Refractive index

The refractive index (or index of refraction) of a medium is a measure for how much the speed of light (or other waves such as sound waves) is reduced inside the medium. Refraction is the change in direction of a Wave due to a change in its Speed. For example, typical glass has a refractive index of 1. Glass in the common sense refers to a Hard, Brittle, transparent Solid, such as that used for Windows many 5, which means that light travels at $1 / 1. 5 = 0. 67$ times the speed in air or vacuum. Two common properties of glass and other transparent materials are directly related to their refractive index. First, light rays change direction when they cross the interface from air to the material, an effect that is used in lenses and glasses. Glasses, also called eyeglasses or spectacles, are frames bearing lenses worn in front of the Eyes normally for vision correction, Second, light reflects partially from surfaces that have a refractive index different from that of their surroundings.

Definition: The refractive index n of a medium is defined as the ratio of the phase velocity c of a wave phenomenon such as light or sound in a reference medium to the phase velocity $v p$ in the medium itself:

$n = \frac{c}{v_{\mathrm {p}}}$

It is most commonly used in the context of light with vacuum as a reference medium, although historically other reference media (e. The phase velocity (or phase speed) of a Wave is the rate at which the phase of the wave propagates in space A wave is a disturbance that propagates through Space and Time, usually with transference of Energy. Light, or visible light, is Electromagnetic radiation of a Wavelength that is visible to the Human eye (about 400–700 Sound' is Vibration transmitted through a Solid, Liquid, or Gas; particularly sound means those vibrations composed of Frequencies Light, or visible light, is Electromagnetic radiation of a Wavelength that is visible to the Human eye (about 400–700 This vacuum means "absence of matter" or "an empty area or space" for the cleaning appliance see Vacuum cleaner. g. air at a standardized pressure and temperature) have been common. Temperature and layers The temperature of the Earth's atmosphere varies with altitude the mathematical relationship between temperature and altitude varies among five Pressure (symbol 'p' is the force per unit Area applied to an object in a direction perpendicular to the surface Temperature is a physical property of a system that underlies the common notions of hot and cold something that is hotter generally has the greater temperature It is usually given the symbol n. In the case of light, it equals

$n=\sqrt{\epsilon_r\mu_r}$ ,

where ε_r is the material's relative permittivity, and μ_r is its relative permeability. Permittivity is a Physical quantity that describes how an Electric field affects and is affected by a Dielectric medium and is determined by the ability In Electromagnetism, permeability is the degree of Magnetization of a material that responds linearly to an applied Magnetic field. For most materials, μ_r is very close to 1 at optical frequencies, therefore n is approximately $\sqrt{\epsilon_r}$ . Contrary to a widespread misconception, n may be less than 1, for example for x-rays. X-radiation (composed of X-rays) is a form of Electromagnetic radiation. ^[1]. This has practical technical applications, such as effective mirrors for x-rays based on total external reflection. Total external reflection is an optical phenomenon where electromagnetic radiation (e

The phase velocity is defined as the rate at which the crests of the waveform propagate; that is, the rate at which the phase of the waveform is moving. The phase velocity (or phase speed) of a Wave is the rate at which the phase of the wave propagates in space waveformogg|right|a sine square and sawtooth wave at 440 hz]] Waveform means the shape and form of a signal such as a Wave moving in a solid liquid or gaseous The phase of an oscillation or wave is the fraction of a complete cycle corresponding to an offset in the displacement from a specified reference point at time t = 0 The group velocity is the rate that the envelope of the waveform is propagating; that is, the rate of variation of the amplitude of the waveform. The group velocity of a Wave is the Velocity with which the variations in the shape of the wave's amplitude (known as the modulation or envelope Amplitude is the magnitude of change in the oscillating variable with each Oscillation, within an oscillating system Provided the waveform is not distorted significantly during propagation, it is the group velocity that represents the rate that information (and energy) may be transmitted by the wave, for example the velocity at which a pulse of light travels down an optical fiber. An optical fiber (or fibre) is a Glass or Plastic fiber that carries Light along its length

1 Speed of light
2 Negative Refractive Index
3 Dispersion and absorption
4 Relation to dielectric constant
5 Anisotropy
6 Nonlinearity
7 Inhomogeneity
8 Relation to density
9 Momentum Paradox
10 Applications
11 See also
12 References
13 External links

Speed of light

$Refraction of light at the interface between two media of different refractive indices, with n2 > n1. Since the phase velocity is lower in the second medium (v2 < v1), the angle of refraction θ2 is less than the angle of incidence θ1; that is, the ray in the higher-index medium is closer to the normal.$

Refraction of light at the interface between two media of different refractive indices, with n₂ > n₁. Refraction is the change in direction of a Wave due to a change in its Speed. Since the phase velocity is lower in the second medium (v₂ < v₁), the angle of refraction θ₂ is less than the angle of incidence θ₁; that is, the ray in the higher-index medium is closer to the normal.

The speed of all electromagnetic radiation in vacuum is the same, approximately 3×10⁸ meters per second, and is denoted by c. Therefore, if v is the phase velocity of radiation of a specific frequency in a specific material, the refractive index is given by

$n =\frac{c}{v}$

or inversely

$v =\frac{c}{n}$

This number is typically greater than one: the higher the index of the material, the more the light is slowed down (see Cherenkov radiation). The phase velocity (or phase speed) of a Wave is the rate at which the phase of the wave propagates in space Čerenkov radiation (also spelled Cerenkov or Cherenkov) is Electromagnetic radiation emitted when a charged particle (such as an However, at certain frequencies (e. g. near absorption resonances, and for X-rays), n will actually be smaller than one. In Physics, absorption of electromagnetic radiation is the process by which the Energy of a Photon is taken up by matter typically the electrons of an X-radiation (composed of X-rays) is a form of Electromagnetic radiation. This does not contradict the theory of relativity, which holds that no information-carrying signal can ever propagate faster than c, because the phase velocity is not the same as the group velocity or the signal velocity. This page is about the scientific concept of relativity for philosophical or sociological theories about relativity see Relativism. In the fields of communications, Signal processing, and in Electrical engineering more generally a signal is any time-varying or spatial-varying quantity The phase velocity (or phase speed) of a Wave is the rate at which the phase of the wave propagates in space The group velocity of a Wave is the Velocity with which the variations in the shape of the wave's amplitude (known as the modulation or envelope The signal velocity is the speed at which a Wave carries information

Sometimes, a "group velocity refractive index", usually called the group index is defined:

$n_g=\frac{c}{v_g}$

where v_g is the group velocity. This value should not be confused with n, which is always defined with respect to the phase velocity. The group index can be written in terms of the wavelength dependence of the refractive index as

$n_g = n - \lambda\frac{dn}{d\lambda},$

where $λ$ is the wavelength in vacuum. 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 permittivity of the medium. In Physics, the space surrounding an Electric charge or in the presence of a time-varying Magnetic field has a property called an electric field (that can The electron is a fundamental Subatomic particle that was identified and assigned the negative charge in 1897 by J Permittivity is a Physical quantity that describes how an Electric field affects and is affected by a Dielectric medium and is determined by the ability The charges will, in general, oscillate slightly out of phase with respect to the driving electric field. The phase of an oscillation or wave is the fraction of a complete cycle corresponding to an offset in the displacement from a specified reference point at time t = 0 The charges thus radiate their own electromagnetic wave that is at the same frequency but with a phase delay. The macroscopic sum of all such contributions in the material is 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 (see scattering). Scattering is a general physical process whereby some forms of Radiation, such as Light, Sound or moving particles for example are forced to deviate from

If the refractive indices of two materials are known for a given frequency, then one can compute the angle by which radiation of that frequency will be refracted as it moves from the first into the second material from Snell's law. Refraction is the change in direction of a Wave due to a change in its Speed. In Optics and Physics, Snell's law (also known as Descartes' law or the law of refraction) is a formula used to describe the relationship

If in a given region the values of refractive indices n or n_g were found to differ from unity (whether homogeneously, or isotropically, or not), then this region was distinct from vacuum in the above sense for lacking Poincaré symmetry. In Physics and Mathematics, the Poincaré group, named after Henri Poincaré, is the group of isometries of Minkowski spacetime

Negative Refractive Index

Recent research has also demonstrated the existence of negative refractive index which can occur if the real parts of both $ε r$ and $μ r$ are simultaneously negative, although such is a necessary but not sufficient condition. A metamaterial (or meta material) is a material which gains its properties from its structure rather than directly from its composition Not thought to occur naturally, this can be achieved with so-called metamaterials and offers the possibility of perfect lenses and other exotic phenomena such as a reversal of Snell's law. A metamaterial (or meta material) is a material which gains its properties from its structure rather than directly from its composition A superlens is a lens which is capable of Subwavelength imaging. In Optics and Physics, Snell's law (also known as Descartes' law or the law of refraction) is a formula used to describe the relationship [1] [2]

Dispersion and absorption

$The variation of refractive index vs. wavelength for various glasses.$

The variation of refractive index vs. wavelength for various glasses.

In real materials, the polarization does not respond instantaneously to an applied field. In Classical electromagnetism, the polarization density (or electric polarization, or simply polarization) is the Vector field that expresses This causes dielectric loss, which can be expressed by a permittivity that is both complex and frequency dependent. Permittivity is a Physical quantity that describes how an Electric field affects and is affected by a Dielectric medium and is determined by the ability Complex plane In Mathematics, the complex numbers are an extension of the Real numbers obtained by adjoining an Imaginary unit, denoted Frequency is a measure of the number of occurrences of a repeating event per unit Time. Real materials are not perfect insulators either, i. An insulator, also called a Dielectric, is a material that resists the flow of Electric current. e. they have non-zero direct current conductivity. Direct current ( DC) is the unidirectional flow of Electric charge. Electrical conductivity or specific conductivity is a measure of a material's ability to conduct an Electric current. Taking both aspects into consideration, we can define a complex index of refraction:

$\tilde{n}=n+i\kappa$

Here, n is the refractive index indicating the phase velocity as above, while κ is called the extinction coefficient, which indicates the amount of absorption loss when the electromagnetic wave propagates through the material. Opacity is the measure of impenetrability to electromagnetic or other kinds of radiation especially visible Light. In Physics, absorption of electromagnetic radiation is the process by which the Energy of a Photon is taken up by matter typically the electrons of an Both n and κ are dependent on the frequency (wavelength). In Physics wavelength is the distance between repeating units of a propagating Wave of a given Frequency. Note that the sign of the complex part is a matter of convention, which is important due to possible confusion between loss and gain. The notation above, which is usually used by physicists, corresponds to waves with time evolution given by $e - i ω t$ .

The effect that n varies with frequency (except in vacuum, where all frequencies travel at the same speed, c) is known as dispersion, and it is what causes a prism to divide white light into its constituent spectral colors, explains rainbows, and is the cause of chromatic aberration in lenses. Frequency is a measure of the number of occurrences of a repeating event per unit Time. In Optics, dispersion is the phenomenon in which the Phase velocity of a wave depends on its frequency In Optics, a dispersive prism is a type of optical prism, normally having the shape of a geometrical triangular prism. A rainbow is an optical and meteorological phenomenon that causes a spectrum of Light to appear in the Sky when the Sun In Optics, chromatic aberration is caused by a lens having a different Refractive index for different Wavelengths of Light A lens is an optical device with perfect or approximate Axial symmetry which transmits and refracts Light, converging or diverging In regions of the spectrum where the material does not absorb, the real part of the refractive index tends to increase with frequency. Near absorption peaks, the curve of the refractive index is a complex form given by the Kramers–Kronig relations, and can decrease with frequency. The Kramers–Kronig relations are mathematical properties connecting the real and imaginary parts of any complex function which is analytic

Since the refractive index of a material varies with the frequency (and thus wavelength) of light, it is usual to specify the corresponding vacuum wavelength at which the refractive index is measured. Typically, this is done at various well-defined spectral emission lines; for example, n_D is the refractive index at the Fraunhofer "D" line, the centre of the yellow sodium double emission at 589. A spectral line is a dark or bright line in an otherwise uniform and continuous spectrum, resulting from an excess or deficiency of photons in a narrow frequency range compared In Physics and Optics, the Fraunhofer lines are a set of Spectral lines named for the German physicist Joseph von Fraunhofer ( 1787 Sodium (ˈsoʊdiəm is an element which has the symbol Na( Latin natrium, from Arabic natrun) atomic number 11 atomic mass 22 29 nm wavelength. A nanometre ( American spelling: nanometer, symbol nm) ( Greek: νάνος nanos dwarf; μετρώ metrό count) is a

The Sellmeier equation is an empirical formula that works well in describing dispersion, and Sellmeier coefficients are often quoted instead of the refractive index in tables. In Optics, the Sellmeier equation is an Empirical relationship between Refractive index n and Wavelength λ for a For some representative refractive indices at different wavelengths, see list of indices of refraction.

As shown above, 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 (κ ≈ 0). However, at higher frequencies (such as visible light), dielectric loss may increase absorption significantly, reducing the material's transparency to these frequencies. In Optics, transparency (also called pellucidity) is the Material property of allowing

The real and imaginary parts of the complex refractive index are related through use of the Kramers–Kronig relations. The Kramers–Kronig relations are mathematical properties connecting the real and imaginary parts of any complex function which is analytic For example, one can determine a material's full complex refractive index as a function of wavelength from an absorption spectrum of the material.

Relation to dielectric constant

The dielectric constant (which is often dependent on wavelength) is simply the square of the (complex) refractive index. Measurement The relative static permittivity εr can be measured for static Electric fields as follows first the Capacitance of a test The refractive index is used for optics in Fresnel equations and Snell's law; while the dielectric constant is used in Maxwell's equations and electronics. In Optics and Physics, Snell's law (also known as Descartes' law or the law of refraction) is a formula used to describe the relationship In Classical electromagnetism, Maxwell's equations are a set of four Partial differential equations that describe the properties of the electric

Where $\tilde\epsilon$ , $ε 1$ , $ε 2$ , $n$ , and $κ$ are functions of wavelength:

$\tilde\epsilon=\epsilon_1+i\epsilon_2= (n+i\kappa)^2$

Conversion between refractive index and dielectric constant is done by:

ε 1 = n 2 - κ 2

ε 2 = 2 n κ

$n = \sqrt{\frac{\sqrt{\epsilon_1^2+\epsilon_2^2}+\epsilon_1}{2}}$ ^[2]

$\kappa = \sqrt{ \frac{ \sqrt{ \epsilon_1^2+ \epsilon_2^2}- \epsilon_1}{2}}$ ^[3]

Anisotropy

A calcite crystal laid upon a paper with some letters showing birefringence

The refractive index of certain media may be different depending on the polarization and direction of propagation of the light through the medium. Birefringence, or double refraction, is the decomposition of a ray of Light into two rays (the ordinary ray and the extraordinary ray Polarization ( ''Brit'' polarisation) is a property of Waves that describes the orientation of their oscillations This is known as birefringence or anisotropy and is described by the field of crystal optics. Birefringence, or double refraction, is the decomposition of a ray of Light into two rays (the ordinary ray and the extraordinary ray Crystal optics is the branch of Optics that describes the behaviour of Light in Anisotropic media, that is media (such as Crystals In the most general case, the dielectric constant is a rank-2 tensor (a 3 by 3 matrix), which cannot simply be described by refractive indices except for polarizations along principal axes. Measurement The relative static permittivity εr can be measured for static Electric fields as follows first the Capacitance of a test History The word tensor was introduced in 1846 by William Rowan Hamilton to describe the norm operation in a certain type of algebraic system (eventually

In magneto-optic (gyro-magnetic) and optically active materials, the principal axes are complex (corresponding to elliptical polarizations), and the dielectric tensor is complex-Hermitian (for lossless media); such materials break time-reversal symmetry and are used e. Optical rotation or optical activity is the rotation of linearly polarized Light as it travels through certain materials A number of Mathematical entities are named Hermitian, after the Mathematician Charles Hermite: Hermitian adjoint g. to construct Faraday isolators. An optical isolator, or optical diode, is an optical component which allows the transmission of light in only one direction

Nonlinearity

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. In Physics, the space surrounding an Electric charge or in the presence of a time-varying Magnetic field has a property called an electric field (that can A laser is a device that emits Light ( Electromagnetic radiation) through a process called Stimulated emission. Nonlinear optics (NLO is the branch of Optics that describes the behaviour of Light in nonlinear media, that is media in which the dielectric polarization If the index varies quadratically with the field (linearly with the intensity), it is called the optical Kerr effect and causes phenomena such as self-focusing and self phase modulation. The Kerr effect or the quadratic electro-optic effect ( QEO effect) is a change in the Refractive index of a material in response to an Electric field Self-focusing is a non-linear optical process induced by the change in Refractive index of materials exposed to intense Electromagnetic radiation. If the index varies linearly with the field (which is only possible in materials that do not possess inversion symmetry), it is known as the Pockels effect. Reflection symmetry, line symmetry, mirror symmetry, mirror-image symmetry, or bilateral symmetry is Symmetry with respect The Pockels effect, or Pockels electro-optic effect produces Birefringence in an optical medium induced by a constant or varying Electric field.

Inhomogeneity

$A gradient-index lens with a parabolic variation of refractive index (n) with radial distance (x). The lens focuses light in the same way as a conventional lens.$

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.

If the refractive index of a medium is not constant, but varies gradually with position, the material is known as a gradient-index medium and is described by gradient index optics. Gradient-index optics is the branch of Optics covering optical effects produced by a gradual variation of the Refractive index of a material Light travelling through such a medium can be bent or focussed, and this effect can be exploited to produce lenses, some optical fibers and other devices. A lens is an optical device with perfect or approximate Axial symmetry which transmits and refracts Light, converging or diverging An optical fiber (or fibre) is a Glass or Plastic fiber that carries Light along its length Some common mirages are caused by a spatially-varying refractive index of air. A mirage is a naturally-occurring Optical phenomenon, in which light rays are bent to produce a displaced image of distant objects or the sky Temperature and layers The temperature of the Earth's atmosphere varies with altitude the mathematical relationship between temperature and altitude varies among five

Relation to density

$Relation between the refractive index and the density of silicate and borosilicate glasses ().$

Relation between the refractive index and the density of silicate and borosilicate glasses (^[4]).

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. Lithium oxide ( Li2[[Oxygen O]] or lithia is an Inorganic Chemical compound. Magnesium oxide, or magnesia, is a white solid Mineral that occurs naturally as Periclase and is a source Lead(II oxide is the Chemical compound with the formula Barium oxide, BaO is a white Hygroscopic compound formed by the burning of Barium in Oxygen, although it is often formed through the decomposition

Momentum Paradox

The momentum of a refracted ray, p, was calculated by Hermann Minkowski^[5] in 1908, where E is energy of the photon, c is the speed of light in vacuum and n is the refractive index of the medium. Hermann Minkowski ( June 22 1864 – January 12 1909) was a Russian born German Mathematician, of Jewish

$p=\frac{nE}{c}$

In 1909 Max Abraham^[6] proposed

$p=\frac{E}{nc}$

Rudolf Peierls raises this in his "More Surprises in Theoretical Physics" Princeton (1991). Max Abraham ( March 26 1875 – November 16 1922) was a German Physicist. Sir Rudolf Ernst Peierls, ( June 5 1907, Berlin &ndash September 19 1995, Oxford) was a German -born British Ulf Leonhardt, Chair in Theoretical Physics at the University of St Andrews has discussed^[7] this including experiments to resolve. The University of St Andrews is the oldest University in Scotland and third oldest in the English-speaking world, having been founded between

Applications

The refractive index of a material is the most important property of any optical system that uses refraction. Refraction is the change in direction of a Wave due to a change in its Speed. It is used to calculate the focusing power of lenses, and the dispersive power of prisms.

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 is used to measure solids (glasses and gemstones), liquids, and gases. Most commonly it is used to measure the concentration of a solute in an aqueous solution. In Chemistry, a solution is a Homogeneous Mixture composed of two or more substances In Chemistry, a solution is a Homogeneous Mixture composed of two or more substances A refractometer is the instrument used to measure refractive index. A refractometer is an Optical instrument that is used to determine the Refractive index of a substance For a solution of sugar, the refractive index can be used to determine the sugar content (see Brix). Degrees Brix (symbol °Bx is a measurement of the dissolved Sugar -to-water mass ratio of a liquid

References

^ Tanya M. Ellipsometry is a versatile and powerful Optical technique for the investigation of the Dielectric properties (complex Refractive index or Dielectric Sansosti, Compound Refractive Lenses for X-Rays. 2002
^ p. 49 Frederick Wooten. Optical properties of solids. Academic Press, New York, 1972
^ p. 49 Frederick Wooten. Optical properties of solids. Academic Press, New York, 1972
^ Glassproperties.com
^ Nacht Ges. Wiss. Göttn. Math. -Phys. Kl. 53 (1908).
^ Rend. Circ. Matem. Palermo 28, 1 (1909).
^ "Optics: Momentum in an uncertain light" (14 December 2006). Nature 444: 823-824. doi:10.1038/444823a. A digital object identifier ( DOI) is a permanent identifier given to an Electronic document.

External links

Dictionary

-noun

(physics) the ratio of the speed of light in air or vacuum to that in another medium

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