corresponds to absorption can be seen by inserting this refractive index into the expression forelectric field of aplane electromagnetic wave traveling in thex-direction. This can be done by relating the complexwave numberk to the complex refractive indexn throughk = 2πn/λ0, withλ0 being the vacuum wavelength; this can be inserted into the plane wave expression for a wave travelling in thex-direction as:
Here we see thatκ gives an exponential decay, as expected from theBeer–Lambert law. Since intensity is proportional to the square of the electric field, intensity will depend on the depth into the material as
and thus theabsorption coefficient isα = 4πκ/λ0,[1]: 128 and thepenetration depth (the distance after which the intensity is reduced by a factor of1/e) isδp = 1/α =λ0/4πκ.
Bothn andκ are dependent on the frequency. In most circumstancesκ > 0 (light is absorbed) orκ = 0 (light travels forever without loss). In special situations, especially in thegain medium oflasers, it is also possible thatκ < 0, corresponding to an amplification of the light.
An alternative convention usesn =n +iκ instead ofn =n −iκ, but whereκ > 0 still corresponds to loss. Therefore, these two conventions are inconsistent and should not be confused. The difference is related to defining sinusoidal time dependence asRe[exp(−iωt)] versusRe[exp(+iωt)]. SeeMathematical descriptions of opacity.
Dielectric loss and non-zero DC conductivity in materials cause absorption. Good dielectric materials such as glass have extremely low DC conductivity, and at low frequencies the dielectric loss is also negligible, resulting in almost no absorption. However, at higher frequencies (such as visible light), dielectric loss may increase absorption significantly, reducing the material'stransparency to these frequencies.
The realn, and imaginaryκ, parts of the complex refractive index are related through theKramers–Kronig relations. In 1986, A.R. Forouhi and I. Bloomer deduced anequation describingκ as a function of photon energy,E, applicable to amorphous materials. Forouhi and Bloomer then applied the Kramers–Kronig relation to derive the corresponding equation forn as a function ofE. The same formalism was applied to crystalline materials by Forouhi and Bloomer in 1988.
The refractive index and extinction coefficient,n andκ, are typically measured from quantities that depend on them, such asreflectance,R, or transmittance,T, or ellipsometric parameters,ψ andδ. The determination ofn andκ from such measured quantities will involve developing a theoretical expression forR orT, orψ andδ in terms of a valid physical model forn andκ. By fitting the theoretical model to the measuredR orT, orψ andδ using regression analysis,n andκ can be deduced.
ForX-ray andextreme ultraviolet radiation the complex refractive index deviates only slightly from unity and usually has a real part smaller than 1. It is therefore normally written asn = 1 −δ +iβ (orn = 1 −δ −iβ with the alternative convention mentioned above).[2] Far above the atomic resonance frequency delta can be given bywherer0 is theclassical electron radius,λ is the X-ray wavelength, andne is the electron density. One may assume the electron density is simply the number of electrons per atomZ multiplied by the atomic density, but more accurate calculation of the refractive index requires replacingZ with the complexatomic form factor. It follows thatwithδ andβ typically of the order of10−5 and10−6.
Optical path length (OPL) is the product of the geometric lengthd of the path light follows through a system, and the index of refraction of the medium through which it propagates,[41]This is an important concept in optics because it determines thephase of the light and governsinterference anddiffraction of light as it propagates. According toFermat's principle, light rays can be characterized as those curves thatoptimize the optical path length.[1]: 68–69
Refraction of light at the interface between two media of different refractive indices, withn2 >n1. Since thephase velocity is lower in the second medium (v2 <v1), the angle of refractionθ2 is less than the angle of incidenceθ1; that is, the ray in the higher-index medium is closer to the normal.
When light moves from one medium to another, it changes direction, i.e. it isrefracted. If it moves from a medium with refractive indexn1 to one with refractive indexn2, with anincidence angle to thesurface normal ofθ1, the refraction angleθ2 can be calculated fromSnell's law:[42]
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 into a medium with lower refractive index, the light will instead be refracted away from the normal, towards the surface.
If there is no angleθ2 fulfilling Snell's law, i.e.,the light cannot be transmitted and will instead undergototal internal reflection.[43]: 49–50 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 incidenceθ1 must be larger than the critical angle[44]
Apart from the transmitted light there is also areflected part. The reflection angle is equal to the incidence angle, and the amount of light that is reflected is determined by thereflectivity of the surface. The reflectivity can be calculated from the refractive index and the incidence angle with theFresnel equations, which fornormal incidence reduces to[43]: 44
For common glass in air,n1 = 1 andn2 = 1.5, and thus about 4% of the incident power is reflected.[45] At other incidence angles the reflectivity will also depend on thepolarization of the incoming light. At a certain angle calledBrewster's angle,p-polarized light (light with the electric field in theplane of incidence) will be totally transmitted. Brewster's angle can be calculated from the two refractive indices of the interface as[1]: 245
Theresolution of a good opticalmicroscope is mainly determined by thenumerical aperture (ANum) of itsobjective lens. The numerical aperture in turn is determined by the refractive indexn of the medium filling the space between the sample and the lens and the half collection angle of lightθ according to Carlsson (2007):[47]: 6
For this reasonoil immersion 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.[47]: 14
The refractive index of electromagnetic radiation equalswhereεr is the material'srelative permittivity, andμr is itsrelative permeability.[48]: 229 The refractive index is used for optics inFresnel equations andSnell's law; while the relative permittivity and permeability are used inMaxwell's equations and electronics. Most naturally occurring materials are non-magnetic at optical frequencies, that isμr is very close to 1, thereforen is approximately√εr.[49] In this particular case, the complex relative permittivityεr, with real and imaginary partsεr andɛ̃r, and the complex refractive indexn, with real and imaginary partsn andκ (the latter called the "extinction coefficient"), follow the relation
The wave impedance of a plane electromagnetic wave in a non-conductive medium is given by
whereZ0 is the vacuum wave impedance,μ andε are the absolute permeability and permittivity of the medium,εr is the material'srelative permittivity, andμr is itsrelative permeability.
In non-magnetic media (that is, in materials withμr = 1), and
Thus refractive index in a non-magnetic media is the ratio of the vacuum wave impedance to the wave impedance of the medium.
The reflectivityR0 between two media can thus be expressed both by the wave impedances and the refractive indices as
In general, it is assumed that the refractive index of a glass increases with itsdensity. 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 asLi2O andMgO, while the opposite trend is observed with glasses containingPbO andBaO as seen in the diagram at the right.
Many oils (such asolive oil) andethanol are examples of liquids that are more refractive, but less dense, than water, contrary to the general correlation between density and refractive index.
For air,n - 1 is proportional to the density of the gas as long as the chemical composition does not change.[52] This means that it is also proportional to the pressure and inversely proportional to the temperature forideal gases. 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.[53] 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.[54] Based on this concept, the refractive indices of organic materials can be calculated.
A scatter plot of bandgap energy versus optical refractive index for many common IV, III-V, and II-VI semiconducting elements / compounds.
The optical refractive index of a semiconductor tends to increase as thebandgap energy decreases. Many attempts[55] have been made to model this relationship beginning with T. S. Moses in 1949.[56] Empirical models can match experimental data over a wide range of materials and yet fail for important cases like InSb, PbS, and Ge.[57]
This negative correlation between refractive index and bandgap energy, along with a negative correlation between bandgap and temperature, means that many semiconductors exhibit a positive correlation between refractive index and temperature.[58] This is the opposite of most materials, where the refractive index decreases with temperature as a result of a decreasing material density.
"Group index" redirects here and is not to be confused withIndex of a subgroup.
Sometimes, a "group velocity refractive index", usually called thegroup index is defined:[citation needed]wherevg is thegroup velocity. This value should not be confused withn, which is always defined with respect to thephase velocity. When thedispersion is small, the group velocity can be linked to the phase velocity by the relation[43]: 22 whereλ 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
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)[59]whereλ0 is the wavelength in vacuum.
As shown in theFizeau experiment, when light is transmitted through a moving medium, its speed relative to an observer traveling with speedv in the same direction as the light is:
The momentum of photons in a medium of refractive indexn is a complex andcontroversial issue with two different values having different physical interpretations.[60]
In atmospheric applications,refractivity is defined asN =n – 1, often rescaled as either[61]N = 106 (n – 1)[62][63] orN = 108 (n – 1);[64] the multiplication factors are used because the refractive index for air,n deviates from unity by at most a few parts per ten thousand.
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.
Acalcite crystal laid upon a paper with some letters showingdouble refraction Birefringent materials can give rise to colors when placed between crossed polarizers. This is the basis forphotoelasticity.
In some materials, the refractive index depends on thepolarization and propagation direction of the light.[65] This is calledbirefringence or opticalanisotropy.
In the simplest form, uniaxial birefringence, there is only one special direction in the material. This axis is known as theoptical axis of the material.[1]: 230 Light with linear polarization perpendicular to this axis will experience anordinary refractive indexno while light polarized in parallel will experience anextraordinary refractive indexne.[1]: 236 The birefringence of the material is the difference between these indices of refraction,Δn =ne −no.[1]: 237 Light propagating in the direction of the optical axis will not be affected by the birefringence since the refractive index will beno 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.[1]: 233 This can be used to change the polarization direction of linearly polarized light or to convert between linear, circular, and elliptical polarizations withwaveplates.[1]: 237
Manycrystals are naturally birefringent, butisotropic materials such asplastics andglass can also often be made birefringent by introducing a preferred direction through, e.g., an external force or electric field. This effect is calledphotoelasticity, and can be used to reveal stresses in structures. The birefringent material is placed between crossedpolarizers. A change in birefringence alters the polarization and thereby the fraction of light that is transmitted through the second polarizer.
In the more general case of trirefringent materials described by the field ofcrystal optics, thedielectric constant is a rank-2tensor (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.
The strongelectric field of high intensity light (such as the output of alaser) may cause a medium's refractive index to vary as the light passes through it, giving rise tononlinear optics.[1]: 502 If the index varies quadratically with the field (linearly with the intensity), it is called theoptical Kerr effect and causes phenomena such asself-focusing andself-phase modulation.[1]: 264 If the index varies linearly with the field (a nontrivial linear coefficient is only possible in materials that do not possessinversion symmetry), it is known as thePockels effect.[1]: 265
A gradient-index lens with a parabolic variation of refractive index (n) with radial distance (x). The lens focuses light in the same way as a conventional lens.
The refractive index of liquids or solids can be measured withrefractometers. They typically measure some angle of refraction or the critical angle for total internal reflection. The firstlaboratory refractometers sold commercially were developed byErnst Abbe in the late 19th century.[66]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 raysparallel 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 atelescope,[clarification needed] or with a digitalphotodetector placed in the focal plane of a lens. The refractive indexn of the liquid can then be calculated from the maximum transmission angleθ asn =nG sinθ, wherenG is the refractive index of the prism.[67]
A handheld refractometer used to measure the sugar content of fruits
Ingemology, a different type of refractometer is used to measure the index of refraction and birefringence ofgemstones. 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.[68]
Unstained biological structures appear mostly transparent underbright-field microscopy 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:
To measure the spatial variation of the refractive index in a samplephase-contrast imaging methods are used. These methods measure the variations inphase of the light wave exiting the sample. The phase is proportional to theoptical path length the light ray has traversed, and thus gives a measure of theintegral 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 intointensity byinterference with a reference beam. In the visual spectrum this is done using Zernikephase-contrast microscopy,differential interference contrast microscopy (DIC), orinterferometry.
There exist severalphase-contrast X-ray imaging techniques to determine 2D or 3D spatial distribution of refractive index of samples in the X-ray regime.[69]
The refractive index is an important property of the components of anyoptical instrument. It determines the focusing power of lenses, the dispersive power of prisms, the reflectivity oflens coatings,[70] and the light-guiding nature ofoptical fiber.[71] 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. It can be used, for example, to measure the concentration of a solute in anaqueous solution.[72] It can also be used as a useful tool to differentiate between different types of gemstone, due to the uniquechatoyance each individual stone displays. Arefractometer 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 (seeBrix).
^One consequence of the real part ofn being less than unity is that it implies that the phase velocity inside the material,c/n, is larger than the velocity of light,c. This does not, however, violate the law of relativity, which requires that only signals carrying information do not travel faster thanc. 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 thanc.[20]
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