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136-417: The common types of polarizers are linear polarizers and circular polarizers. Polarizers can also be made for other types of electromagnetic waves besides visible light, such as radio waves , microwaves , and X-rays . Linear polarizers can be divided into two general categories: absorptive polarizers, where the unwanted polarization states are absorbed by the device, and beam-splitting polarizers, where

272-404: A magnetic field which is in phase with, and perpendicular to, the electric field being displayed in these illustrations. To understand the effect the quarter-wave plate has on the linearly polarized light it is useful to think of the light as being divided into two components which are at right angles ( orthogonal ) to each other. Towards this end, the blue and green lines are projections of

408-435: A magnetic-dipole –type that dies out with distance from the current. In a similar manner, moving charges pushed apart in a conductor by a changing electrical potential (such as in an antenna) produce an electric-dipole –type electrical field, but this also declines with distance. These fields make up the near field. Neither of these behaviours is responsible for EM radiation. Instead, they only efficiently transfer energy to

544-422: A microwave oven . These interactions produce either electric currents or heat, or both. Like radio and microwave, infrared (IR) also is reflected by metals (and also most EMR, well into the ultraviolet range). However, unlike lower-frequency radio and microwave radiation, Infrared EMR commonly interacts with dipoles present in single molecules, which change as atoms vibrate at the ends of a single chemical bond. It

680-461: A transverse wave , where the electric field E and the magnetic field B are both perpendicular to the direction of wave propagation. The electric and magnetic parts of the field in an electromagnetic wave stand in a fixed ratio of strengths to satisfy the two Maxwell equations that specify how one is produced from the other. In dissipation-less (lossless) media, these E and B fields are also in phase, with both reaching maxima and minima at

816-440: A vacuum , electromagnetic waves travel at the speed of light , commonly denoted c . There, depending on the frequency of oscillation, different wavelengths of electromagnetic spectrum are produced. In homogeneous, isotropic media, the oscillations of the two fields are on average perpendicular to each other and perpendicular to the direction of energy and wave propagation, forming a transverse wave . Electromagnetic radiation

952-611: A wave form of the electric and magnetic equations , thus uncovering the wave-like nature of electric and magnetic fields and their symmetry . Because the speed of EM waves predicted by the wave equation coincided with the measured speed of light , Maxwell concluded that light itself is an EM wave. Maxwell's equations were confirmed by Heinrich Hertz through experiments with radio waves. Maxwell's equations established that some charges and currents ( sources ) produce local electromagnetic fields near them that do not radiate. Currents directly produce magnetic fields, but such fields of

1088-471: A boundary between two media with different refractive indices , some of it is usually reflected as shown in the figure above. The fraction that is reflected is described by the Fresnel equations , and depends on the incoming light's polarization and angle of incidence. The Fresnel equations predict that light with the p polarization ( electric field polarized in the same plane as the incident ray and

1224-581: A bulk collection of charges which are spread out over large numbers of affected atoms. In electrical conductors , such induced bulk movement of charges ( electric currents ) results in absorption of the EMR, or else separations of charges that cause generation of new EMR (effective reflection of the EMR). An example is absorption or emission of radio waves by antennas, or absorption of microwaves by water or other molecules with an electric dipole moment, as for example inside

1360-411: A certain minimum frequency, which depended on the particular metal, no current would flow regardless of the intensity. These observations appeared to contradict the wave theory, and for years physicists tried in vain to find an explanation. In 1905, Einstein explained this puzzle by resurrecting the particle theory of light to explain the observed effect. Because of the preponderance of evidence in favor of

1496-605: A component wave is said to be monochromatic . A monochromatic electromagnetic wave can be characterized by its frequency or wavelength, its peak amplitude, its phase relative to some reference phase, its direction of propagation, and its polarization. Interference is the superposition of two or more waves resulting in a new wave pattern. If the fields have components in the same direction, they constructively interfere, while opposite directions cause destructive interference. Additionally, multiple polarization signals can be combined (i.e. interfered) to form new states of polarization, which

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1632-403: A dielectric, and for electric field components parallel to the wires, the medium behaves like a metal (reflective). Malus' law ( / m ə ˈ l uː s / ), which is named after Étienne-Louis Malus , says that when a perfect polarizer is placed in a polarized beam of light, the irradiance , I , of the light that passes through is given by where I 0 is the initial intensity and θ i

1768-499: A fluorescence on a nearby plate of coated glass. In one month, he discovered X-rays' main properties. The last portion of the EM spectrum to be discovered was associated with radioactivity . Henri Becquerel found that uranium salts caused fogging of an unexposed photographic plate through a covering paper in a manner similar to X-rays, and Marie Curie discovered that only certain elements gave off these rays of energy, soon discovering

1904-576: A higher energy (and hence shorter wavelength) than gamma rays and vice versa. The origin of the ray differentiates them, gamma rays tend to be natural phenomena originating from the unstable nucleus of an atom and X-rays are electrically generated (and hence man-made) unless they are as a result of bremsstrahlung X-radiation caused by the interaction of fast moving particles (such as beta particles) colliding with certain materials, usually of higher atomic numbers. EM radiation (the designation 'radiation' excludes static electric and magnetic and near fields )

2040-459: A laser at Brewster's angle to the interface and observation at the angle of reflection, the uniform liquid does not reflect, appearing black in the image. However any molecular layers or artifacts at the surface, whose refractive index or physical structure contrasts with the liquid, allows for some reflection against that black background which is captured by a camera. Gas lasers using an external cavity (reflection by one or both mirrors outside

2176-528: A linear medium such as a vacuum. However, in nonlinear media, such as some crystals , interactions can occur between light and static electric and magnetic fields—these interactions include the Faraday effect and the Kerr effect . In refraction , a wave crossing from one medium to another of different density alters its speed and direction upon entering the new medium. The ratio of the refractive indices of

2312-539: A lower energy level, it emits a photon of light at a frequency corresponding to the energy difference. Since the energy levels of electrons in atoms are discrete, each element and each molecule emits and absorbs its own characteristic frequencies. Immediate photon emission is called fluorescence , a type of photoluminescence . An example is visible light emitted from fluorescent paints, in response to ultraviolet ( blacklight ). Many other fluorescent emissions are known in spectral bands other than visible light. Delayed emission

2448-417: A particular star. Spectroscopy is also used in the determination of the distance of a star, using the red shift . When any wire (or other conducting object such as an antenna ) conducts alternating current , electromagnetic radiation is propagated at the same frequency as the current. As a wave, light is characterized by a velocity (the speed of light ), wavelength , and frequency . As particles, light

2584-400: A plane. WGPs mostly reflect the non-transmitted polarization and can thus be used as polarizing beam splitters. The parasitic absorption is relatively high compared to most of the dielectric polarizers though much lower than in absorptive polarizers. Electromagnetic waves that have a component of their electric fields aligned parallel to the wires will induce the movement of electrons along

2720-408: A polarizer which creates a given handedness of circularly polarized light also passes that same handedness of polarized light. First, given the dual usefulness of this image, begin by imagining the circularly polarized light displayed at the top as still leaving the quarter-wave plate and traveling toward the left. Observe that had the horizontal component of the linearly polarized light been retarded by

2856-401: A quarter of wavelength twice, which would amount to a full half wavelength, the result would have been linearly polarized light that was at a right angle to the light that entered. If such orthogonally polarized light were rotated on the horizontal plane and directed back through the linear polarizer section of the circular polarizer it would clearly pass through given its orientation. Now imagine

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2992-417: A receiver very close to the source, such as inside a transformer . The near field has strong effects its source, with any energy withdrawn by a receiver causing increased load (decreased electrical reactance ) on the source. The near field does not propagate freely into space, carrying energy away without a distance limit, but rather oscillates, returning its energy to the transmitter if it is not absorbed by

3128-467: A receiver. By contrast, the far field is composed of radiation that is free of the transmitter, in the sense that the transmitter requires the same power to send changes in the field out regardless of whether anything absorbs the signal, e.g. a radio station does not need to increase its power when more receivers use the signal. This far part of the electromagnetic field is electromagnetic radiation. The far fields propagate (radiate) without allowing

3264-405: A special optical coating is applied. Either Brewster's angle reflections or interference effects in the film cause them to act as beam-splitting polarizers. The substrate for the film can either be a plate, which is inserted into the beam at a particular angle, or a wedge of glass that is cemented to a second wedge to form a cube with the film cutting diagonally across the center (one form of this

3400-405: A stack of glass plates at Brewster's angle to the beam. Some of the s -polarized light is reflected from each surface of each plate. For a stack of plates, each reflection depletes the incident beam of s -polarized light, leaving a greater fraction of p -polarized light in the transmitted beam at each stage. For visible light in air and typical glass, Brewster's angle is about 57°, and about 16% of

3536-437: A stack of plates placed at Brewster's angle in a light beam can, thus, be used as a polarizer . The concept of a polarizing angle can be extended to the concept of a Brewster wavenumber to cover planar interfaces between two linear bianisotropic materials . In the case of reflection at Brewster's angle, the reflected and refracted rays are mutually perpendicular. For magnetic materials, Brewster's angle can exist for only one of

3672-445: A third type of radiation, which in 1903 Rutherford named gamma rays . In 1910 British physicist William Henry Bragg demonstrated that gamma rays are electromagnetic radiation, not particles, and in 1914 Rutherford and Edward Andrade measured their wavelengths, finding that they were similar to X-rays but with shorter wavelengths and higher frequency, although a 'cross-over' between X and gamma rays makes it possible to have X-rays with

3808-431: A very large (ideally infinite) distance from the source. Both types of waves can have a waveform which is an arbitrary time function (so long as it is sufficiently differentiable to conform to the wave equation). As with any time function, this can be decomposed by means of Fourier analysis into its frequency spectrum , or individual sinusoidal components, each of which contains a single frequency, amplitude and phase. Such

3944-467: A wave is its rate of oscillation and is measured in hertz , the SI unit of frequency, where one hertz is equal to one oscillation per second. Light usually has multiple frequencies that sum to form the resultant wave. Different frequencies undergo different angles of refraction, a phenomenon known as dispersion . A monochromatic wave (a wave of a single frequency) consists of successive troughs and crests, and

4080-522: Is quantized and proportional to frequency according to Planck's equation E = hf , where E is the energy per photon, f is the frequency of the photon, and h is the Planck constant . Thus, higher frequency photons have more energy. For example, a 10  Hz gamma ray photon has 10 times the energy of a 10  Hz extremely low frequency radio wave photon. The effects of EMR upon chemical compounds and biological organisms depend both upon

4216-472: Is a more subtle affair. Some experiments display both the wave and particle natures of electromagnetic waves, such as the self-interference of a single photon . When a single photon is sent through an interferometer , it passes through both paths, interfering with itself, as waves do, yet is detected by a photomultiplier or other sensitive detector only once. A quantum theory of the interaction between electromagnetic radiation and matter such as electrons

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4352-404: Is a stream of photons . Each has an energy related to the frequency of the wave given by Planck's relation E = hf , where E is the energy of the photon, h is the Planck constant , 6.626 × 10 J·s, and f is the frequency of the wave. In a medium (other than vacuum), velocity factor or refractive index are considered, depending on frequency and application. Both of these are ratios of

4488-416: Is approximately 53°. Since the refractive index for a given medium changes depending on the wavelength of light, Brewster's angle will also vary with wavelength. The phenomenon of light being polarized by reflection from a surface at a particular angle was first observed by Étienne-Louis Malus in 1808. He attempted to relate the polarizing angle to the refractive index of the material, but was frustrated by

4624-523: Is associated with those EM waves that are free to propagate themselves ("radiate") without the continuing influence of the moving charges that produced them, because they have achieved sufficient distance from those charges. Thus, EMR is sometimes referred to as the far field , while the near field refers to EM fields near the charges and current that directly produced them, specifically electromagnetic induction and electrostatic induction phenomena. In quantum mechanics , an alternate way of viewing EMR

4760-422: Is called phosphorescence . The modern theory that explains the nature of light includes the notion of wave–particle duality. Together, wave and particle effects fully explain the emission and absorption spectra of EM radiation. The matter-composition of the medium through which the light travels determines the nature of the absorption and emission spectrum. These bands correspond to the allowed energy levels in

4896-563: Is classified by wavelength into radio , microwave , infrared , visible , ultraviolet , X-rays and gamma rays . Arbitrary electromagnetic waves can be expressed by Fourier analysis in terms of sinusoidal waves ( monochromatic radiation ), which in turn can each be classified into these regions of the EMR spectrum. For certain classes of EM waves, the waveform is most usefully treated as random , and then spectral analysis must be done by slightly different mathematical techniques appropriate to random or stochastic processes . In such cases,

5032-424: Is commonly referred to as "light", EM, EMR, or electromagnetic waves. The position of an electromagnetic wave within the electromagnetic spectrum can be characterized by either its frequency of oscillation or its wavelength. Electromagnetic waves of different frequency are called by different names since they have different sources and effects on matter. In order of increasing frequency and decreasing wavelength,

5168-672: Is consequently absorbed by a wide range of substances, causing them to increase in temperature as the vibrations dissipate as heat. The same process, run in reverse, causes bulk substances to radiate in the infrared spontaneously (see thermal radiation section below). Infrared radiation is divided into spectral subregions. While different subdivision schemes exist, the spectrum is commonly divided as near-infrared (0.75–1.4 μm), short-wavelength infrared (1.4–3 μm), mid-wavelength infrared (3–8 μm), long-wavelength infrared (8–15 μm) and far infrared (15–1000 μm). Brewster%27s angle Brewster's angle (also known as

5304-729: Is described by the theory of quantum electrodynamics . Electromagnetic waves can be polarized , reflected, refracted, or diffracted , and can interfere with each other. In homogeneous, isotropic media, electromagnetic radiation is a transverse wave , meaning that its oscillations are perpendicular to the direction of energy transfer and travel. It comes from the following equations : ∇ ⋅ E = 0 ∇ ⋅ B = 0 {\displaystyle {\begin{aligned}\nabla \cdot \mathbf {E} &=0\\\nabla \cdot \mathbf {B} &=0\end{aligned}}} These equations predicate that any electromagnetic wave must be

5440-636: Is easy to appreciate that by reversing the positions of the transmitting and absorbing axes of the linear polarizer relative to the quarter-wave plate, one changes which handedness of polarized light gets transmitted and which gets absorbed. Electromagnetic wave In physics , electromagnetic radiation ( EMR ) consists of waves of the electromagnetic (EM) field , which propagate through space and carry momentum and electromagnetic radiant energy . Classically , electromagnetic radiation consists of electromagnetic waves , which are synchronized oscillations of electric and magnetic fields . In

5576-409: Is going to be retarded a second time by one quarter of a wavelength. Whether that horizontal component is retarded by one quarter of a wavelength in two distinct steps or retarded a full half wavelength all at once, the orientation of the resulting linearly polarized light will be such that it passes through the linear polarizer. Had it been right-handed, clockwise circularly polarized light approaching

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5712-406: Is happening. In the case of linearly and circularly polarized light, at each point in space, there is always a single electric field with a distinct vector direction, the quarter-wave plate merely has the effect of transforming this single electric field. Circular polarizers can also be used to selectively absorb or pass right-handed or left-handed circularly polarized light. It is this feature which

5848-453: Is known as parallel polarization state generation . The energy in electromagnetic waves is sometimes called radiant energy . An anomaly arose in the late 19th century involving a contradiction between the wave theory of light and measurements of the electromagnetic spectra that were being emitted by thermal radiators known as black bodies . Physicists struggled with this problem unsuccessfully for many years, and it later became known as

5984-472: Is lost in the polarizer and the actual transmission will be somewhat lower than this, around 38% for Polaroid-type polarizers but considerably higher (>49.9%) for some birefringent prism types. If two polarizers are placed one after another (the second polarizer is generally called an analyzer ), the mutual angle between their polarizing axes gives the value of θ in Malus's law. If the two axes are orthogonal,

6120-467: Is polarized in particular directions. They can therefore be used as linear polarizers. The best known crystal of this type is tourmaline . However, this crystal is seldom used as a polarizer, since the dichroic effect is strongly wavelength dependent and the crystal appears coloured. Herapathite is also dichroic, and is not strongly coloured, but is difficult to grow in large crystals. A Polaroid polarizing filter functions similarly on an atomic scale to

6256-453: Is represented with an orange line. The quarter-wave plate has a horizontal slow axis and a vertical fast axis and they are also represented using orange lines. In this instance the unpolarized light entering the linear polarizer is displayed as a single wave whose amplitude and angle of linear polarization are suddenly changing. When one attempts to pass unpolarized light through the linear polarizer, only light that has its electric field at

6392-477: Is that it consists of photons , uncharged elementary particles with zero rest mass which are the quanta of the electromagnetic field , responsible for all electromagnetic interactions. Quantum electrodynamics is the theory of how EMR interacts with matter on an atomic level. Quantum effects provide additional sources of EMR, such as the transition of electrons to lower energy levels in an atom and black-body radiation . The energy of an individual photon

6528-486: Is the emission spectrum of nebulae . Rapidly moving electrons are most sharply accelerated when they encounter a region of force, so they are responsible for producing much of the highest frequency electromagnetic radiation observed in nature. These phenomena can aid various chemical determinations for the composition of gases lit from behind (absorption spectra) and for glowing gases (emission spectra). Spectroscopy (for example) determines what chemical elements comprise

6664-422: Is the angle between the light's initial polarization direction and the axis of the polarizer. A beam of unpolarized light can be thought of as containing a uniform mixture of linear polarizations at all possible angles. Since the average value of cos 2 ⁡ θ {\displaystyle \cos ^{2}\theta } is 1/2, the transmission coefficient becomes In practice, some light

6800-427: Is the angle of reflection (or incidence) and θ 2 is the angle of refraction. Using Snell's law , one can calculate the incident angle θ 1 = θ B at which no light is reflected: Solving for θ B gives The physical explanation of why the transmitted ray should be at 90 ∘ {\displaystyle 90^{\circ }} to the reflected ray can be difficult to grasp, but

6936-483: Is the same as the angle of reflection defined by the angle observed from) is dominant, but even diffuse reflections from roads for instance, are also significantly reduced. Photographers also use polarizing filters to remove reflections from water so that they can photograph objects beneath the surface. Using a polarizing camera attachment which can be rotated, such a filter can be adjusted to reduce reflections from objects other than horizontal surfaces, such as seen in

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7072-486: Is the very common MacNeille cube). Thin-film polarizers generally do not perform as well as Glan-type polarizers, but they are inexpensive and provide two beams that are about equally well polarized. The cube-type polarizers generally perform better than the plate polarizers. The former are easily confused with Glan-type birefringent polarizers. One of the simplest linear polarizers is the wire-grid polarizer (WGP), which consists of many fine parallel metallic wires placed in

7208-398: Is used in polarimetry to measure the optical activity of a sample. Real polarizers are also not perfect blockers of the polarization orthogonal to their polarization axis; the ratio of the transmission of the unwanted component to the wanted component is called the extinction ratio , and varies from around 1:500 for Polaroid to about 1:10 for Glan–Taylor prism polarizers. In X-ray

7344-400: Is utilized by the 3D glasses in stereoscopic cinemas such as RealD Cinema . A given polarizer which creates one of the two polarizations of light will pass that same polarization of light when that light is sent through it in the other direction. In contrast it will block light of the opposite polarization. The illustration above is identical to the previous similar one with the exception that

7480-414: Is very low in this case. Adding more plates and reducing the angle allows a better compromise between transmission and polarization to be achieved. Because their polarization vectors depend on incidence angle, polarizers based on Fresnel reflection inherently tend to produce s – p polarization rather than Cartesian polarization, which limits their use in some applications. Other linear polarizers exploit

7616-488: The Glan–Thompson prism , Glan–Foucault prism , and Glan–Taylor prism . These prisms are not true polarizing beamsplitters since only the transmitted beam is fully polarized. A Wollaston prism is another birefringent polarizer consisting of two triangular calcite prisms with orthogonal crystal axes that are cemented together. At the internal interface, an unpolarized beam splits into two linearly polarized rays which leave

7752-648: The Planck energy or exceeding it (far too high to have ever been observed) will require new physical theories to describe. When radio waves impinge upon a conductor , they couple to the conductor, travel along it and induce an electric current on the conductor surface by moving the electrons of the conducting material in correlated bunches of charge. Electromagnetic radiation phenomena with wavelengths ranging from as long as one meter to as short as one millimeter are called microwaves; with frequencies between 300 MHz (0.3 GHz) and 300 GHz. At radio and microwave frequencies, EMR interacts with matter largely as

7888-473: The Planck–Einstein equation . In quantum theory (see first quantization ) the energy of the photons is thus directly proportional to the frequency of the EMR wave. Likewise, the momentum p of a photon is also proportional to its frequency and inversely proportional to its wavelength: The source of Einstein's proposal that light was composed of particles (or could act as particles in some circumstances)

8024-400: The birefringent properties of crystals such as quartz and calcite . In these crystals, a beam of unpolarized light incident on their surface is split by refraction into two rays. Snell's law holds for both of these rays, the ordinary or o -ray, and the extraordinary or e -ray, with each ray experiencing a different index of refraction (this is called double refraction). In general

8160-455: The gain medium ) generally seal the tube using windows tilted at Brewster's angle. This prevents light in the intended polarization from being lost through reflection (and reducing the round-trip gain of the laser) which is critical in lasers having a low round-trip gain. On the other hand, it does remove s polarized light, increasing the round trip loss for that polarization, and ensuring the laser only oscillates in one linear polarization, as

8296-479: The o -ray occurs at the balsam interface, since it experiences a larger refractive index in calcite than in the balsam, and the ray is deflected to the side of the crystal. The e -ray, which sees a smaller refractive index in the calcite, is transmitted through the interface without deflection. Nicol prisms produce a very high purity of polarized light, and were extensively used in microscopy , though in modern use they have been mostly replaced with alternatives such as

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8432-447: The plane of incidence and light polarized perpendicular to it. Light polarized in the plane is said to be p -polarized, while that polarized perpendicular to it is s -polarized. At a special angle known as Brewster's angle , no p -polarized light is reflected from the surface, thus all reflected light must be s -polarized, with an electric field perpendicular to the plane of incidence. A simple linear polarizer can be made by tilting

8568-490: The polarization 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 polarized. The angle is named after the Scottish physicist Sir David Brewster (1781–1868). When light encounters

8704-676: The s polarization, almost up to 90° incidence where the reflectivity of each rises towards unity. Thus reflected light from horizontal surfaces (such as the surface of a road) at a distance much greater than one's height (so that the incidence angle of specularly reflected light is near, or usually well beyond the Brewster angle) is strongly s -polarized. Polarized sunglasses use a sheet of polarizing material to block horizontally-polarized light and thus reduce glare in such situations. These are most effective with smooth surfaces where specular reflection (thus from light whose angle of incidence

8840-477: The s -polarized light present in the beam is reflected for each air-to-glass or glass-to-air transition. It takes many plates to achieve even mediocre polarization of the transmitted beam with this approach. For a stack of 10 plates (20 reflections), about 3% (= (1 − 0.16)) of the s -polarized light is transmitted. The reflected beam, while fully polarized, is spread out and may not be very useful. A more useful polarized beam can be obtained by tilting

8976-435: The surface normal at the point of incidence) will not be reflected if the angle of incidence is where n 1 is the refractive index of the initial medium through which the light propagates (the "incident medium"), and n 2 is the index of the other medium. This equation is known as Brewster's law , and the angle defined by it is Brewster's angle. The physical mechanism for this can be qualitatively understood from

9112-418: The ultraviolet catastrophe . In 1900, Max Planck developed a new theory of black-body radiation that explained the observed spectrum. Planck's theory was based on the idea that black bodies emit light (and other electromagnetic radiation) only as discrete bundles or packets of energy. These packets were called quanta . In 1905, Albert Einstein proposed that light quanta be regarded as real particles. Later

9248-414: The Brewster angle result also follows simply from the Fresnel equations for reflectivity, which state that for p-polarized light The reflection goes to zero when We can now use Snell's Law to eliminate θ 2 {\displaystyle \theta _{2}} as follows: we multiply Snell by n 1 {\displaystyle n_{1}} and square both sides; multiply

9384-791: The Malus' law ( relativistic form): where f 0 {\displaystyle f_{0}} – frequency of the polarized radiation falling on the polarizer, f {\displaystyle f} – frequency of the radiation passes through polarizer, λ {\displaystyle \lambda } – Compton wavelength of electron, c {\displaystyle c} – speed of light in vacuum. Circular polarizers ( CPL or circular polarizing filters ) can be used to create circularly polarized light or alternatively to selectively absorb or pass clockwise and counter-clockwise circularly polarized light. They are used as polarizing filters in photography to reduce oblique reflections from non-metallic surfaces, and are

9520-401: The absorbing axis of the linear polarizer, which is at right angles to the transmission axis, and it would have therefore been blocked. To understand this process, refer to the illustration on the right. It is absolutely identical to the earlier illustration even though the circularly polarized light at the top is now considered to be approaching the polarizer from the left. One can observe from

9656-424: The accompanying photograph (right) where the s polarization (approximately vertical) has been eliminated using such a filter. When recording a classical hologram , the bright reference beam is typically arranged to strike the film in the p polarization at Brewster's angle. By thus eliminating reflection of the reference beam at the transparent back surface of the holographic film, unwanted interference effects in

9792-432: The atoms in the star's atmosphere. A similar phenomenon occurs for emission , which is seen when an emitting gas glows due to excitation of the atoms from any mechanism, including heat. As electrons descend to lower energy levels, a spectrum is emitted that represents the jumps between the energy levels of the electrons, but lines are seen because again emission happens only at particular energies after excitation. An example

9928-413: The atoms. Dark bands in the absorption spectrum are due to the atoms in an intervening medium between source and observer. The atoms absorb certain frequencies of the light between emitter and detector/eye, then emit them in all directions. A dark band appears to the detector, due to the radiation scattered out of the light beam . For instance, dark bands in the light emitted by a distant star are due to

10064-403: The average number of photons in the cube of the relevant wavelength is much smaller than 1. It is not so difficult to experimentally observe non-uniform deposition of energy when light is absorbed, however this alone is not evidence of "particulate" behavior. Rather, it reflects the quantum nature of matter . Demonstrating that the light itself is quantized, not merely its interaction with matter,

10200-502: The axis of the quarter-wave plate 90° relative to the linear polarizer. This reverses the fast and slow axes of the wave plate relative to the transmission axis of the linear polarizer reversing which component leads and which component lags. In trying to appreciate how the quarter-wave plate transforms the linearly polarized light, it is important to realize that the two components discussed are not entities in and of themselves but are merely mental constructs one uses to help appreciate what

10336-834: The chains is absorbed by the sheet; light polarized perpendicularly to the chains is transmitted. The durability and practicality of Polaroid makes it the most common type of polarizer in use, for example for sunglasses , photographic filters , and liquid crystal displays . It is also much cheaper than other types of polarizer. A modern type of absorptive polarizer is made of elongated silver nano-particles embedded in thin (≤0.5 mm) glass plates. These polarizers are more durable, and can polarize light much better than plastic Polaroid film, achieving polarization ratios as high as 100,000:1 and absorption of correctly polarized light as low as 1.5%. Such glass polarizers perform best for long-wavelength infrared light, and are widely used in fiber-optic communication . Beam-splitting polarizers split

10472-445: The circular polarizer from the left, its horizontal component would have also been retarded, however the resulting linearly polarized light would have been polarized along the absorbing axis of the linear polarizer and it would not have passed. To create a circular polarizer that instead passes right-handed polarized light and absorbs left-handed light, one again rotates the wave plate and linear polarizer 90° relative to each another. It

10608-402: The circularly polarized light which has already passed through the quarter-wave plate once, turned around and directed back toward the circular polarizer again. Let the circularly polarized light illustrated at the top now represent that light. Such light is going to travel through the quarter-wave plate a second time before reaching the linear polarizer and in the process, its horizontal component

10744-408: The combined energy transfer of many photons. In contrast, high frequency ultraviolet, X-rays and gamma rays are ionizing – individual photons of such high frequency have enough energy to ionize molecules or break chemical bonds . Ionizing radiation can cause chemical reactions and damage living cells beyond simply heating, and can be a health hazard and dangerous. James Clerk Maxwell derived

10880-409: The desired result follows (which then allows reverse proof that θ 1 + θ 2 = 90 ∘ {\displaystyle \theta _{1}+\theta _{2}=90^{\circ }} ). For a glass medium ( n 2 ≈ 1.5 ) in air ( n 1 ≈ 1 ), Brewster's angle for visible light is approximately 56°, while for an air-water interface ( n 2 ≈ 1.33 ), it

11016-434: The direction of a surface (usually found with Fresnel reflection), they are usually termed s and p . This distinction between Cartesian and s – p polarization can be negligible in many cases, but it becomes significant for achieving high contrast and with wide angular spreads of the incident light. Certain crystals , due to the effects described by crystal optics , show dichroism , preferential absorption of light which

11152-412: The direction of travel. All the electric field vectors have the same magnitude indicating that the strength of the electric field does not change. The direction of the electric field however steadily rotates. The blue and green lines are projections of the helix onto the vertical and horizontal planes respectively and represent how the electric field changes in the direction of those two planes. Notice how

11288-400: The distance between two adjacent crests or troughs is called the wavelength . Waves of the electromagnetic spectrum vary in size, from very long radio waves longer than a continent to very short gamma rays smaller than atom nuclei. Frequency is inversely proportional to wavelength, according to the equation: where v is the speed of the wave ( c in a vacuum or less in other media), f is

11424-524: The electromagnetic spectrum includes: radio waves , microwaves , infrared , visible light , ultraviolet , X-rays , and gamma rays . Electromagnetic waves are emitted by electrically charged particles undergoing acceleration , and these waves can subsequently interact with other charged particles, exerting force on them. EM waves carry energy, momentum , and angular momentum away from their source particle and can impart those quantities to matter with which they interact. Electromagnetic radiation

11560-447: The electromagnetic vacuum. The behavior of EM radiation and its interaction with matter depends on its frequency, and changes qualitatively as the frequency changes. Lower frequencies have longer wavelengths, and higher frequencies have shorter wavelengths, and are associated with photons of higher energy. There is no fundamental limit known to these wavelengths or energies, at either end of the spectrum, although photons with energies near

11696-424: The energy of the rejected polarization state, and so they are more suitable for use with high intensity beams such as laser light. True polarizing beamsplitters are also useful where the two polarization components are to be analyzed or used simultaneously. When light reflects (by Fresnel reflection) at an angle from an interface between two transparent materials, the reflectivity is different for light polarized in

11832-506: The fast and slow axes of the quarter-wave plate and the handedness of the circularly polarized light. In the illustration, the left-handed circularly polarized light entering the polarizer is transformed into linearly polarized light which has its direction of polarization along the transmission axis of the linear polarizer and it therefore passes. In contrast right-handed circularly polarized light would have been transformed into linearly polarized light that had its direction of polarization along

11968-527: The fields present in the same space due to other causes. Further, as they are vector fields, all magnetic and electric field vectors add together according to vector addition . For example, in optics two or more coherent light waves may interact and by constructive or destructive interference yield a resultant irradiance deviating from the sum of the component irradiances of the individual light waves. The electromagnetic fields of light are not affected by traveling through static electric or magnetic fields in

12104-406: The frequency and λ is the wavelength. As waves cross boundaries between different media, their speeds change but their frequencies remain constant. Electromagnetic waves in free space must be solutions of Maxwell's electromagnetic wave equation . Two main classes of solutions are known, namely plane waves and spherical waves. The plane waves may be viewed as the limiting case of spherical waves at

12240-406: The horizontal component is delayed relative to vertical component before the light leaves the wave plate and they begin again to travel at the same speed. When the light leaves the quarter-wave plate the rightward horizontal component will be exactly one quarter of a wavelength behind the vertical component making the light left-hand circularly polarized when viewed from the receiver. At the top of

12376-418: The horizontal component which is along the slow axis of the wave plate will travel at a slower speed than the component that is directed along the vertical fast axis. Initially the two components are in phase, but as the two components travel through the wave plate the horizontal component of the light drifts farther behind that of the vertical. By adjusting the thickness of the wave plate one can control how much

12512-415: The illustration that the leftward horizontal (as observed looking along the direction of travel) component is leading the vertical component and that when the horizontal component is retarded by one quarter of a wavelength it will be transformed into the linearly polarized light illustrated at the bottom and it will pass through the linear polarizer. There is a relatively straightforward way to appreciate why

12648-417: The illustration toward the right is the circularly polarized light after it leaves the wave plate. Directly below it, for comparison purposes, is the linearly polarized light that entered the quarter-wave plate. In the upper image, because this is a plane wave, each vector leading from the axis to the helix represents the magnitude and direction of the electric field for an entire plane that is perpendicular to

12784-420: The incident beam into two beams of differing linear polarization . For an ideal polarizing beamsplitter these would be fully polarized, with orthogonal polarizations. For many common beam-splitting polarizers, however, only one of the two output beams is fully polarized. The other contains a mixture of polarization states. Unlike absorptive polarizers, beam splitting polarizers do not need to absorb and dissipate

12920-416: The incident wave polarizations, as determined by the relative strengths of the dielectric permittivity and magnetic permeability. This has implications for the existence of generalized Brewster angles for dielectric metasurfaces. While at the Brewster angle there is no reflection of the p polarization, at yet greater angles the reflection coefficient of the p polarization is always less than that of

13056-436: The inconsistent quality of glasses available at that time. In 1815, Brewster experimented with higher-quality materials and showed that this angle was a function of the refractive index, defining Brewster's law. Brewster's angle is often referred to as the "polarizing angle", because light that reflects from a surface at this angle is entirely polarized perpendicular to the plane of incidence (" s -polarized"). A glass plate or

13192-477: The individual frequency components are represented in terms of their power content, and the phase information is not preserved. Such a representation is called the power spectral density of the random process. Random electromagnetic radiation requiring this kind of analysis is, for example, encountered in the interior of stars, and in certain other very wideband forms of radiation such as the Zero point wave field of

13328-544: The intense radiation of radium . The radiation from pitchblende was differentiated into alpha rays ( alpha particles ) and beta rays ( beta particles ) by Ernest Rutherford through simple experimentation in 1899, but these proved to be charged particulate types of radiation. However, in 1900 the French scientist Paul Villard discovered a third neutrally charged and especially penetrating type of radiation from radium, and after he described it, Rutherford realized it must be yet

13464-800: The known speed of light. Maxwell therefore suggested that visible light (as well as invisible infrared and ultraviolet rays by inference) all consisted of propagating disturbances (or radiation) in the electromagnetic field. Radio waves were first produced deliberately by Heinrich Hertz in 1887, using electrical circuits calculated to produce oscillations at a much lower frequency than that of visible light, following recipes for producing oscillating charges and currents suggested by Maxwell's equations. Hertz also developed ways to detect these waves, and produced and characterized what were later termed radio waves and microwaves . Wilhelm Röntgen discovered and named X-rays . After experimenting with high voltages applied to an evacuated tube on 8 November 1895, he noticed

13600-410: The left-handed circularly polarized light is now approaching the polarizer from the opposite direction and linearly polarized light is exiting the polarizer toward the right. First note that a quarter-wave plate always transforms circularly polarized light into linearly polarized light. It is only the resulting angle of polarization of the linearly polarized light that is determined by the orientation of

13736-406: The length of the wires. Since the electrons are free to move in this direction, the polarizer behaves in a similar manner to the surface of a metal when reflecting light, and the wave is reflected backwards along the incident beam (minus a small amount of energy lost to Joule heating of the wire). For waves with electric fields perpendicular to the wires, the electrons cannot move very far across

13872-472: The lenses of the 3D glasses worn for viewing some stereoscopic movies (notably, the RealD 3D variety), where the polarization of light is used to differentiate which image should be seen by the left and right eye. There are several ways to create circularly polarized light, the cheapest and most common involves placing a quarter-wave plate after a linear polarizer and directing unpolarized light through

14008-422: The linear polarizer. The linearly polarized light leaving the linear polarizer is transformed into circularly polarized light by the quarter wave plate. The transmission axis of the linear polarizer needs to be half way (45°) between the fast and slow axes of the quarter-wave plate. In the arrangement above, the transmission axis of the linear polarizer is at a positive 45° angle relative to the right horizontal and

14144-401: The magnitude and direction of the electric field varies along the direction of travel. For this plane electromagnetic wave, each vector represents the magnitude and direction of the electric field for an entire plane that is perpendicular to the direction of travel. (Refer to these two images in the plane wave article to better appreciate this.) Light and all other electromagnetic waves have

14280-432: The manner in which electric dipoles in the media respond to p -polarized light. One can imagine that light incident on the surface is absorbed, and then re-radiated by oscillating electric dipoles at the interface between the two media. The polarization of freely propagating light is always perpendicular to the direction in which the light is travelling. The dipoles that produce the transmitted (refracted) light oscillate in

14416-447: The media determines the degree of refraction, and is summarized by Snell's law . Light of composite wavelengths (natural sunlight) disperses into a visible spectrum passing through a prism, because of the wavelength-dependent refractive index of the prism material ( dispersion ); that is, each component wave within the composite light is bent a different amount. EM radiation exhibits both wave properties and particle properties at

14552-407: The nearby violet light. Ritter's experiments were an early precursor to what would become photography. Ritter noted that the ultraviolet rays (which at first were called "chemical rays") were capable of causing chemical reactions. In 1862–64 James Clerk Maxwell developed equations for the electromagnetic field which suggested that waves in the field would travel with a speed that was very close to

14688-401: The particle of light was given the name photon , to correspond with other particles being described around this time, such as the electron and proton . A photon has an energy, E , proportional to its frequency, f , by where h is the Planck constant , λ {\displaystyle \lambda } is the wavelength and c is the speed of light . This is sometimes known as

14824-410: The pile of plates at a steeper angle to the incident beam. Counterintuitively, using incident angles greater than Brewster's angle yields a higher degree of polarization of the transmitted beam, at the expense of decreased overall transmission. For angles of incidence steeper than 80° the polarization of the transmitted beam can approach 100% with as few as four plates, although the transmitted intensity

14960-541: The polarization direction of that light. These same oscillating dipoles also generate the reflected light. However, dipoles do not radiate any energy in the direction of the dipole moment . If the refracted light is p -polarized and propagates exactly perpendicular to the direction in which the light is predicted to be specularly reflected , the dipoles point along the specular reflection direction and therefore no light can be reflected. (See diagram, above) With simple geometry this condition can be expressed as where θ 1

15096-400: The polarization of visible or infrared light to a useful degree. Since the degree of polarization depends little on wavelength and angle of incidence, they are used for broad-band applications such as projection. Analytical solutions using rigorous coupled-wave analysis for wire grid polarizers have shown that for electric field components perpendicular to the wires, the medium behaves like

15232-486: The polarizers are crossed and in theory no light is transmitted, though again practically speaking no polarizer is perfect and the transmission is not exactly zero (for example, crossed Polaroid sheets appear slightly blue in colour because their extinction ratio is better in the red). If a transparent object is placed between the crossed polarizers, any polarization effects present in the sample (such as birefringence) will be shown as an increase in transmission. This effect

15368-477: The positive 45° angle leaves the linear polarizer and enters the quarter-wave plate. In the illustration, the three wavelengths of unpolarized light represented would be transformed into the three wavelengths of linearly polarized light on the other side of the linear polarizer. In the illustration toward the right is the electric field of the linearly polarized light just before it enters the quarter-wave plate. The red line and associated field vectors represent how

15504-600: The prism at a divergence angle of 15°–45°. The Rochon and Sénarmont prisms are similar, but use different optical axis orientations in the two prisms. The Sénarmont prism is air spaced, unlike the Wollaston and Rochon prisms. These prisms truly split the beam into two fully polarized beams with perpendicular polarizations. The Nomarski prism is a variant of the Wollaston prism, which is widely used in differential interference contrast microscopy . Thin-film linear polarizers (also known as TFPN) are glass substrates on which

15640-428: The radiation's power and its frequency. EMR of lower energy ultraviolet or lower frequencies (i.e., near ultraviolet , visible light, infrared, microwaves, and radio waves) is non-ionizing because its photons do not individually have enough energy to ionize atoms or molecules or to break chemical bonds . The effect of non-ionizing radiation on chemical systems and living tissue is primarily simply heating, through

15776-408: The red line onto the vertical and horizontal planes respectively and represent how the electric field changes in the direction of those two planes. The two components have the same amplitude and are in phase. Because the quarter-wave plate is made of a birefringent material, when in the wave plate, the light travels at different speeds depending on the direction of its electric field. This means that

15912-470: The red part of the spectrum, through an increase in the temperature recorded with a thermometer . These "calorific rays" were later termed infrared. In 1801, German physicist Johann Wilhelm Ritter discovered ultraviolet in an experiment similar to Herschel's, using sunlight and a glass prism. Ritter noted that invisible rays near the violet edge of a solar spectrum dispersed by a triangular prism darkened silver chloride preparations more quickly than did

16048-411: The resulting hologram are avoided. Entrance windows or prisms with their surfaces at the Brewster angle are commonly used in optics and laser physics in particular. The polarized laser light enters the prism at Brewster's angle without any reflective losses. In surface science, Brewster angle microscopes are used to image layers of particles or molecules at air-liquid interfaces. Using illumination by

16184-403: The rightward horizontal component is now one quarter of a wavelength behind the vertical component. It is this quarter of a wavelength phase shift that results in the rotational nature of the electric field. When the magnitude of one component is at a maximum the magnitude of the other component is always zero. This is the reason that there are helix vectors which exactly correspond to the maxima of

16320-412: The same points in space (see illustrations). In the far-field EM radiation which is described by the two source-free Maxwell curl operator equations, a time-change in one type of field is proportional to the curl of the other. These derivatives require that the E and B fields in EMR are in-phase (see mathematics section below). An important aspect of light's nature is its frequency . The frequency of

16456-464: The same time (see wave-particle duality ). Both wave and particle characteristics have been confirmed in many experiments. Wave characteristics are more apparent when EM radiation is measured over relatively large timescales and over large distances while particle characteristics are more evident when measuring small timescales and distances. For example, when electromagnetic radiation is absorbed by matter, particle-like properties will be more obvious when

16592-556: The separation between wires must be less than the wavelength of the incident radiation. In addition, the width of each wire should be small compared to the spacing between wires. Therefore, it is relatively easy to construct wire-grid polarizers for microwaves , far- infrared , and mid- infrared radiation. For far-infrared optics, the polarizer can be even made as free standing mesh, entirely without transmissive optics. In addition, advanced lithographic techniques can also build very tight pitch metallic grids (typ. 50‒100 nm), allowing for

16728-472: The source, the power density of EM radiation from an isotropic source decreases with the inverse square of the distance from the source; this is called the inverse-square law . This is in contrast to dipole parts of the EM field, the near field, which varies in intensity according to an inverse cube power law, and thus does not transport a conserved amount of energy over distances but instead fades with distance, with its energy (as noted) rapidly returning to

16864-549: The speed in a medium to speed in a vacuum. Electromagnetic radiation of wavelengths other than those of visible light were discovered in the early 19th century. The discovery of infrared radiation is ascribed to astronomer William Herschel , who published his results in 1800 before the Royal Society of London . Herschel used a glass prism to refract light from the Sun and detected invisible rays that caused heating beyond

17000-410: The term associated with the changing static electric field of the particle and the magnetic term that results from the particle's uniform velocity are both associated with the near field, and do not comprise electromagnetic radiation. Electric and magnetic fields obey the properties of superposition . Thus, a field due to any particular particle or time-varying electric or magnetic field contributes to

17136-475: The transmitter or absorbed by a nearby receiver (such as a transformer secondary coil). In the Liénard–Wiechert potential formulation of the electric and magnetic fields due to motion of a single particle (according to Maxwell's equations), the terms associated with acceleration of the particle are those that are responsible for the part of the field that is regarded as electromagnetic radiation. By contrast,

17272-427: The transmitter to affect them. This causes them to be independent in the sense that their existence and their energy, after they have left the transmitter, is completely independent of both transmitter and receiver. Due to conservation of energy , the amount of power passing through any spherical surface drawn around the source is the same. Because such a surface has an area proportional to the square of its distance from

17408-399: The two components. In the instance just cited, using the handedness convention used in many optics textbooks, the light is considered left-handed/counter-clockwise circularly polarized. Referring to the accompanying animation, it is considered left-handed because if one points one's left thumb against the direction of travel, ones fingers curl in the direction the electric field rotates as

17544-452: The two rays will be in different polarization states, though not in linear polarization states except for certain propagation directions relative to the crystal axis. A Nicol prism was an early type of birefringent polarizer, that consists of a crystal of calcite which has been split and rejoined with Canada balsam . The crystal is cut such that the o - and e -rays are in orthogonal linear polarization states. Total internal reflection of

17680-440: The unpolarized beam is split into two beams with opposite polarization states. Polarizers which maintain the same axes of polarization with varying angles of incidence are often called Cartesian polarizers , since the polarization vectors can be described with simple Cartesian coordinates (for example, horizontal vs. vertical) independent from the orientation of the polarizer surface. When the two polarization states are relative to

17816-448: The wave passes a given point in space. The helix also forms a left-handed helix in space. Similarly this light is considered counter-clockwise circularly polarized because if a stationary observer faces against the direction of travel, the person will observe its electric field rotate in the counter-clockwise direction as the wave passes a given point in space. To create right-handed, clockwise circularly polarized light one simply rotates

17952-524: The wave theory, however, Einstein's ideas were met initially with great skepticism among established physicists. Eventually Einstein's explanation was accepted as new particle-like behavior of light was observed, such as the Compton effect . As a photon is absorbed by an atom , it excites the atom, elevating an electron to a higher energy level (one that is on average farther from the nucleus). When an electron in an excited molecule or atom descends to

18088-424: The width of each wire. Therefore, little energy is reflected and the incident wave is able to pass through the grid. In this case the grid behaves like a dielectric material . Overall, this causes the transmitted wave to be linearly polarized with an electric field completely perpendicular to the wires. The hypothesis that the waves "slip through" the gaps between the wires is incorrect. For practical purposes,

18224-500: The wire-grid polarizer. It was originally made of microscopic herapathite crystals. Its current H-sheet form is made from polyvinyl alcohol (PVA) plastic with an iodine doping. Stretching of the sheet during manufacture causes the PVA chains to align in one particular direction. Valence electrons from the iodine dopant are able to move linearly along the polymer chains, but not transverse to them. So incident light polarized parallel to

18360-617: The zero-reflection condition just obtained by n 2 {\displaystyle n_{2}} and square both sides; and add the equations. This produces We finally divide both sides by n 1 4 cos 2 ⁡ θ 1 {\displaystyle n_{1}^{4}\cos ^{2}\theta _{1}} , collect terms and rearrange to produce tan 2 ⁡ θ 1 = n 2 2 / n 1 2 {\displaystyle \tan ^{2}\theta _{1}=n_{2}^{2}/n_{1}^{2}} , from which

18496-422: Was an experimental anomaly not explained by the wave theory: the photoelectric effect , in which light striking a metal surface ejected electrons from the surface, causing an electric current to flow across an applied voltage . Experimental measurements demonstrated that the energy of individual ejected electrons was proportional to the frequency , rather than the intensity , of the light. Furthermore, below

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