In optics, the refractive index or index of refraction of a material is a dimensionless number that describes how light propagates through that medium. It is defined as n = c v , displaystyle n= frac c v , where c is the speed of light in vacuum and v is the phase velocity of light in the medium. For example, the refractive index of water is 1.333, meaning that light travels 1.333 times faster in vacuum than in the water.
Refraction
The refractive index determines how much the path of light is bent, or
refracted, when entering a material. This is the first documented use
of refractive indices and is described by
Snell's law
Contents 1 Definition 2 History 3 Typical values 3.1
Refractive index
4 Microscopic explanation 5 Dispersion 6 Complex refractive index 7 Relations to other quantities 7.1 Optical path length
7.2 Refraction
7.3 Total internal reflection
7.4 Reflectivity
7.5 Lenses
7.6
Microscope
8 Nonscalar, nonlinear, or nonhomogeneous refraction 8.1 Birefringence 8.2 Nonlinearity 8.3 Inhomogeneity 9
Refractive index
9.1 Homogeneous media
9.2
Refractive index
10 Applications 11 See also 12 References 13 External links Definition[edit] The refractive index n of an optical medium is defined as the ratio of the speed of light in vacuum, c = 7008299792458000000♠299792458 m/s, and the phase velocity v of light in the medium,[1] n = c v . displaystyle n= frac c v . The phase velocity is the speed at which the crests or the phase of the wave moves, which may be different from the group velocity, the speed at which the pulse of light or the envelope of the wave moves. The definition above is sometimes referred to as the absolute refractive index or the absolute index of refraction to distinguish it from definitions where the speed of light in other reference media than vacuum is used.[1] Historically air at a standardized pressure and temperature has been common as a reference medium. History[edit] Thomas Young coined the term index of refraction. 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 next years, others started using different symbols: n, m, and µ.[8][9][10] The symbol n gradually prevailed. Typical values[edit] Diamonds have a very high refractive index of 2.42. Selected refractive indices at λ=589 nm. For references, see the extended List of refractive indices. Material n Vacuum 7000100000000000000♠1 Gases at 0 °C and 1 atm Air 7000100029300000000♠1.000293 Helium 7000100003600000000♠1.000036 Hydrogen 7000100013200000000♠1.000132 Carbon dioxide 7000100045000000000♠1.00045 Liquids at 20 °C Water 1.333 Ethanol 1.36 Olive oil 1.47 Solids Ice 1.31 PMMA (acrylic, plexiglas, lucite, perspex) 1.49 Window glass 1.52[11]
Polycarbonate
Flint glass
Sapphire 1.77[13] Cubic zirconia 2.15 Diamond 2.42 Moissanite 2.65 See also: List of refractive indices
For visible light most transparent media have refractive indices
between 1 and 2. A few examples are given in the adjacent table. These
values are measured at the yellow doublet Dline of sodium, with a
wavelength of 589 nanometers, as is conventionally done.[14] Gases at
atmospheric pressure have refractive indices close to 1 because of
their low density. Almost all solids and liquids have refractive
indices above 1.3, with aerogel as the clear exception.
Aerogel
A splitring resonator array arranged to produce a negative index of refraction for microwaves Recent research has also demonstrated the existence of materials with a negative refractive index, which can occur if permittivity and permeability have simultaneous negative values.[22] This can be achieved with periodically constructed metamaterials. The resulting negative refraction (i.e., a reversal of Snell's law) offers the possibility of the superlens and other exotic phenomena.[23] Microscopic explanation[edit] Main article: Ewald–Oseen extinction theorem At the microscale, an electromagnetic wave's phase velocity is slowed in a material because the electric field creates a disturbance in the charges of each atom (primarily the electrons) proportional to the electric susceptibility of the medium. (Similarly, the magnetic field creates a disturbance proportional to the magnetic susceptibility.) As the electromagnetic fields oscillate in the wave, 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 a phase delay, as the charges may move out of phase with the force driving them (see sinusoidally driven harmonic oscillator). The light wave traveling in the medium is the macroscopic superposition (sum) of all such contributions in the material: the original wave plus the waves radiated by all the moving charges. This wave is typically a wave with the same frequency but shorter wavelength than the original, leading to a slowing of the wave's phase velocity. Most of the radiation from oscillating material charges will modify the incoming wave, changing its velocity. However, some net energy will be radiated in other directions or even at other frequencies (see scattering). Depending on 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.[24] 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 Xrays in ordinary materials, and with radio waves in Earth's ionosphere. It corresponds to a permittivity less than 1, which causes the refractive index to be also less than unity and the phase velocity of light greater than the speed of light in vacuum c (note that the signal velocity is still less than c, as discussed above). If the response is sufficiently strong and outofphase, the result is a negative value of permittivity and imaginary index of refraction, as observed in metals or plasma.[24] 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 light absorption in opaque materials and corresponds to an imaginary 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 in lasers due to stimulated emission. It corresponds to an imaginary index of refraction, with the opposite sign to that of absorption. For most materials at visiblelight frequencies, the phase is somewhere between 90° and 180°, corresponding to a combination of both refraction and absorption. Dispersion[edit] Light of different colors has slightly different refractive indices in water and therefore shows up at different positions in the rainbow. In a prism, dispersion causes different colors to refract at different angles, splitting white light into a rainbow of colors. The variation of refractive index with wavelength for various glasses, the red zone indicates the range of visible light. Main article: Dispersion (optics) The refractive index of materials varies with the wavelength (and frequency) of light.[25] This is called dispersion and causes prisms and rainbows to divide white light into its constituent spectral colors.[26] As the refractive index varies with wavelength, so will the refraction angle as light goes from one material to another. Dispersion also causes the focal length of lenses to be wavelength dependent. This is a type of chromatic aberration, which often needs to be corrected for in imaging systems. In regions of the spectrum where the material does not absorb light, the refractive index tends to decrease with increasing wavelength, and thus increase with frequency. This is called "normal dispersion", in contrast to "anomalous dispersion", where the refractive index increases with wavelength.[25] For visible light normal dispersion means that the refractive index is higher for blue light than for red. For optics in the visual range, the amount of dispersion of a lens material is often quantified by the Abbe number:[26] V = n y e l l o w − 1 n b l u e − n r e d . displaystyle V= frac n_ mathrm yellow 1 n_ mathrm blue n_ mathrm red . For a more accurate description of the wavelength dependence of the
refractive index, the
Sellmeier equation
A graduated neutral density filter showing light absorption in the upper half See also: Mathematical descriptions of opacity When light passes through a medium, some part of it will always be attenuated. This can be conveniently taken into account by defining a complex refractive index, n _ = n + i κ . displaystyle underline n =n+ikappa . Here, the real part n is the refractive index and indicates the phase velocity, while the imaginary part κ is called the extinction coefficient — although κ can also refer to the mass attenuation coefficient—[28]:3 and indicates the amount of attenuation when the electromagnetic wave propagates through the material.[1]:128 That κ corresponds to attenuation can be seen by inserting this refractive index into the expression for electric field of a plane electromagnetic wave traveling in the zdirection. We can do this by relating the complex wave number k to the complex refractive index n through k = 2πn/λ0, with λ0 being the vacuum wavelength; this can be inserted into the plane wave expression as E ( z , t ) = Re [ E 0 e i ( k _ z − ω t ) ] = Re [ E 0 e i ( 2 π ( n + i κ ) z / λ 0 − ω t ) ] = e − 2 π κ z / λ 0 Re [ E 0 e i ( k z − ω t ) ] . displaystyle mathbf E (z,t)=operatorname Re !left[mathbf E _ 0 e^ i( underline k zomega t) right]=operatorname Re !left[mathbf E _ 0 e^ i(2pi (n+ikappa )z/lambda _ 0 omega t) right]=e^ 2pi kappa z/lambda _ 0 operatorname Re !left[mathbf E _ 0 e^ i(kzomega t) right]. Here we see that κ gives an exponential decay, as expected from the
Beer–Lambert law. Since intensity is proportional to the square of
the electric field, it will depend on the depth into the material as
exp(−4πκz/λ0), and the attenuation coefficient becomes α =
4πκ/λ0.[1]:128 This also relates it to the penetration depth, the
distance after which the intensity is reduced by 1/e, δp = 1/α =
λ0/(4πκ).
Both n and κ are dependent on the frequency. In most circumstances κ
> 0 (light is absorbed) or κ = 0 (light travels forever without
loss). In special situations, especially in the gain medium of lasers,
it is also possible that κ < 0, corresponding to an amplification
of the light.
An alternative convention uses n = n − iκ instead of n = n + iκ,
but where κ > 0 still corresponds to loss. Therefore, these two
conventions are inconsistent and should not be confused. The
difference is related to defining sinusoidal time dependence as
Re[exp(−iωt)] versus Re[exp(+iωt)]. See Mathematical descriptions
of opacity.
Dielectric loss and nonzero 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's transparency to
these frequencies.
The real, n, and imaginary, κ, parts of the complex refractive index
are related through the Kramers–Kronig relations. In 1986 A.R.
Forouhi and I. Bloomer deduced an equation describing κ as a function
of photon energy, E, applicable to amorphous materials. Forouhi and
Bloomer then applied the
Kramers–Kronig relation
δ = r 0 λ 2 n e 2 π displaystyle delta = frac r_ 0 lambda ^ 2 n_ e 2pi where r 0 displaystyle r_ 0 is the classical electron radius, λ displaystyle lambda is the
Xray
n e displaystyle n_ e is the electron density. One may assume the electron density is simply the number of electrons per atom Z multiplied by the atomic density, but more accurate calculation of the refractive index requires replacing Z with the complex atomic form factor f = Z + f ′ + i f ″ displaystyle f=Z+f'+if'' . It follows that δ = r 0 λ 2 2 π ( Z + f ′ ) n A t o m displaystyle delta = frac r_ 0 lambda ^ 2 2pi (Z+f')n_ Atom β = r 0 λ 2 2 π f ″ n A t o m displaystyle beta = frac r_ 0 lambda ^ 2 2pi f''n_ Atom with δ displaystyle delta and β displaystyle beta typically of the order of 10−5 and 10−6. Relations to other quantities[edit] Optical path length[edit] The colors of a soap bubble are determined by the optical path length through the thin soap film in a phenomenon called thinfilm interference. Optical path length (OPL) is the product of the geometric length d of the path light follows through a system, and the index of refraction of the medium through which it propagates,[29] OPL = n d . displaystyle text OPL =nd. This is an important concept in optics because it determines the phase of the light and governs interference and diffraction of light as it propagates. According to Fermat's principle, light rays can be characterized as those curves that optimize the optical path length.[1]:68–69 Refraction[edit] Main article: Refraction
Refraction
When light moves from one medium to another, it changes direction, i.e. it is refracted. If it moves from a medium with refractive index n1 to one with refractive index n2, with an incidence angle to the surface normal of θ1, the refraction angle θ2 can be calculated from Snell's law:[30] n 1 sin θ 1 = n 2 sin θ 2 . displaystyle n_ 1 sin theta _ 1 =n_ 2 sin theta _ 2 . 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. Total internal reflection[edit] Main article: Total internal reflection
Total internal reflection
If there is no angle θ2 fulfilling Snell's law, i.e., n 1 n 2 sin θ 1 > 1 , displaystyle frac n_ 1 n_ 2 sin theta _ 1 >1, the light cannot be transmitted and will instead undergo total internal reflection.[31]: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 incidence θ1 must be larger than the critical angle[32] θ c = arcsin ( n 2 n 1 ) . displaystyle theta _ mathrm c =arcsin !left( frac n_ 2 n_ 1 right)!. Reflectivity[edit] Apart from the transmitted light there is also a reflected part. The reflection angle is equal to the incidence angle, and the amount of light that is reflected is determined by the reflectivity of the surface. The reflectivity can be calculated from the refractive index and the incidence angle with the Fresnel equations, which for normal incidence reduces to[31]:44 R 0 =
n 1 − n 2 n 1 + n 2
2 . displaystyle R_ 0 =left frac n_ 1 n_ 2 n_ 1 +n_ 2 right^ 2 !. For common glass in air, n1 = 1 and n2 = 1.5, and thus about 4% of the
incident power is reflected.[33] At other incidence angles the
reflectivity will also depend on the polarization of the incoming
light. At a certain angle called Brewster's angle, ppolarized light
(light with the electric field in the plane of incidence) will be
totally transmitted.
Brewster's angle
θ B = arctan ( n 2 n 1 ) . displaystyle theta _ mathrm B =arctan !left( frac n_ 2 n_ 1 right)!. Lenses[edit] The power of a magnifying glass is determined by the shape and refractive index of the lens. The focal length of a lens is determined by its refractive index n and the radii of curvature R1 and R2 of its surfaces. The power of a thin lens in air is given by the Lensmaker's formula:[34] 1 f = ( n − 1 ) ( 1 R 1 − 1 R 2 ) , displaystyle frac 1 f =(n1)!left( frac 1 R_ 1  frac 1 R_ 2 right)!, where f is the focal length of the lens.
Microscope
N A = n sin θ . displaystyle mathrm NA =nsin theta . For this reason oil 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.[35]:14
Relative permittivity
n = ε r μ r , displaystyle n= sqrt varepsilon _ mathrm r mu _ mathrm r , where εr is the material's relative permittivity, and μr is its
relative permeability.[36]:229 The refractive index is used for optics
in
Fresnel equations
ε _ r = ε r + i ε ~ r = n _ 2 = ( n + i κ ) 2 , displaystyle underline varepsilon _ mathrm r =varepsilon _ mathrm r +i tilde varepsilon _ mathrm r = underline n ^ 2 =(n+ikappa )^ 2 , and their components are related by:[37] ε r = n 2 − κ 2 , displaystyle varepsilon _ mathrm r =n^ 2 kappa ^ 2 , ε ~ r = 2 n κ , displaystyle tilde varepsilon _ mathrm r =2nkappa , and: n =
ε _ r
+ ε r 2 , displaystyle n= sqrt frac underline varepsilon _ mathrm r +varepsilon _ mathrm r 2 , κ =
ε _ r
− ε r 2 . displaystyle kappa = sqrt frac underline varepsilon _ mathrm r varepsilon _ mathrm r 2 . where
ε _ r
= ε r 2 + ε ~ r 2 displaystyle underline varepsilon _ mathrm r = sqrt varepsilon _ mathrm r ^ 2 + tilde varepsilon _ mathrm r ^ 2 is the complex modulus. Density[edit] Relation between the refractive index and the density of silicate and borosilicate glasses[38] In general, the refractive index of a glass increases with its density. However, there does not exist an overall linear relation 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 Li2O and MgO, while the opposite trend is observed with glasses containing PbO and BaO as seen in the diagram at the right. Many oils (such as olive oil) and ethyl alcohol are examples of liquids which are more refractive, but less dense, than water, contrary to the general correlation between density and refractive index. For gases, n − 1 is proportional to the density of the gas as long as the chemical composition does not change.[39] This means that it is also proportional to the pressure and inversely proportional to the temperature for ideal gases. Group index[edit] Sometimes, a "group velocity refractive index", usually called the group index is defined:[citation needed] n g = c v g , displaystyle n_ mathrm g = frac mathrm c v_ mathrm g , where vg is the group velocity. This value should not be confused with n, which is always defined with respect to the phase velocity. When the dispersion is small, the group velocity can be linked to the phase velocity by the relation[31]:22 v g = v − λ d v d λ , displaystyle v_ mathrm g =vlambda frac mathrm d v mathrm d lambda , where λ 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 n g = n 1 + λ n d n d λ . displaystyle n_ mathrm g = frac n 1+ frac lambda n frac mathrm d n mathrm d lambda . 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) [40] v g = c ( n − λ 0 d n d λ 0 ) − 1 , displaystyle v_ mathrm g =mathrm c !left(nlambda _ 0 frac mathrm d n mathrm d lambda _ 0 right)^ 1 !, n g = n − λ 0 d n d λ 0 , displaystyle n_ mathrm g =nlambda _ 0 frac mathrm d n mathrm d lambda _ 0 , where λ0 is the wavelength in vacuum.
Momentum (Abraham–Minkowski controversy)[edit]
Main article: Abraham–Minkowski controversy
In 1908,
Hermann Minkowski
p = n E c , displaystyle p= frac nE mathrm c , where E is energy of the photon, c is the speed of light in vacuum and
n is the refractive index of the medium. In 1909,
Max Abraham
p = E n c . displaystyle p= frac E nmathrm c . A 2010 study suggested that both equations are correct, with the Abraham version being the kinetic momentum and the Minkowski version being the canonical momentum, and claims to explain the contradicting experimental results using this interpretation.[43] Other relations[edit] As shown in the Fizeau experiment, when light is transmitted through a moving medium, its speed relative to an observer traveling with speed v in the same direction as the light is: V = c n + v ( 1 − 1 n 2 ) 1 + v c n ≈ c n + v ( 1 − 1 n 2 ) . displaystyle V= frac mathrm c n + frac vleft(1 frac 1 n^ 2 right) 1+ frac v cn approx frac mathrm c n +vleft(1 frac 1 n^ 2 right) . The refractive index of a substance can be related to its polarizability with the Lorentz–Lorenz equation or to the molar refractivities of its constituents by the Gladstone–Dale relation. Refractivity[edit] In atmospheric applications, the refractivity is taken as N = n – 1. Atmospheric refractivity is often expressed as either[44] N = 7006100000000000000♠106(n – 1)[45][46] or N = 7008100000000000000♠108(n – 1)[47] The multiplication factors are used because the refractive index for air, n deviates from unity by at most a few parts per ten thousand. Molar refractivity, on the other hand, is a measure of the total polarizability of a mole of a substance and can be calculated from the refractive index as A = M ρ n 2 − 1 n 2 + 2 , displaystyle A= frac M rho frac n^ 2 1 n^ 2 +2 , where ρ is the density, and M is the molar mass.[31]:93 Nonscalar, nonlinear, or nonhomogeneous refraction[edit] 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. Birefringence[edit] Main article: Birefringence A calcite crystal laid upon a paper with some letters showing double refraction Birefringent materials can give rise to colors when placed between crossed polarizers. This is the basis for photoelasticity. In some materials the refractive index depends on the polarization and propagation direction of the light.[48] This is called birefringence or optical anisotropy. In the simplest form, uniaxial birefringence, there is only one special direction in the material. This axis is known as the optical axis of the material.[1]:230 Light with linear polarization perpendicular to this axis will experience an ordinary refractive index no while light polarized in parallel will experience an extraordinary refractive index ne.[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 be no 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 with waveplates.[1]:237 Many crystals are naturally birefringent, but isotropic materials such as plastics and glass can also often be made birefringent by introducing a preferred direction through, e.g., an external force or electric field. This can be utilized in the determination of stresses in structures using photoelasticity. The birefringent material is then placed between crossed polarizers. A change in birefringence will alter 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 of crystal optics, the dielectric constant is a rank2 tensor (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. Nonlinearity[edit] Main article: Nonlinear optics The strong electric field of high intensity light (such as output of a laser) may cause a medium's refractive index to vary as the light passes through it, giving rise to nonlinear optics.[1]:502 If the index varies quadratically with the field (linearly with the intensity), it is called the optical Kerr effect and causes phenomena such as selffocusing and selfphase modulation.[1]:264 If the index varies linearly with the field (a nontrivial linear coefficient is only possible in materials that do not possess inversion symmetry), it is known as the Pockels effect.[1]:265 Inhomogeneity[edit] A gradientindex 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. If the refractive index of a medium is not constant, but varies
gradually with position, the material is known as a gradientindex or
GRIN medium and is described by gradient index optics.[1]:273 Light
traveling through such a medium can be bent or focused, and this
effect can be exploited to produce lenses, some optical fibers and
other devices. Introducing GRIN 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.[1]:276 The crystalline lens of the human eye is an
example of a GRIN lens with a refractive index varying from about
1.406 in the inner core to approximately 1.386 at the less dense
cortex.[1]:203 Some common mirages are caused by a spatially varying
refractive index of air.
Refractive index
The principle of many refractometers The refractive index of liquids or solids can be measured with
refractometers. They typically measure some angle of refraction or the
critical angle for total internal reflection. The first laboratory
refractometers sold commercially were developed by
Ernst Abbe
A handheld refractometer used to measure sugar content of fruits This type of devices are commonly used in chemical laboratories for
identification of substances and for quality control. Handheld
variants are used in agriculture by, e.g., wine makers to determine
sugar content in grape juice, and inline process refractometers are
used in, e.g., chemical and pharmaceutical industry for process
control.
In gemology a different type of refractometer is used to measure index
of refraction and birefringence of gemstones. 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.[51]
Refractive index
A differential interference contrast microscopy image of yeast cells Unstained biological structures appear mostly transparent under
Brightfield microscopy
This section does not cite any sources. Please help improve this section by adding citations to reliable sources. Unsourced material may be challenged and removed. (September 2014) (Learn how and when to remove this template message) The refractive index is a very important property of the components of
any optical instrument that uses refraction. It determines the
focusing power of lenses, the dispersive power of prisms, and
generally the path of light through the system. It is the increase in
refractive index in the core that guides the light in an optical
fiber, and the variations in refractive index that reduces the
reflectivity of a surface treated with an antireflective coating.
Variant refractive index can generate resonant cavity that can enhance
phase shift of output light. This is important for design and
fabricate a variety of optoelectronic devices such as hologram and
lens.[53]
Since 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.
Refractive index
Fermat's principle
Calculation of glass properties
Clausius–Mossotti relation
Ellipsometry
Indexmatching material
Index ellipsoid
Laser
References[edit] ^ a b c d e f g h i j k l m n o p q r s Hecht, Eugene (2002). Optics.
AddisonWesley. ISBN 0321188780.
^ a b Attwood, David (1999). Soft Xrays and extreme ultraviolet
radiation: principles and applications. p. 60.
ISBN 052102997X.
^ Kinsler, Lawrence E. (2000). Fundamentals of Acoustics. John Wiley.
p. 136. ISBN 0471847895.
^ Young, Thomas (1807). A course of lectures on natural philosophy and
the mechanical arts. p. 413. Archived from the original on
20170222.
^ Newton, Isaac (1730). Opticks: Or, A Treatise of the Reflections,
Refractions, Inflections and Colours of Light. p. 247. Archived
from the original on 20151128.
^ Hauksbee, Francis (1710). "A Description of the Apparatus for Making
Experiments on the Refractions of Fluids". Philosophical Transactions
of the Royal Society of London. 27 (325–336): 207.
doi:10.1098/rstl.1710.0015.
^ Hutton, Charles (1795). Philosophical and mathematical dictionary.
p. 299. Archived from the original on 20170222.
^ von Fraunhofer, Joseph (1817). "Bestimmung des Brechungs und
Farbenzerstreuungs Vermogens verschiedener Glasarten". Denkschriften
der Königlichen Akademie der Wissenschaften zu München. 5: 208.
Archived from the original on 20170222. Exponent des
Brechungsverhältnisses is index of refraction
^ Brewster, David (1815). "On the structure of doubly refracting
crystals". Philosophical Magazine. 45: 126.
doi:10.1080/14786441508638398. Archived from the original on
20170222.
^ Herschel, John F.W. (1828). On the Theory of Light. p. 368.
Archived from the original on 20151124.
^ Faick, C.A.; Finn, A.N. (July 1931). "The Index of
Refraction
External links[edit] NIST calculator for determining the refractive index of air
Dielectric materials
Science World
Filmetrics' online database Free database of refractive index and
absorption coefficient information
RefractiveIndex.INFO
Refractive index
