Refractive index
Overview
 
In optics
Optics
Optics is the branch of physics which involves the behavior and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behavior of visible, ultraviolet, and infrared light...

 the refractive index or index of refraction of a substance or medium is a measure of the speed of light
Speed of light
The speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...

 in that medium. It is expressed as a ratio of the speed of light in vacuum
Vacuum
In everyday usage, vacuum is a volume of space that is essentially empty of matter, such that its gaseous pressure is much less than atmospheric pressure. The word comes from the Latin term for "empty". A perfect vacuum would be one with no particles in it at all, which is impossible to achieve in...

 relative to that in the considered medium.
This can be written mathematically as:
n = speed of light in a vacuum / speed of light in medium.

For example, the refractive index of water
Water
Water is a chemical substance with the chemical formula H2O. A water molecule contains one oxygen and two hydrogen atoms connected by covalent bonds. Water is a liquid at ambient conditions, but it often co-exists on Earth with its solid state, ice, and gaseous state . Water also exists in a...

 is 1.33, meaning that light travels 1.33 times as fast in vacuum as it does in water.
Encyclopedia
In optics
Optics
Optics is the branch of physics which involves the behavior and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behavior of visible, ultraviolet, and infrared light...

 the refractive index or index of refraction of a substance or medium is a measure of the speed of light
Speed of light
The speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...

 in that medium. It is expressed as a ratio of the speed of light in vacuum
Vacuum
In everyday usage, vacuum is a volume of space that is essentially empty of matter, such that its gaseous pressure is much less than atmospheric pressure. The word comes from the Latin term for "empty". A perfect vacuum would be one with no particles in it at all, which is impossible to achieve in...

 relative to that in the considered medium.
This can be written mathematically as:
n = speed of light in a vacuum / speed of light in medium.

For example, the refractive index of water
Water
Water is a chemical substance with the chemical formula H2O. A water molecule contains one oxygen and two hydrogen atoms connected by covalent bonds. Water is a liquid at ambient conditions, but it often co-exists on Earth with its solid state, ice, and gaseous state . Water also exists in a...

 is 1.33, meaning that light travels 1.33 times as fast in vacuum as it does in water. (See typical values for different materials here.)

As light moves from a medium, such as air, water, or glass, into another it may change its propagation
Wave propagation
Wave propagation is any of the ways in which waves travel.With respect to the direction of the oscillation relative to the propagation direction, we can distinguish between longitudinal wave and transverse waves....

 direction in proportion to the change in refractive index. This refraction
Refraction
Refraction is the change in direction of a wave due to a change in its speed. It is essentially a surface phenomenon . The phenomenon is mainly in governance to the law of conservation of energy. The proper explanation would be that due to change of medium, the phase velocity of the wave is changed...

 is governed by Snell's law
Snell's law
In optics and physics, Snell's law is a formula used to describe the relationship between the angles of incidence and refraction, when referring to light or other waves passing through a boundary between two different isotropic media, such as water and glass...

, and is illustrated in the figure to the right. Refractive index of materials varies with the wavelength
Wavelength
In physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...

 of light. This is called dispersion
Dispersion (optics)
In optics, dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency, or alternatively when the group velocity depends on the frequency.Media having such a property are termed dispersive media...

 and results in a slightly different refractive index for each color
Color
Color or colour is the visual perceptual property corresponding in humans to the categories called red, green, blue and others. Color derives from the spectrum of light interacting in the eye with the spectral sensitivities of the light receptors...

.

The wavelength of light in a material is determined by the refractive index according to , where is the wavelength of the light in vacuum. Brewster's angle
Brewster's angle
Brewster's angle is an angle of incidence at which light with a particular polarization is perfectly transmitted through a transparent dielectric surface, with no reflection. When unpolarized light is incident at this angle, the light that is reflected from the surface is therefore perfectly...

, the critical angle for total internal reflection
Total internal reflection
Total internal reflection is an optical phenomenon that happens when a ray of light strikes a medium boundary at an angle larger than a particular critical angle with respect to the normal to the surface. If the refractive index is lower on the other side of the boundary and the incident angle is...

, and the reflectivity
Reflectivity
In optics and photometry, reflectivity is the fraction of incident radiation reflected by a surface. In general it must be treated as a directional property that is a function of the reflected direction, the incident direction, and the incident wavelength...

 of a surface is also affected by the refractive index. These material parameters can be calculated using the Fresnel equations
Fresnel equations
The Fresnel equations , deduced by Augustin-Jean Fresnel , describe the behaviour of light when moving between media of differing refractive indices...

.

The concept of refractive index is widely used within the full electromagnetic spectrum
Electromagnetic spectrum
The electromagnetic spectrum is the range of all possible frequencies of electromagnetic radiation. The "electromagnetic spectrum" of an object is the characteristic distribution of electromagnetic radiation emitted or absorbed by that particular object....

, from x-ray
X-ray
X-radiation is a form of electromagnetic radiation. X-rays have a wavelength in the range of 0.01 to 10 nanometers, corresponding to frequencies in the range 30 petahertz to 30 exahertz and energies in the range 120 eV to 120 keV. They are shorter in wavelength than UV rays and longer than gamma...

s to radio wave
Radio Wave
Radio Wave may refer to:*Radio frequency*Radio Wave 96.5, a radio station in Blackpool, UK...

s. It can also be used with wave
Wave
In physics, a wave is a disturbance that travels through space and time, accompanied by the transfer of energy.Waves travel and the wave motion transfers energy from one point to another, often with no permanent displacement of the particles of the medium—that is, with little or no associated mass...

 phenomena other than light, e.g. sound
Sound
Sound is a mechanical wave that is an oscillation of pressure transmitted through a solid, liquid, or gas, composed of frequencies within the range of hearing and of a level sufficiently strong to be heard, or the sensation stimulated in organs of hearing by such vibrations.-Propagation of...

. In this case the speed of sound is used instead of that of light and a reference medium other than vacuum must be chosen.

Definitions

The refractive index, n, of a medium is defined as the ratio of the speed, c, of a wave
Wave
In physics, a wave is a disturbance that travels through space and time, accompanied by the transfer of energy.Waves travel and the wave motion transfers energy from one point to another, often with no permanent displacement of the particles of the medium—that is, with little or no associated mass...

 phenomenon such as light
Light
Light or visible light is electromagnetic radiation that is visible to the human eye, and is responsible for the sense of sight. Visible light has wavelength in a range from about 380 nanometres to about 740 nm, with a frequency range of about 405 THz to 790 THz...

 or sound
Sound
Sound is a mechanical wave that is an oscillation of pressure transmitted through a solid, liquid, or gas, composed of frequencies within the range of hearing and of a level sufficiently strong to be heard, or the sensation stimulated in organs of hearing by such vibrations.-Propagation of...

 in a reference medium to the phase speed, vp, of the wave in the medium in question:
It is most commonly used in the context of light
Light
Light or visible light is electromagnetic radiation that is visible to the human eye, and is responsible for the sense of sight. Visible light has wavelength in a range from about 380 nanometres to about 740 nm, with a frequency range of about 405 THz to 790 THz...

 with vacuum
Vacuum
In everyday usage, vacuum is a volume of space that is essentially empty of matter, such that its gaseous pressure is much less than atmospheric pressure. The word comes from the Latin term for "empty". A perfect vacuum would be one with no particles in it at all, which is impossible to achieve in...

 as a reference medium, although historically other reference media (e.g. air at a standardized pressure
Pressure
Pressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.- Definition :...

 and temperature
Temperature
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...

) have been common. It is usually given the symbol n. In the case of light, it equals


where is the material's relative permittivity
Permittivity
In electromagnetism, absolute permittivity is the measure of the resistance that is encountered when forming an electric field in a medium. In other words, permittivity is a measure of how an electric field affects, and is affected by, a dielectric medium. The permittivity of a medium describes how...

, and μr is its relative permeability
Permeability (electromagnetism)
In electromagnetism, permeability is the measure of the ability of a material to support the formation of a magnetic field within itself. In other words, it is the degree of magnetization that a material obtains in response to an applied magnetic field. Magnetic permeability is typically...

. For most naturally occurring materials, μr is very close to 1 at optical frequencies, therefore n is approximately . Contrary to a widespread misconception, the real part of a complex n may be less than one, depending upon the material and wavelength (see dispersion (optics)
Dispersion (optics)
In optics, dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency, or alternatively when the group velocity depends on the frequency.Media having such a property are termed dispersive media...

). This has practical technical applications, such as effective mirrors for X-rays based on total external reflection
Total external reflection
Total external reflection is an optical phenomenon where electromagnetic radiation can, at certain angles, be totally reflected from an interface between two media of different indices of refraction...

.

The phase speed is defined as the rate at which the crests of the waveform
Waveform
Waveform means the shape and form of a signal such as a wave moving in a physical medium or an abstract representation.In many cases the medium in which the wave is being propagated does not permit a direct visual image of the form. In these cases, the term 'waveform' refers to the shape of a graph...

 propagate; that is, the rate at which the phase
Phase (waves)
Phase in waves is the fraction of a wave cycle which has elapsed relative to an arbitrary point.-Formula:The phase of an oscillation or wave refers to a sinusoidal function such as the following:...

 of the waveform is moving. The group speed
Group velocity
The group velocity of a wave is the velocity with which the overall shape of the wave's amplitudes — known as the modulation or envelope of the wave — propagates through space....

is the rate at which the envelope of the waveform is propagating; that is, the rate of variation of the amplitude
Amplitude
Amplitude is the magnitude of change in the oscillating variable with each oscillation within an oscillating system. For example, sound waves in air are oscillations in atmospheric pressure and their amplitudes are proportional to the change in pressure during one oscillation...

 of the waveform. Provided the waveform is not distorted significantly during propagation, it is the group speed that represents the rate at which information (and energy) may be transmitted by the wave (for example, the speed at which a pulse of light travels down an optical fiber
Optical fiber
An optical fiber is a flexible, transparent fiber made of a pure glass not much wider than a human hair. It functions as a waveguide, or "light pipe", to transmit light between the two ends of the fiber. The field of applied science and engineering concerned with the design and application of...

). For the analytic properties constraining the unequal phase and group speeds in dispersive media, refer to dispersion (optics)
Dispersion (optics)
In optics, dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency, or alternatively when the group velocity depends on the frequency.Media having such a property are termed dispersive media...

.

Another common definition of the refractive index comes from the refraction of a light ray entering a medium. The refractive index is the ratio of the sines of the angles of incidence and refraction as light passes into the medium
or mathematically
The angles are measured to the normal
Surface normal
A surface normal, or simply normal, to a flat surface is a vector that is perpendicular to that surface. A normal to a non-flat surface at a point P on the surface is a vector perpendicular to the tangent plane to that surface at P. The word "normal" is also used as an adjective: a line normal to a...

 of the surface. This definition is based on Snell's law
Snell's law
In optics and physics, Snell's law is a formula used to describe the relationship between the angles of incidence and refraction, when referring to light or other waves passing through a boundary between two different isotropic media, such as water and glass...

 and is equivalent to the definition above if the light enters from the reference medium (normally vacuum).

A complex refractive index is often used to take absorption
Absorption (electromagnetic radiation)
In physics, absorption of electromagnetic radiation is the way by which the energy of a photon is taken up by matter, typically the electrons of an atom. Thus, the electromagnetic energy is transformed to other forms of energy for example, to heat. The absorption of light during wave propagation is...

 into account. This is further discussed in the Dispersion and absorption section below.

A closely related quantity is refractivity, which in atmospheric applications is denoted N and defined as N = (n - 1). The 106 factor is used because for air, n deviates from unity at most a few parts per thousand.

Typical values

Selected refractive indices at  nm (more extensive list here).
Material n
Gas
Gas
Gas is one of the three classical states of matter . Near absolute zero, a substance exists as a solid. As heat is added to this substance it melts into a liquid at its melting point , boils into a gas at its boiling point, and if heated high enough would enter a plasma state in which the electrons...

es at 0 °C and 1 atm
Air 
Helium
Helium
Helium is the chemical element with atomic number 2 and an atomic weight of 4.002602, which is represented by the symbol He. It is a colorless, odorless, tasteless, non-toxic, inert, monatomic gas that heads the noble gas group in the periodic table...

 
Hydrogen
Hydrogen
Hydrogen is the chemical element with atomic number 1. It is represented by the symbol H. With an average atomic weight of , hydrogen is the lightest and most abundant chemical element, constituting roughly 75% of the Universe's chemical elemental mass. Stars in the main sequence are mainly...

 
Carbon dioxide
Carbon dioxide
Carbon dioxide is a naturally occurring chemical compound composed of two oxygen atoms covalently bonded to a single carbon atom...

 
Liquid
Liquid
Liquid is one of the three classical states of matter . Like a gas, a liquid is able to flow and take the shape of a container. Some liquids resist compression, while others can be compressed. Unlike a gas, a liquid does not disperse to fill every space of a container, and maintains a fairly...

s at 20 °C
Water
Water
Water is a chemical substance with the chemical formula H2O. A water molecule contains one oxygen and two hydrogen atoms connected by covalent bonds. Water is a liquid at ambient conditions, but it often co-exists on Earth with its solid state, ice, and gaseous state . Water also exists in a...

 
1.333
Ethanol
Ethanol
Ethanol, also called ethyl alcohol, pure alcohol, grain alcohol, or drinking alcohol, is a volatile, flammable, colorless liquid. It is a psychoactive drug and one of the oldest recreational drugs. Best known as the type of alcohol found in alcoholic beverages, it is also used in thermometers, as a...

 
1.36
Methanol
Methanol
Methanol, also known as methyl alcohol, wood alcohol, wood naphtha or wood spirits, is a chemical with the formula CH3OH . It is the simplest alcohol, and is a light, volatile, colorless, flammable liquid with a distinctive odor very similar to, but slightly sweeter than, ethanol...

 
1.329
Benzene
Benzene
Benzene is an organic chemical compound. It is composed of 6 carbon atoms in a ring, with 1 hydrogen atom attached to each carbon atom, with the molecular formula C6H6....

 
1.501
Glycerine  1.473
Solid
Solid
Solid is one of the three classical states of matter . It is characterized by structural rigidity and resistance to changes of shape or volume. Unlike a liquid, a solid object does not flow to take on the shape of its container, nor does it expand to fill the entire volume available to it like a...

s
Ice
Ice
Ice is water frozen into the solid state. Usually ice is the phase known as ice Ih, which is the most abundant of the varying solid phases on the Earth's surface. It can appear transparent or opaque bluish-white color, depending on the presence of impurities or air inclusions...

 
1.309
Fused silica  1.46
PMMA  1.49
Crown glass
Crown glass (optics)
Crown glass is type of optical glass used in lenses and other optical components. It has relatively low refractive index and low dispersion...

 (typical)
1.52
Flint glass
Flint glass
Flint glass is optical glass that has relatively high refractive index and low Abbe number. Flint glasses are arbitrarily defined as having an Abbe number of 50 to 55 or less. The currently known flint glasses have refractive indices ranging between 1.45 and 2.00...

 (typical)
1.62
Diamond
Diamond
In mineralogy, diamond is an allotrope of carbon, where the carbon atoms are arranged in a variation of the face-centered cubic crystal structure called a diamond lattice. Diamond is less stable than graphite, but the conversion rate from diamond to graphite is negligible at ambient conditions...

 
2.42

For visible light most transparent
Transparency and translucency
In the field of optics, transparency is the physical property of allowing light to pass through a material; translucency only allows light to pass through diffusely. The opposite property is opacity...

 media have refractive indices between 1 and 2. A few examples are given in the table to the right. These values are measured at the yellow doublet sodium
Sodium
Sodium is a chemical element with the symbol Na and atomic number 11. It is a soft, silvery-white, highly reactive metal and is a member of the alkali metals; its only stable isotope is 23Na. It is an abundant element that exists in numerous minerals, most commonly as sodium chloride...

 D-line, with a wavelength of 589 nanometres, as is conventionally done. Gases at atmospheric pressure have refractive indices close to 1 because of their low density. Most plastics have refractive indices in the range from 1.3 to 1.7, but some high-refractive-index polymers can have a value as high as 1.76.

For infrared
Infrared
Infrared light is electromagnetic radiation with a wavelength longer than that of visible light, measured from the nominal edge of visible red light at 0.74 micrometres , and extending conventionally to 300 µm...

 light refractive indices can be considerably higher. Germanium
Germanium
Germanium is a chemical element with the symbol Ge and atomic number 32. It is a lustrous, hard, grayish-white metalloid in the carbon group, chemically similar to its group neighbors tin and silicon. The isolated element is a semiconductor, with an appearance most similar to elemental silicon....

 is transparent in this region and has a refractive index of about 4, making it an important material for infrared optics.

Refractive index below 1

A widespread misconception is that since, according to the theory of relativity
Theory of relativity
The theory of relativity, or simply relativity, encompasses two theories of Albert Einstein: special relativity and general relativity. However, the word relativity is sometimes used in reference to Galilean invariance....

, nothing can travel faster than the speed of light in vacuum, the refractive index cannot be lower than 1. This is erroneous since the refractive index measures the phase velocity
Phase velocity
The phase velocity of a wave is the rate at which the phase of the wave propagates in space. This is the speed at which the phase of any one frequency component of the wave travels. For such a component, any given phase of the wave will appear to travel at the phase velocity...

 of light, which does not carry energy
Energy
In physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems...

 or information
Information
Information in its most restricted technical sense is a message or collection of messages that consists of an ordered sequence of symbols, or it is the meaning that can be interpreted from such a message or collection of messages. Information can be recorded or transmitted. It can be recorded as...

, the two things limited in propagation speed. The phase velocity is the speed at which the crests of the wave move and can be faster than the speed of light in vacuum, and thereby give a refractive index below 1. This can occur close to resonance frequencies, in plasma
Plasma (physics)
In physics and chemistry, plasma is a state of matter similar to gas in which a certain portion of the particles are ionized. Heating a gas may ionize its molecules or atoms , thus turning it into a plasma, which contains charged particles: positive ions and negative electrons or ions...

s, and for x-ray
X-ray
X-radiation is a form of electromagnetic radiation. X-rays have a wavelength in the range of 0.01 to 10 nanometers, corresponding to frequencies in the range 30 petahertz to 30 exahertz and energies in the range 120 eV to 120 keV. They are shorter in wavelength than UV rays and longer than gamma...

s. In the x-ray regime the refractive indices are lower than but very close to 1 (exceptions close to some resonance frequencies).
As an example, water has a refractive index of 1− at a photon energy of (0.04 nm wavelength).

Negative refractive index

Recent research has also demonstrated the existence of the negative refractive index, which can occur if permittivity
Permittivity
In electromagnetism, absolute permittivity is the measure of the resistance that is encountered when forming an electric field in a medium. In other words, permittivity is a measure of how an electric field affects, and is affected by, a dielectric medium. The permittivity of a medium describes how...

 and permeability have simultaneous negative values. This can be achieved with periodically constructed metamaterials. The resulting negative refraction
Negative refraction
Negative refraction is the name for an electromagnetic phenomenon where light rays are refracted at an interface in the reverse sense to that normally expected...

 (i.e., a reversal of Snell's law) offers the possibility of the superlens
Superlens
A superlens, super lens or perfect lens is a lens which uses metamaterials to go beyond the diffraction limit. The diffraction limit is an inherent limitation in conventional optical devices or lenses. In 2000, a type of lens was proposed, consisting of a metamaterial that compensates for wave...

 and other exotic phenomena.

Microscopic explanation

At the microscale, an electromagnetic wave's phase speed is slowed in a material because the electric field
Electric field
In physics, an electric field surrounds electrically charged particles and time-varying magnetic fields. The electric field depicts the force exerted on other electrically charged objects by the electrically charged particle the field is surrounding...

 creates a disturbance in the charges of each atom (primarily the electron
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...

s) proportional to the electric susceptibility
Electric susceptibility
In electromagnetism, the electric susceptibility \chi_e is a dimensionless proportionality constant that indicates the degree of polarization of a dielectric material in response to an applied electric field...

 of the medium. (Similarly, the magnetic field
Magnetic field
A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...

 creates a disturbance proportional to the magnetic susceptibility
Magnetic susceptibility
In electromagnetism, the magnetic susceptibility \chi_m is a dimensionless proportionality constant that indicates the degree of magnetization of a material in response to an applied magnetic field...

.) As the electromagnetic fields oscillate in the wave, the charges in the material will be "shaken" back and forth at the same frequency. The charges thus radiate their own electromagnetic wave that is at the same frequency, but usually with a phase delay
Phase (waves)
Phase in waves is the fraction of a wave cycle which has elapsed relative to an arbitrary point.-Formula:The phase of an oscillation or wave refers to a sinusoidal function such as the following:...

, 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)
Superposition principle
In physics and systems theory, the superposition principle , also known as superposition property, states that, for all linear systems, the net response at a given place and time caused by two or more stimuli is the sum of the responses which would have been caused by each stimulus individually...

 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 speed. 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
Scattering
Scattering is a general physical process where some forms of radiation, such as light, sound, or moving particles, are forced to deviate from a straight trajectory by one or more localized non-uniformities in the medium through which they pass. In conventional use, this also includes deviation of...

).

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 more slowly. 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.
  • If the electrons emit a light wave which is 270° out of phase with the light wave shaking them, it will cause the total light wave to travel more quickly. This is called "anomalous refraction", and is observed close to absorption lines, with X-ray
    X-ray
    X-radiation is a form of electromagnetic radiation. X-rays have a wavelength in the range of 0.01 to 10 nanometers, corresponding to frequencies in the range 30 petahertz to 30 exahertz and energies in the range 120 eV to 120 keV. They are shorter in wavelength than UV rays and longer than gamma...

    s, and in some microwave systems. It corresponds to a refractive index less than 1. (Even though the phase velocity
    Phase velocity
    The phase velocity of a wave is the rate at which the phase of the wave propagates in space. This is the speed at which the phase of any one frequency component of the wave travels. For such a component, any given phase of the wave will appear to travel at the phase velocity...

     of light is greater than the speed of light in vacuum
    Speed of light
    The speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...

     c, the signal velocity
    Signal velocity
    The signal velocity is the speed at which a wave carries information. It describes how quickly a message can be communicated between two separated parties...

     is not, as discussed above). If the response is sufficiently strong and out-of-phase, the result is negative refractive index discussed below.
  • 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
    Absorption (electromagnetic radiation)
    In physics, absorption of electromagnetic radiation is the way by which the energy of a photon is taken up by matter, typically the electrons of an atom. Thus, the electromagnetic energy is transformed to other forms of energy for example, to heat. The absorption of light during wave propagation is...

     and corresponds to an imaginary
    Imaginary number
    An imaginary number is any number whose square is a real number less than zero. When any real number is squared, the result is never negative, but the square of an imaginary number is always negative...

     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 laser
    Laser
    A laser is a device that emits light through a process of optical amplification based on the stimulated emission of photons. The term "laser" originated as an acronym for Light Amplification by Stimulated Emission of Radiation...

    s due to stimulated emission
    Stimulated emission
    In optics, stimulated emission is the process by which an atomic electron interacting with an electromagnetic wave of a certain frequency may drop to a lower energy level, transferring its energy to that field. A photon created in this manner has the same phase, frequency, polarization, and...

    . It corresponds to an imaginary index of refraction, with the opposite sign as 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.

Dispersion

The refractive index of materials varies with the wavelength (and frequency
Frequency
Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...

) of light. This is called dispersion and causes prism
Prism (optics)
In optics, a prism is a transparent optical element with flat, polished surfaces that refract light. The exact angles between the surfaces depend on the application. The traditional geometrical shape is that of a triangular prism with a triangular base and rectangular sides, and in colloquial use...

s to divide white light into its constituent spectral color
Color
Color or colour is the visual perceptual property corresponding in humans to the categories called red, green, blue and others. Color derives from the spectrum of light interacting in the eye with the spectral sensitivities of the light receptors...

s, and explains how rainbow
Rainbow
A rainbow is an optical and meteorological phenomenon that causes a spectrum of light to appear in the sky when the Sun shines on to droplets of moisture in the Earth's atmosphere. It takes the form of a multicoloured arc...

s are formed. As the refractive index varies with wavelength, according to Snell's law, so will the refraction angle as light goes from one material to another. This makes different colors go in different directions. Dispersion also causes the focal length
Focal length
The focal length of an optical system is a measure of how strongly the system converges or diverges light. For an optical system in air, it is the distance over which initially collimated rays are brought to a focus...

 of lenses
Lens (optics)
A lens is an optical device with perfect or approximate axial symmetry which transmits and refracts light, converging or diverging the beam. A simple lens consists of a single optical element...

 to be wavelength dependent. This is a type of chromatic aberration
Chromatic aberration
In optics, chromatic aberration is a type of distortion in which there is a failure of a lens to focus all colors to the same convergence point. It occurs because lenses have a different refractive index for different wavelengths of light...

, which often needs to be corrected for in imaging systems.

In regions of the spectrum where the material does not absorb, 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. 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
Abbe number
In physics and optics, the Abbe number, also known as the V-number or constringence of a transparent material, is a measure of the material's dispersion in relation to the refractive index...

 . For a more accurate description of the wavelength dependence of the refractive index the Sellmeier equation
Sellmeier equation
The Sellmeier equation is an empirical relationship between refractive index and wavelength for a particular transparent medium. The equation is used to determine the dispersion of light in the medium....

 can be used. 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 at which a 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
Fraunhofer lines
In physics and optics, the Fraunhofer lines are a set of spectral lines named for the German physicist Joseph von Fraunhofer . The lines were originally observed as dark features in the optical spectrum of the Sun....

 "D" line, the centre of the yellow sodium
Sodium
Sodium is a chemical element with the symbol Na and atomic number 11. It is a soft, silvery-white, highly reactive metal and is a member of the alkali metals; its only stable isotope is 23Na. It is an abundant element that exists in numerous minerals, most commonly as sodium chloride...

 double emission at 589.29 nm
Nanometre
A nanometre is a unit of length in the metric system, equal to one billionth of a metre. The name combines the SI prefix nano- with the parent unit name metre .The nanometre is often used to express dimensions on the atomic scale: the diameter...

 wavelength.

Complex index of refraction and absorption

When light passes through a medium, some part of it will always be absorbed
Absorption (electromagnetic radiation)
In physics, absorption of electromagnetic radiation is the way by which the energy of a photon is taken up by matter, typically the electrons of an atom. Thus, the electromagnetic energy is transformed to other forms of energy for example, to heat. The absorption of light during wave propagation is...

. This can be conveniently taken into account by defining a complex index of refraction,
Here, the real part of the refractive index indicates the phase speed, while the imaginary part indicates the amount of absorption loss when the electromagnetic wave propagates through the material.

That corresponds to absorption can be seen by inserting this refractive index into the expression for electric field
Electric field
In physics, an electric field surrounds electrically charged particles and time-varying magnetic fields. The electric field depicts the force exerted on other electrically charged objects by the electrically charged particle the field is surrounding...

 of a plane
Plane wave
In the physics of wave propagation, a plane wave is a constant-frequency wave whose wavefronts are infinite parallel planes of constant peak-to-peak amplitude normal to the phase velocity vector....

 electromagnetic wave traveling in the -direction. We can do this by relating the wave number to the refractive index through , with being the vacuum wavelength. With complex wave number and refractive index this can be inserted into the plane wave expression as
Here we see that gives an exponential decay, as expected from the Beer–Lambert law.

κ is often called the extinction coefficient in physics although this has a different definition within chemistry. Both n and κ are dependent on the frequency. In most circumstances (light is absorbed) or (light travels forever without loss). In special situations, especially in the gain medium of laser
Laser
A laser is a device that emits light through a process of optical amplification based on the stimulated emission of photons. The term "laser" originated as an acronym for Light Amplification by Stimulated Emission of Radiation...

s, it is also possible that , corresponding to an amplification of the light.

An alternative convention uses instead of , but where 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 versus . See Mathematical descriptions of opacity
Mathematical descriptions of opacity
When an electromagnetic wave travels through a medium in which it gets absorbed , it undergoes exponential decay as described by the Beer–Lambert law. However, there are many possible ways to characterize the wave and how quickly it is absorbed...

.

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.

The real and imaginary parts of the complex refractive index are related through 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.

For X-ray
X-ray
X-radiation is a form of electromagnetic radiation. X-rays have a wavelength in the range of 0.01 to 10 nanometers, corresponding to frequencies in the range 30 petahertz to 30 exahertz and energies in the range 120 eV to 120 keV. They are shorter in wavelength than UV rays and longer than gamma...

 and extreme ultraviolet
Extreme ultraviolet
Extreme Ultraviolet radiation is high-energy ultraviolet radiation, generally defined to be electromagnetic radiation in the part of the electromagnetic spectrum spanning wavelengths from 120 nm down to 10 nm, and therefore having photons with energies from 10 eV up to 124 eV...

 radiation the complex refractive index deviates only slightly from unity and usually has a real part smaller than 1. It is therefore normally written as (or ).

Refraction

When light moves from one medium to another as in the figure to the right, it changes direction, i.e. it is refracted
Refraction
Refraction is the change in direction of a wave due to a change in its speed. It is essentially a surface phenomenon . The phenomenon is mainly in governance to the law of conservation of energy. The proper explanation would be that due to change of medium, the phase velocity of the wave is changed...

. If it goes from a medium with refractive index to one with refractive index , with an incidence angle to the surface normal of , the transmission angle can be calculated from Snell's law
Snell's law
In optics and physics, Snell's law is a formula used to describe the relationship between the angles of incidence and refraction, when referring to light or other waves passing through a boundary between two different isotropic media, such as water and glass...

:.

If there is no angle fulfilling Snell's law, i.e.,
the light cannot be transmitted and will instead undergo total internal reflection
Total internal reflection
Total internal reflection is an optical phenomenon that happens when a ray of light strikes a medium boundary at an angle larger than a particular critical angle with respect to the normal to the surface. If the refractive index is lower on the other side of the boundary and the incident angle is...

.

Reflectivity

Apart from the transmitted light there is also a reflected
Reflection (physics)
Reflection is the change in direction of a wavefront at an interface between two differentmedia so that the wavefront returns into the medium from which it originated. Common examples include the reflection of light, sound and water waves...

 part. The reflection angle is equal to the incidence angle, and the amount of light that is reflected is determined by the reflectivity
Reflectivity
In optics and photometry, reflectivity is the fraction of incident radiation reflected by a surface. In general it must be treated as a directional property that is a function of the reflected direction, the incident direction, and the incident wavelength...

 of the surface. The reflectivity can be calculated from the refractive index and the incidence angle with the Fresnel equations
Fresnel equations
The Fresnel equations , deduced by Augustin-Jean Fresnel , describe the behaviour of light when moving between media of differing refractive indices...

, which for normal incidence reduces to.
For common glass in air, and , and thus about 4% of the incident power is reflected.
At other incidence angles the reflectivity will also depend on the polarization of the incoming light. At a certain angle called Brewster's angle
Brewster's angle
Brewster's angle is an angle of incidence at which light with a particular polarization is perfectly transmitted through a transparent dielectric surface, with no reflection. When unpolarized light is incident at this angle, the light that is reflected from the surface is therefore perfectly...

, p-polarized light (light with the electric field in the plane of incidence
Plane of incidence
In optical reflection, the plane of incidence is the plane spanned by the surface normal and the propagation vector of the incoming radiation. In wave optics, the latter is the k-vector of the incoming wave....

) will be totally transmitted. Brewster's angle can be calculated from the two refractive indices of the interface as

Lenses

The focal length
Focal length
The focal length of an optical system is a measure of how strongly the system converges or diverges light. For an optical system in air, it is the distance over which initially collimated rays are brought to a focus...

 of a lens
Lens (optics)
A lens is an optical device with perfect or approximate axial symmetry which transmits and refracts light, converging or diverging the beam. A simple lens consists of a single optical element...

 is determined by its refractive index and the radii of curvature and of its surfaces. The power of a thin lens
Thin lens
[Image:Lens1.svg|thumb|A lens can be considered a thin lens if d [Image:Lens1.svg|thumb|A lens can be considered a thin lens if d [Image:Lens1.svg|thumb|A lens can be considered a thin lens if d...

 in air is given by the Lensmaker's formula:

Dielectric constant

The frequency dependent dielectric constant
Dielectric constant
The relative permittivity of a material under given conditions reflects the extent to which it concentrates electrostatic lines of flux. In technical terms, it is the ratio of the amount of electrical energy stored in a material by an applied voltage, relative to that stored in a vacuum...

 is simply the square of the (complex) refractive index in a non-magnetic medium (one with a relative permeability
Permeability (electromagnetism)
In electromagnetism, permeability is the measure of the ability of a material to support the formation of a magnetic field within itself. In other words, it is the degree of magnetization that a material obtains in response to an applied magnetic field. Magnetic permeability is typically...

 of unity). The refractive index is used for optics in Fresnel equations
Fresnel equations
The Fresnel equations , deduced by Augustin-Jean Fresnel , describe the behaviour of light when moving between media of differing refractive indices...

 and Snell's law
Snell's law
In optics and physics, Snell's law is a formula used to describe the relationship between the angles of incidence and refraction, when referring to light or other waves passing through a boundary between two different isotropic media, such as water and glass...

; while the dielectric constant is used in Maxwell's equations
Maxwell's equations
Maxwell's equations are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electrodynamics, classical optics, and electric circuits. These fields in turn underlie modern electrical and communications technologies.Maxwell's equations...

 and electronics.

Where is the complex dielectric constant with real and imaginary parts and , and and are the real and imaginary parts of the refractive index, all functions of frequency:


Conversion between refractive index and dielectric constant is done by:




Density

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
Lithium oxide
Lithium oxide or lithia is an inorganic chemical compound. Lithium oxide is formed along with small amounts of lithium peroxide when lithium metal is burned in the air and combines with oxygen:Pure can be produced by the thermal decomposition of lithium peroxide, at 450°C-Structure:In the solid...

 and MgO
Magnesium oxide
Magnesium oxide , or magnesia, is a white hygroscopic solid mineral that occurs naturally as periclase and is a source of magnesium . It has an empirical formula of and consists of a lattice of Mg2+ ions and O2– ions held together by ionic bonds...

, while the opposite trend is observed with glasses containing PbO
Lead(II) oxide
Lead oxide is the inorganic compound with the formula PbO. Lead oxide occurs in two polymorphs, red, having a tetragonal crystal structure and yellow, having an orthorhombic crystal structure...

 and BaO
Barium oxide
Barium oxide, BaO, is a white hygroscopic compound formed by the burning of barium in oxygen, although it is often formed through the decomposition of other barium salts.It reacts with water to form barium hydroxide.-Uses:...

 as seen in the diagram at the right.

Group index

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


where vg is the group velocity
Group velocity
The group velocity of a wave is the velocity with which the overall shape of the wave's amplitudes — known as the modulation or envelope of the wave — propagates through space....

. This value should not be confused with n, which is always defined with respect to the phase velocity
Phase velocity
The phase velocity of a wave is the rate at which the phase of the wave propagates in space. This is the speed at which the phase of any one frequency component of the wave travels. For such a component, any given phase of the wave will appear to travel at the phase velocity...

. When the dispersion
Dispersion (optics)
In optics, dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency, or alternatively when the group velocity depends on the frequency.Media having such a property are termed dispersive media...

 is small, the group velocity can be linked to the phase velocity by the relation
In this case the group index can thus be written in terms of the wavelength dependence of the refractive index as
where is the wavelength in the medium.

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)
where is the wavelength in vacuum.

Other relations

As shown in the Fizeau experiment
Fizeau experiment
The Fizeau experiment was carried out by Hippolyte Fizeau in 1851 to measure the relative speeds of light in moving water. Albert Einstein later pointed out the importance of the experiment for special relativity...

, when light is transmitted through a moving medium, its speed relative to a stationary observer is:

The refractive index of a substance can be related to its polarizability
Polarizability
Polarizability is the measure of the change in a molecule's electron distribution in response to an applied electric field, which can also be induced by electric interactions with solvents or ionic reagents. It is a property of matter...

 with the Lorentz–Lorenz equation or to the molar refractivities of its constituents by the Gladstone–Dale relation.

Birefringence

In some materials the refractive index depends on the polarization and propagation direction of the light. This is called birefringence
Birefringence
Birefringence, or double refraction, is the decomposition of a ray of light into two rays when it passes through certain anisotropic materials, such as crystals of calcite or boron nitride. The effect was first described by the Danish scientist Rasmus Bartholin in 1669, who saw it in calcite...

 or optical anisotropy
Anisotropy
Anisotropy is the property of being directionally dependent, as opposed to isotropy, which implies identical properties in all directions. It can be defined as a difference, when measured along different axes, in a material's physical or mechanical properties An example of anisotropy is the light...

.

In the simplest form, uniaxial birefringence, there is only one special direction in the material. This axis is known as the optical axis
Optic axis of a crystal
The optic axis of a crystal is the direction in which a ray of transmitted light suffers no birefringence . Due to the internal structure of the crystal , light propagates along the optical axis differently than in other directions...

 of the material. Light with linear polarization perpendicular to this axis will experience an ordinary refractive index while light polarized in parallel will experience an extraordinary refractive index . The birefringence of the material is the difference between these indices of refraction, . Light propagating in the direction of the optical axis will not be affected by the birefringence since the refractive index will be independent of polarization. For other propagation directions the light will split into two linearly polarized beams. For light traveling perpendicularly to the optical axis the beams will have the same direction. This can be used to change the polarization direction of linearly polarized light or to convert between linear, circular and elliptical polarizations with waveplates.

Many crystal
Crystal
A crystal or crystalline solid is a solid material whose constituent atoms, molecules, or ions are arranged in an orderly repeating pattern extending in all three spatial dimensions. The scientific study of crystals and crystal formation is known as crystallography...

s are naturally birefringent, but isotropic materials such as plastic
Plastic
A plastic material is any of a wide range of synthetic or semi-synthetic organic solids used in the manufacture of industrial products. Plastics are typically polymers of high molecular mass, and may contain other substances to improve performance and/or reduce production costs...

s and glass
Glass
Glass is an amorphous solid material. Glasses are typically brittle and optically transparent.The most familiar type of glass, used for centuries in windows and drinking vessels, is soda-lime glass, composed of about 75% silica plus Na2O, CaO, and several minor additives...

 can also often be made birefringent by introducing a prefered direction through e.g. an external force or electric field. This can be utilized in the determination of stresses in structures using photoelasticity
Photoelasticity
Photoelasticity is an experimental method to determine the stress distribution in a material. The method is mostly used in cases where mathematical methods become quite cumbersome. Unlike the analytical methods of stress determination, photoelasticity gives a fairly accurate picture of stress...

. 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
Crystal optics
Crystal optics is the branch of optics that describes the behaviour of light in anisotropic media, that is, media in which light behaves differently depending on which direction the light is propagating. The index of refraction depends on both composition and crystal structure and can be...

, the dielectric constant is a rank-2 tensor
Tensor
Tensors are geometric objects that describe linear relations between vectors, scalars, and other tensors. Elementary examples include the dot product, the cross product, and linear maps. Vectors and scalars themselves are also tensors. A tensor can be represented as a multi-dimensional array of...

 (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

The strong electric field
Electric field
In physics, an electric field surrounds electrically charged particles and time-varying magnetic fields. The electric field depicts the force exerted on other electrically charged objects by the electrically charged particle the field is surrounding...

 of high intensity light (such as output of a laser
Laser
A laser is a device that emits light through a process of optical amplification based on the stimulated emission of photons. The term "laser" originated as an acronym for Light Amplification by Stimulated Emission of Radiation...

) may cause a medium's refractive index to vary as the light passes through it, giving rise to nonlinear optics
Nonlinear optics
Nonlinear optics is the branch of optics that describes the behavior of light in nonlinear media, that is, media in which the dielectric polarization P responds nonlinearly to the electric field E of the light...

. If the index varies quadratically with the field (linearly with the intensity), it is called the optical Kerr effect
Kerr effect
The Kerr effect, also called the quadratic electro-optic effect , is a change in the refractive index of a material in response to an applied electric field. The Kerr effect is distinct from the Pockels effect in that the induced index change is directly proportional to the square of the electric...

 and causes phenomena such as self-focusing
Self-focusing
Self-focusing is a non-linear optical process induced by the change in refractive index of materials exposed to intense electromagnetic radiation. A medium whose refractive index increases with the electric field intensity acts as a focusing lens for an electromagnetic wave characterised by an...

 and self-phase modulation
Self-phase modulation
Self-phase modulation is a nonlinear optical effect of light-matter interaction.An ultrashort pulse of light, when travelling in a medium, will induce a varying refractive index of the medium due to the optical Kerr effect...

. 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
Pockels effect
The Pockels effect , or Pockels electro-optic effect, produces birefringence in an optical medium induced by a constant or varying electric field. It is distinguished from the Kerr effect by the fact that the birefringence is proportional to the electric field, whereas in the Kerr effect it is...

.

Inhomogeneity

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
Gradient-index optics is the branch of optics covering optical effects produced by a gradual variation of the refractive index of a material. Such variations can be used to produce lenses with flat surfaces, or lenses that do not have the aberrations typical of traditional spherical lenses...

. Light traveling through such a medium can be bent or focused, and this effect can be exploited to produce lenses
Lens (optics)
A lens is an optical device with perfect or approximate axial symmetry which transmits and refracts light, converging or diverging the beam. A simple lens consists of a single optical element...

, some optical fiber
Optical fiber
An optical fiber is a flexible, transparent fiber made of a pure glass not much wider than a human hair. It functions as a waveguide, or "light pipe", to transmit light between the two ends of the fiber. The field of applied science and engineering concerned with the design and application of...

s and other devices. Some common mirage
Mirage
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. The word comes to English via the French mirage, from the Latin mirare, meaning "to look at, to wonder at"...

s are caused by a spatially-varying refractive index of air
Earth's atmosphere
The atmosphere of Earth is a layer of gases surrounding the planet Earth that is retained by Earth's gravity. The atmosphere protects life on Earth by absorbing ultraviolet solar radiation, warming the surface through heat retention , and reducing temperature extremes between day and night...

.

Homogeneous media

The refractive index of liquids or solids can be measured with refractometer
Refractometer
A refractometer is a laboratory or field device for the measurement of an index of refraction . The index of refraction is calculated from Snell's law and can be calculated from the composition of the material using the Gladstone-Dale relation....

s. They typically measure some angle of refraction or the critical angle for total internal reflection. The first laboratory refractometer
Abbe refractometer
An Abbe refractometer is a bench-top device for the high-precision measurement of an index of refraction.- Details :Ernst Abbe , working for the Zeiss Company in Jena, Germany in the late 19th century, was the first to develop a laboratory refractometer...

s sold commercially were developed by Ernst Abbe in the late 19th century.
The same principles are still used today. In this instrument a thin layer of the liquid to be measured is placed between two prism
Prism
-Science and mathematics:* Prism , a transparent object which refracts light** Dispersive prism, the most familiar type of optical prism* Prism , a kind of polyhedron* Prism , a type of sedimentary deposit-Books, comics and magazines:...

s. Light is shone through the liquid at incidence angles all the way up to 90°, i.e. light rays parallel
Parallel
-Mathematics and science:* Parallel , an imaginary east-west line circling a globe* Parallel circuits, as opposed to series* Parallel * Parallel evolution* Parallel transport* Parallel of declination, used in astronomy-Computing:...

 to the surface. The second prism should have an index of refraction higher than that of the liquid, so that light only enters the prism at angles smaller than the critical angle for total reflection. This angle can then be measured either by looking through a telescope
Telescope
A telescope is an instrument that aids in the observation of remote objects by collecting electromagnetic radiation . The first known practical telescopes were invented in the Netherlands at the beginning of the 1600s , using glass lenses...

, or with a digital photodetector
Photodetector
Photosensors or photodetectors are sensors of light or other electromagnetic energy. There are several varieties:*Active pixel sensors are image sensors consisting of an integrated circuit that contains an array of pixel sensors, each pixel containing a both a light sensor and an active amplifier...

 placed in the focal plane of a lens. The refractive index of the liquid can then be calculated from the maximum transmission angle as , where is the refractive index of the prism.

This type of devices are commonly used in chemical
Chemistry
Chemistry is the science of matter, especially its chemical reactions, but also its composition, structure and properties. Chemistry is concerned with atoms and their interactions with other atoms, and particularly with the properties of chemical bonds....

 laboratories for identification of substances
Chemical substance
In chemistry, a chemical substance is a form of matter that has constant chemical composition and characteristic properties. It cannot be separated into components by physical separation methods, i.e. without breaking chemical bonds. They can be solids, liquids or gases.Chemical substances are...

 and for quality control
Quality control
Quality control, or QC for short, is a process by which entities review the quality of all factors involved in production. This approach places an emphasis on three aspects:...

. Handheld variants
Digital handheld refractometer
A digital handheld refractometer is an instrument for measuring the refractive index of materials.-Principle of operation:Most operate on the same general critical angle principle as a traditional handheld refractometer. The difference is that light from an LED light source is focused on the...

 are used in agriculture
Agriculture
Agriculture is the cultivation of animals, plants, fungi and other life forms for food, fiber, and other products used to sustain life. Agriculture was the key implement in the rise of sedentary human civilization, whereby farming of domesticated species created food surpluses that nurtured the...

 by e.g. wine makers to determine sugar content
Brix
Degrees Brix is the sugar content of an aqueous solution.One degree Brix is 1 gram of sucrose in 100 grams of solution and represents the strength of the solution as percentage by weight . If the solution contains dissolved solids other than pure sucrose, then the °Bx is only approximate the...

 in grape
Grape
A grape is a non-climacteric fruit, specifically a berry, that grows on the perennial and deciduous woody vines of the genus Vitis. Grapes can be eaten raw or they can be used for making jam, juice, jelly, vinegar, wine, grape seed extracts, raisins, molasses and grape seed oil. Grapes are also...

 juice, and inline process refractometer
Inline process refractometer
Inline process refractometers are a type of refractometer designed for the continuous measurement of a fluid flowing through a pipe or inside a tank. These refractometers typically consist of a sensor, placed inline with the fluid flow, coupled to a control box...

s are used in e.g. chemical
Chemical industry
The chemical industry comprises the companies that produce industrial chemicals. Central to the modern world economy, it converts raw materials into more than 70,000 different products.-Products:...

 and pharmaceutical industry for process control
Process control
Process control is a statistics and engineering discipline that deals with architectures, mechanisms and algorithms for maintaining the output of a specific process within a desired range...

.

In gemology
Gemology
Gemology or gemmology is the science dealing with natural and artificial gems and gemstones. It is considered a geoscience and a branch of mineralogy...

 a different type of refractometer is used to measure index of refraction and birefringence of gemstones
Gemstones
Gemstones is the third solo album by Adam Green, released in 2005. The album is characterised by the heavy presence of Wurlitzer piano, whereas its predecessor relied on a string section in its instrumentation.-Track listing:#Gemstones – 2:24...

. 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.

Refractive index variations

To measure the spatial variation of refractive index in a sample phase-contrast imaging
Phase-contrast imaging
Phase-contrast imaging is a method of imaging that has a range of different applications. It exploits differences in the refractive index of different materials to differentiate between structures under analysis...

 methods are used. These methods measure the variations in phase
Phase (waves)
Phase in waves is the fraction of a wave cycle which has elapsed relative to an arbitrary point.-Formula:The phase of an oscillation or wave refers to a sinusoidal function such as the following:...

 of the light wave exiting the sample. The phase is proportional to the optical path length
Optical path length
In optics, optical path length or optical distance is the product of the geometric length of the path light follows through the system, and the index of refraction of the medium through which it propagates. A difference in optical path length between two paths is often called the optical path...

 the light ray has traversed, and thus gives a measure of the integral
Integral
Integration is an important concept in mathematics and, together with its inverse, differentiation, is one of the two main operations in calculus...

 of the refractive index along the ray path. The phase cannot be measured directly at optical or higher frequencies, and therefore needs to be converted into intensity by interference with a reference beam. In the visual spectrum this is done using Zernike phase-contrast microscopy, differential interference contrast microscopy
Differential interference contrast microscopy
Differential interference contrast microscopy , also known as Nomarski Interference Contrast or Nomarski microscopy, is an optical microscopy illumination technique used to enhance the contrast in unstained, transparent samples...

 (DIC) or interferometry
Interferometry
Interferometry refers to a family of techniques in which electromagnetic waves are superimposed in order to extract information about the waves. An instrument used to interfere waves is called an interferometer. Interferometry is an important investigative technique in the fields of astronomy,...

.

Zernike phase-contrast microscopy introduces a phase shift to the low spatial frequency
Spatial frequency
In mathematics, physics, and engineering, spatial frequency is a characteristic of any structure that is periodic across position in space. The spatial frequency is a measure of how often sinusoidal components of the structure repeat per unit of distance. The SI unit of spatial frequency is...

 components of the image
Real image
In optics, a real image is a representation of an object in which the perceived location is actually a point of convergence of the rays of light that make up the image. If a screen is placed in the plane of a real image the image will generally become visible on the screen...

 with a phase-shifting annulus
Annulus
Annulus or annular may refer to:Annulus is Latin for little ring.- Human anatomy :* Annulus fibrosus disci intervertebralis, spinal structure...

 in the Fourier plane
Fourier optics
Fourier optics is the study of classical optics using Fourier transforms and can be seen as the dual of the Huygens-Fresnel principle. In the latter case, the wave is regarded as a superposition of expanding spherical waves which radiate outward from actual current sources via a Green's function...

 of the sample, so that higher frequency parts of the image can interfere with the low frequency reference beam. In DIC the illumination is split up into two beams that are given different polarizations, are phase shifted differently, and are shifted transversely with slightly different amounts. After the specimen the two parts are made to interfere giving an image of the derivative of the optical path length in the direction of the difference in transverse shift.
In interferometry the illumination is split up into two beams by a partially reflective mirror
Beam splitter
A beam splitter is an optical device that splits a beam of light in two. It is the crucial part of most interferometers.In its most common form, a rectangle, it is made from two triangular glass prisms which are glued together at their base using Canada balsam...

. One of the beams is let through the sample before they are combined to interfere and give a direct image of the phase shifts. If the optical path length variations are more than a wavelength the image will contain fringes.

There exist several x-ray phase-contrast imaging techniques to determine 2D or 3D spatial distribution of refractive index of samples in the x-ray regime.

Abraham–Minkowski controversy

In 1908, Hermann Minkowski
Hermann Minkowski
Hermann Minkowski was a German mathematician of Ashkenazi Jewish descent, who created and developed the geometry of numbers and who used geometrical methods to solve difficult problems in number theory, mathematical physics, and the theory of relativity.- Life and work :Hermann Minkowski was born...

 calculated the momentum of a refracted ray, p, where E is energy of the photon, c is the speed of light in vacuum and n is the refractive index of the medium as follows:
In 1909, Max Abraham
Max Abraham
Max Abraham was a German physicist.Abraham was born in Danzig, Imperial Germany to a family of Jewish merchants. His father was Moritz Abraham and his mother was Selma Moritzsohn. Attending the University of Berlin, he studied under Max Planck. He graduated in 1897...

 proposed the following formula for this calculation:
A 2010 study suggested that both equations are correct, with the Abraham version being the kinetic momentum
Kinetic momentum
In physics, in particular electromagnetism, the kinetic momentum is a nonstandard term for the momentum of a charged particle due to its inertia. When a charged particle interacts with an electromagnetic field , there are two momenta: due to its inertia and due to the field...

 and the Minkowski version being the canonical momentum, and claims to explain the contradicting experimental results using this interpretation.

Applications

The refractive index of a material is the most important property of any optical
Optics
Optics is the branch of physics which involves the behavior and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behavior of visible, ultraviolet, and infrared light...

 system that uses refraction
Refraction
Refraction is the change in direction of a wave due to a change in its speed. It is essentially a surface phenomenon . The phenomenon is mainly in governance to the law of conservation of energy. The proper explanation would be that due to change of medium, the phase velocity of the wave is changed...

. It is used to calculate the focusing power of lenses, and the dispersive power of prisms. It can also be used as a useful tool to differentiate between different types of gemstone, due to the unique chatoyance
Chatoyancy
In gemology, chatoyancy , or chatoyance, is an optical reflectance effect seen in certain gemstones. Coined from the French "œil de chat," meaning "cat's eye," chatoyancy arises either from the fibrous structure of a material, as in tiger eye quartz, or from fibrous inclusions or cavities within...

 each individual stone displays.

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
Solution
In chemistry, a solution is a homogeneous mixture composed of only one phase. In such a mixture, a solute is dissolved in another substance, known as a solvent. The solvent does the dissolving.- Types of solutions :...

. A refractometer
Refractometer
A refractometer is a laboratory or field device for the measurement of an index of refraction . The index of refraction is calculated from Snell's law and can be calculated from the composition of the material using the Gladstone-Dale relation....

 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
Brix
Degrees Brix is the sugar content of an aqueous solution.One degree Brix is 1 gram of sucrose in 100 grams of solution and represents the strength of the solution as percentage by weight . If the solution contains dissolved solids other than pure sucrose, then the °Bx is only approximate the...

).

In GPS, the index of refraction is utilized in ray-tracing to account for the radio propagation
Radio propagation
Radio propagation is the behavior of radio waves when they are transmitted, or propagated from one point on the Earth to another, or into various parts of the atmosphere...

 delay due to the Earth's electrically neutral atmosphere. It is also used in Satellite link design for the Computation of radiowave attenuation in the atmosphere
Computation of radiowave attenuation in the atmosphere
One of the causes of attenuation of radio propagation is the absorption by the atmosphere. There are many well known facts on the phenomenon and qualitative treatments in textbooks. A document published by the International Telecommunication Union...


See also

  • Calculation of glass properties
    Calculation of glass properties
    The calculation of glass properties is used to predict glass properties of interest or glass behavior under certain conditions without experimental investigation, based on past data and experience, with the intention to save time, material, financial, and environmental resources, or to gain...

  • Clausius–Mossotti relation
  • Ellipsometry
    Ellipsometry
    Ellipsometry is an optical technique for the investigation of the dielectric properties of thin films....

  • High refractive index polymers
    High refractive index polymers
    A high-refractive-index polymer is a polymer that has a refractive index greater than 1.50.Such materials are required for anti-reflective coating and photonic devices such as light emitting diodes and image sensors...

  • Index-matching material
    Index-matching material
    In optics and fiber optics, an index-matching material is a substance, usually a liquid, cement , or gel, which has an index of refraction that closely approximates that of an optical element or fiber, and is used to reduce Fresnel reflection at the surface of the element.In fiber optics and...

  • Index ellipsoid
    Index ellipsoid
    In optics, an index ellipsoid is a diagram of an ellipsoid that depicts the orientation and relative magnitude of refractive indices in a crystal....

  • Optical properties of water and ice
    Optical properties of water and ice
    The refractive index of water at 20°C is 1.332986. The refractive index of normal ice is 1.31. In general, an index of refraction is a complex number with both a real and imaginary part, where the latter indicates the strength of absorption loss at a particular wavelength...



External links

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