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Encyclopedia > 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. For example, typical glass has a refractive index of 1.5, 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. Second, light reflects partially from surfaces that have a refractive index different from that of their surroundings. The straw seems to be broken, due to refraction of light as it emerges into the air. ... Glass can be made transparent and flat, or into other shapes and colors as shown in this sphere from the Verrerie of Brehat in Brittany. ... This article does not adequately cite its references or sources. ...

Contents

Definition

The refractive index of a medium is defined as the ratio of the phase velocity of a wave phenomenon such as light or sound in a reference medium to the velocity in the medium itself. It is most commonly used in the context of light with vacuum as a reference medium, although historically other reference media (e.g. air at a standardized pressure and temperature) have been common. It is usually given the symbol n. In the case of light, it equals The phase velocity of a wave is the rate at which the phase of the wave propagates in space. ... This article is about waves in the most general scientific sense. ... This article or section does not cite any references or sources. ... Sound is a disturbance of mechanical energy that propagates through matter as a longitudinal wave, and therefore is a mechanical wave. ... This article or section does not cite any references or sources. ... Look up Vacuum in Wiktionary, the free dictionary. ... Layers of Atmosphere (NOAA) Air redirects here. ... The use of water pressure - the Captain Cook Memorial Jet in Lake Burley Griffin in Canberra, Australia. ... Fig. ...

n=sqrt{epsilon_r}sqrt{mu_r},

where εr is the material's relative permittivity, and μr is its relative permeability. For most materials, μr 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.[1]. This has practical technical applications, such as effective mirrors for x-rays based on total internal reflection. 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 of a material to polarize in response to an applied electric field, and thereby to cancel, partially, the field inside the material. ... In electromagnetism, permeability is the degree of magnetization of a material that responds linearly to an applied magnetic field. ... In the NATO phonetic alphabet, X-ray represents the letter X. An X-ray picture (radiograph) taken by Röntgen An X-ray is a form of electromagnetic radiation with a wavelength approximately in the range of 5 pm to 10 nanometers (corresponding to frequencies in the range 30 PHz... The larger the angle to the normal, the smaller is the fraction of light transmitted, until the angle when total internal reflection occurs. ...


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 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. 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. The phase velocity of a wave is the rate at which the phase of the wave propagates in space. ... Waveform quite literally means the shape and form of a signal, such as a wave moving across the surface of water, or the vibration of a plucked string. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... The group velocity of a wave is the velocity with which the variations in the shape of the waves amplitude (known as the modulation or envelope of the wave) propagate through space. ... Amplitude is a nonnegative scalar measure of a waves magnitude of oscillation, that is, magnitude of the maximum disturbance in the medium during one wave cycle. ... Optical fibers An optical fiber (or fibre) is a glass or plastic fiber designed to guide light along its length by confining as much light as possible in a propagating form. ...


The 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.

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 Image File history File links Snells_law. ... Image File history File links Snells_law. ... The straw seems to be broken, due to refraction of light as it emerges into the air. ... A line showing the speed of light on a scale model of Earth and the Moon The speed of light in a vacuum is an important physical constant denoted by the letter c for constant or the Latin word celeritas meaning swiftness. It is the speed of all electromagnetic radiation... The phase velocity of a wave is the rate at which the phase of the wave propagates in space. ...

n =frac{c}{v}.

This number is typically greater than one: the higher the index of the material, the more the light is slowed down. However, at certain frequencies (e.g. near absorption resonances, and for X-rays), n will actually be smaller than one. 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. Absorption, in optics, is the process by which the energy of a photon is taken up by another entity, for example, by an atom whose valence electrons make a transition between two electronic energy levels. ... In the NATO phonetic alphabet, X-ray represents the letter X. An X-ray picture (radiograph) taken by Röntgen An X-ray is a form of electromagnetic radiation with a wavelength approximately in the range of 5 pm to 10 nanometers (corresponding to frequencies in the range 30 PHz... Two-dimensional analogy of space-time curvature described in General Relativity. ... In the fields of communications, signal processing, and in electrical engineering more generally, a signal is any time-varying quantity. ... The phase velocity 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 waves amplitude (known as the modulation or envelope of the wave) propagate through space. ... The signal velocity of a wave is the speed at which a pulse travels through a medium. ...


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

n_g=frac{c}{v_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. The group index can be written in terms of the wavelength dependence of the refractive index as

n_g = n - lambdafrac{dn}{dlambda},

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. The charges will, in general, oscillate slightly out of phase with respect to the driving electric field. 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). It has been suggested that optical field be merged into this article or section. ... e- redirects here. ... 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 of a material to polarize in response to an applied electric field, and thereby to cancel, partially, the field inside the material. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... In particle physics, scattering is a class of phenomena by which particles are deflected by collisions with other particles. ...


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. The straw seems to be broken, due to refraction of light as it emerges into the air. ... Refraction of light at the interface between two media of different refractive indices, with n2 > n1. ...


If in a given region the values of refractive indices n or ng were found to differ from unity (whether homogeniously, 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 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 εr and μr are simultaneously negative, although that is a sufficient but not necessary condition. 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. [1] [2] In electromagnetism (covering areas like optics and photonics), a meta material (or metamaterial) is an object that gains its (electromagnetic) material properties from its structure rather than inheriting them directly from the materials it is composed of. ... A metamaterial (or meta material) is a material that gains its properties from its structure rather than directly from its composition. ... Refraction of light at the interface between two media of different refractive indices, with n2 > n1. ...


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. This causes dielectric loss, which can be expressed by a permittivity that is both complex and frequency dependent. Real materials are not perfect insulators either, i.e. they have non-zero direct current conductivity. Taking both aspects into consideration, we can define a complex index of refraction: Image File history File links Dispersion-curve. ... Image File history File links Dispersion-curve. ... In electrostatics, the polarization is the vector field that results from permanent or induced electric dipole moments in a dielectric material. ... 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 of a material to polarize in response to an applied electric field, and thereby to cancel, partially, the field inside the material. ... In mathematics, a complex number is a number of the form where a and b are real numbers, and i is the imaginary unit, with the property i 2 = −1. ... FreQuency is a music video game developed by Harmonix and published by SCEI. It was released in November 2001. ... This article or section is in need of attention from an expert on the subject. ... Direct current (DC or continuous current) is the continuous flow of electricity through a conductor such as a wire from high to low potential. ... Electrical conductivity or specific conductivity is a measure of a materials ability to conduct an electric current. ...

tilde{n}=n-ikappa

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. Both n and κ are dependent on the frequency (wavelength). The parameter used to describe the interaction of electromagnetic radiation with matter is the complex index of refraction, ñ, which is a combination of a real part and an imaginary part. ... Absorption, in optics, is the process by which the energy of a photon is taken up by another entity, for example, by an atom whose valence electrons make a transition between two electronic energy levels. ... The wavelength is the distance between repeating units of a wave pattern. ...


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. 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. FreQuency is a music video game developed by Harmonix and published by SCEI. It was released in November 2001. ... Dispersion of a light beam in a prism. ... Diagram of a triangular prism, dispersing light Lamps as seen through a prism. ... Color is an important part of the visual arts. ... Full featured double rainbow in Wrangell-St. ... Chromatic aberration is caused by the dispersion of the lens material, the variation of its refractive index n with the wavelength of light. ... A lens. ... In mathematics and physics, the Kramers-Kronig relations describe the relation between the real and imaginary part of a certain class of complex-valued functions. ...


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, nD is the refractive index at the Fraunhofer "D" line, the centre of the yellow sodium double emission at 589.29 nm wavelength. 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 with the nearby frequencies. ... Solar Fraunhofer lines In physics and optics, the Fraunhofer lines are a set of spectral lines named for the German physicist Joseph von Fraunhofer (1787--1826). ... General Name, Symbol, Number sodium, Na, 11 Chemical series alkali metals Group, Period, Block 1, 3, s Appearance silvery white Standard atomic weight 22. ... A nanometre (American spelling: nanometer, symbol nm) is a unit of length in the metric system, equal to one thousand-millionth of a metre, which is the current SI base unit of length. ...


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. For some representative refractive indices at different wavelengths, see list of indices of refraction. A plot of the refractive index vs. ... Many materials have a well-characterized refractive index, but these indices depend strongly upon the wavelength of light. ...


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. Transparent glass ball In optics, transparency is the property of allowing light to pass. ...


The real and imaginary parts of the complex refractive index are related through use of the Kramers-Kronig relations. For example, one can determine a material's full complex refractive index as a function of wavelength from an absorption spectrum of the material. In mathematics and physics, the Kramers-Kronig relations describe the relation between the real and imaginary part of a certain class of complex-valued functions. ...


Anisotropy

A calcite crystal laid upon a paper with some letters showing birefringence
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. This is known as birefringence or anisotropy and is described by the field of crystal optics. 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. ImageMetadata File history File links Download high resolution version (2592x1944, 1296 KB) Calcite 方解石 Shizhao摄于北京动物园 File links The following pages link to this file: Calcite ... ImageMetadata File history File links Download high resolution version (2592x1944, 1296 KB) Calcite 方解石 Shizhao摄于北京动物园 File links The following pages link to this file: Calcite ... A calcite crystal laid upon a paper with some letters showing the double refraction Birefringence, or double refraction, is the decomposition of a ray of light into two rays (the ordinary ray and the extraordinary ray) when it passes through certain types of material, such as calcite crystals, depending on... In electrodynamics, polarization (also spelled polarisation) is the property of electromagnetic waves, such as light, that describes the direction of their transverse electric field. ... A calcite crystal laid upon a paper with some letters showing the double refraction Birefringence, or double refraction, is the decomposition of a ray of light into two rays (the ordinary ray and the extraordinary ray) when it passes through certain types of material, such as calcite crystals, depending on... Crystal optics is the branch of optics that describes the behaviour of light in anisotropic media, that is, media (such as crystals) in which light behaves differently depending on which direction the light is propagating. ... The relative dielectric constant of a material under given conditions is a measure of the extent to which it concentrates electrostatic lines of flux. ... In mathematics, a tensor is (in an informal sense) a generalized linear quantity or geometrical entity that can be expressed as a multi-dimensional array relative to a choice of basis; however, as an object in and of itself, a tensor is independent of any chosen frame of reference. ...


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.g. to construct Faraday isolators. When polarized light is passed through a substance containing chiral molecules (or nonchiral molecules arranged asymmetrically), the direction of polarization can be changed. ... A number of mathematical entities are named Hermitian, after the mathematician Charles Hermite: Hermitian matrix Hermitian operator Hermitian adjoint Hermitian form Hermitian metric See also: self-adjoint This is a disambiguation page &#8212; a navigational aid which lists other pages that might otherwise share the same title. ... A Faraday isolator or optical isolator is an optical component which allows the transmission of polarised 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. 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. 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. It has been suggested that optical field be merged into this article or section. ... Experiment with a laser (likely an argon type) (US Military) In physics, a laser is a device that emits light through a specific mechanism for which the term laser is an acronym: light amplification by stimulated emission of radiation. ... Nonlinear optics is the branch of optics that describes the behaviour of light in nonlinear media, that is, media in which the polarization P responds nonlinearly to the electric field E of the light. ... The Kerr effect or the quadratic electro-optic effect is a change in the refractive index of a material in response to the intensity of an external electric field. ... Figures with the axes of symmetry drawn in. ... The Pockels effect, or Pockels electro-optic effect, is the production of 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.

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. 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. Some common mirages are caused by a spatially-varying refractive index of air. Image File history File links No higher resolution available. ... Image File history File links No higher resolution available. ... Gradient index optics is the branch of optics covering optical effects produced by a gradual variation of the refractive index of a material. ... A lens. ... Optical fibers An optical fiber (or fibre) is a glass or plastic fiber designed to guide light along its length by confining as much light as possible in a propagating form. ... This article is about mirage, an optical phenomenon. ... Layers of Atmosphere - not to scale (NOAA)[3] Earths atmosphere is a layer of gases surrounding the planet Earth and retained by the Earths gravity. ...


Applications

The refractive index of a material is the most important property of any optical system that uses refraction. It is used to calculate the focusing power of lenses, and the dispersive power of prisms. Table of Opticks, 1728 Cyclopaedia Optics ( appearance or look in ancient Greek) is a branch of physics that describes the behavior and properties of light and the interaction of light with matter. ... The straw seems to be broken, due to refraction of light as it emerges into the air. ...


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. A refractometer is the instrument used to measure refractive index. For a solution of sugar, the refractive index can be used to determine the sugar content (see Brix). A substance is soluble in a fluid if it dissolves in the fluid. ... Drinking water This article focuses on water as we experience it every day. ... Dissolving table salt (NaCl) in water This article is about a chemical solution; for other uses of the term solution, see solution (disambiguation). ... A refractometer is an optical instrument that is used to determine the refractive index of a substance or some physical property of a substance that is directly related to its refractive index. ... Brix Flight Brix Flight is a 14 year old who is wishing to become famous one day. ...


See also

Many materials have a well-characterized refractive index, but these indices depend strongly upon the frequency of light. ... Optical properties of water and ice - define how electromagnetic radiation interacts with bulk water and ice. ... A plot of the refractive index vs. ... The larger the angle to the normal, the smaller is the fraction of light transmitted, until the angle when total internal reflection occurs. ... In electromagnetism (covering areas like optics and photonics), a meta material (or metamaterial) is an object that gains its (electromagnetic) material properties from its structure rather than inheriting them directly from the materials it is composed of. ... A metamaterial (or meta material) is a material that gains its properties from its structure rather than directly from its composition. ... In telecommunication, an index-matching material is a substance, usually a liquid, cement (adhesive), or gel, which has an index of refraction that closely approximates that of an optical fiber, and is used to reduce Fresnel reflection at the fiber endface. ... A calcite crystal laid upon a paper with some letters showing the double refraction Birefringence, or double refraction, is the decomposition of a ray of light into two rays (the ordinary ray and the extraordinary ray) when it passes through certain types of material, such as calcite crystals, depending on...

External links


  Results from FactBites:
 
METTLER TOLEDO - Sverige - Refractive index concentration tables (197 words)
With predefined formulas or concentration tables the refractometer converts the measured refractice index automatically into the desired concentration unit.
The refractometers from Mettler Toledo have already built in formulas and concentration tables for the most common applications.
The concentration tables are based on the "Handbook of Chemistry and Physics" 70th Edition and can be downloaded as EXCEL files.
Refractive index (276 words)
Refraction is due to a change in the speed of light as it passes from one medium to another.
The ratio of sines of the angles of incidence and refraction is a constant.
The incident and refracted rays are on opposite sides of the normal at the point of incidence.
  More results at FactBites »

 
 

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