A polarizer or polariser is an optical filter that lets light waves of a specific polarization pass through while blocking light waves of other polarizations. It can filter a beam of light of undefined or mixed polarization into a beam of well-defined polarization, polarized light; the common types of polarizers are circular polarizers. Polarizers are used in many optical techniques and instruments, polarizing filters find applications in photography and LCD technology. Polarizers can be made for other types of electromagnetic waves besides light, such as radio waves, X-rays. Linear polarizers can be divided into two general categories: absorptive polarizers, where the unwanted polarization states are absorbed by the device, beam-splitting polarizers, where 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 called Cartesian polarizers, since the polarization vectors can be described with simple Cartesian coordinates independent from the orientation of the polarizer surface.
When the two polarization states are relative to the direction of a surface, they are 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, 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 used as a polarizer, since the dichroic effect is wavelength dependent and the crystal appears coloured. Herapathite is dichroic, is not coloured, but is difficult to grow in large crystals. A Polaroid polarizing filter functions on an atomic scale to the wire-grid polarizer, it was made of microscopic herapathite crystals. Its current H-sheet form is made from polyvinyl alcohol 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; the durability and practicality of Polaroid makes it the most common type of polarizer in use, for example for sunglasses, photographic filters, liquid crystal displays. It is much cheaper than other types of polarizer. A modern type of absorptive polarizer is made of elongated silver nano-particles embedded in thin glass plates; these polarizers are more durable, can polarize light much better than plastic Polaroid film, achieving polarization ratios as high as 100,000:1 and absorption of polarized light as low as 1.5%. Such glass polarizers perform best for short-wavelength infrared light, are used in optical fiber communications. Beam-splitting polarizers split the incident beam into two beams of differing linear polarization. For an ideal polarizing beamsplitter these would be polarized, with orthogonal polarizations. For many common beam-splitting polarizers, only one of the two output beams is polarized.
The other contains a mixture of polarization states. Unlike absorptive polarizers, beam splitting polarizers do not need to absorb and dissipate the energy of the rejected polarization state, so they are more suitable for use with high intensity beams such as laser light. True polarizing beamsplitters are useful where the two polarization components are to be analyzed or used simultaneously; when light reflects at an angle from an interface between two transparent materials, the reflectivity is different for light polarized in 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 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°, about 16% of 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 mediocre polarization of the transmitted beam with this approach. For a stack of 10 plates, about 3% of the s-polarized light is transmitted; the reflected beam, while polarized, is spread out and may not be useful. A more useful polarized beam can be obtained by tilting 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 is low in this case.
Adding more plates and reducing
In optics, the refractive index or index of refraction of a material is a dimensionless number that describes how fast light propagates through the material. It is defined as n = c v, where c is the speed of light in vacuum and v is the phase velocity of light in the medium. For example, the refractive index of water is 1.333, meaning that light travels 1.333 times as fast in vacuum as in water. The refractive index determines how much the path of light is bent, or refracted, when entering a material; this is described by Snell's law of refraction, n1 sinθ1 = n2 sinθ2, where θ1 and θ2 are the angles of incidence and refraction of a ray crossing the interface between two media with refractive indices n1 and n2. The refractive indices determine the amount of light, reflected when reaching the interface, as well as the critical angle for total internal reflection and Brewster's angle; the refractive index can be seen as the factor by which the speed and the wavelength of the radiation are reduced with respect to their vacuum values: the speed of light in a medium is v = c/n, the wavelength in that medium is λ = λ0/n, where λ0 is the wavelength of that light in vacuum.
This implies that vacuum has a refractive index of 1, that the frequency of the wave is not affected by the refractive index. As a result, the energy of the photon, therefore the perceived color of the refracted light to a human eye which depends on photon energy, is not affected by the refraction or the refractive index of the medium. While the refractive index affects wavelength, it depends on photon frequency and energy so the resulting difference in the bending angle causes white light to split into its constituent colors; this is called dispersion. It can be observed in prisms and rainbows, chromatic aberration in lenses. Light propagation in absorbing materials can be described using a complex-valued refractive index; the imaginary part handles the attenuation, while the real part accounts for refraction. The concept of refractive index applies within the full electromagnetic spectrum, from X-rays to radio waves, it can be applied to wave phenomena such as sound. In this case the speed of sound is used instead of that of light, a reference medium other than vacuum must be chosen.
The refractive index n of an optical medium is defined as the ratio of the speed of light in vacuum, c = 299792458 m/s, the phase velocity v of light in the medium, n = c v. The phase velocity is the speed at which the crests or the phase of the wave moves, which may be different from the group velocity, the speed at which the pulse of light or the envelope of the wave moves; the definition above is sometimes referred to as the absolute refractive index or the absolute index of refraction to distinguish it from definitions where the speed of light in other reference media than vacuum is used. Air at a standardized pressure and temperature has been common as a reference medium. Thomas Young was the person who first used, invented, the name "index of refraction", in 1807. At the same time he changed this value of refractive power into a single number, instead of the traditional ratio of two numbers; the ratio had the disadvantage of different appearances. Newton, who called it the "proportion of the sines of incidence and refraction", wrote it as a ratio of two numbers, like "529 to 396".
Hauksbee, who called it the "ratio of refraction", wrote it as a ratio with a fixed numerator, like "10000 to 7451.9". Hutton wrote it as a ratio with a fixed denominator, like 1.3358 to 1. Young did not use a symbol for the index of refraction, in 1807. In the next years, others started using different symbols: n, m, µ; the symbol n prevailed. For visible light most transparent media have refractive indices between 1 and 2. A few examples are given in the adjacent table; these values are measured at the yellow doublet D-line of sodium, with a wavelength of 589 nanometers, as is conventionally done. Gases at atmospheric pressure have refractive indices close to 1 because of their low density. All solids and liquids have refractive indices above 1.3, with aerogel as the clear exception. Aerogel is a low density solid that can be produced with refractive index in the range from 1.002 to 1.265. Moissanite lies at the other end of the range with a refractive index as high as 2.65. Most plastics have refractive indices in the range from 1.3 to 1.7, but some high-refractive-index polymers can have values as high as 1.76.
For infrared light refractive indices can be higher. Germanium is transparent in the wavelength region from 2 to 14 µm and has a refractive index of about 4. A type of new materials, called topological insulator, was found holding higher refractive index of up to 6 in near to mid infrared frequency range. Moreover, topological insulator material are transparent; these excellent properties make them a type of significant materials for infrared optics. According to the theory of relativity, no information can travel faster than the speed of light in vacuum, but this does not mean that the refractive index cannot be lower than 1; the refractive index measures the phase velocity of light. 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, thereby give a refractive index below 1; this can occur close to resonance frequencies, for absorbing media, in plasmas, for X-rays. In the X-ray regime the refractive indices are
Wood is a porous and fibrous structural tissue found in the stems and roots of trees and other woody plants. It is an organic material, a natural composite of cellulose fibers that are strong in tension and embedded in a matrix of lignin that resists compression. Wood is sometimes defined as only the secondary xylem in the stems of trees, or it is defined more broadly to include the same type of tissue elsewhere such as in the roots of trees or shrubs. In a living tree it performs a support function, enabling woody plants to grow large or to stand up by themselves, it conveys water and nutrients between the leaves, other growing tissues, the roots. Wood may refer to other plant materials with comparable properties, to material engineered from wood, or wood chips or fiber. Wood has been used for thousands of years for fuel, as a construction material, for making tools and weapons and paper. More it emerged as a feedstock for the production of purified cellulose and its derivatives, such as cellophane and cellulose acetate.
As of 2005, the growing stock of forests worldwide was about 434 billion cubic meters, 47% of, commercial. As an abundant, carbon-neutral renewable resource, woody materials have been of intense interest as a source of renewable energy. In 1991 3.5 billion cubic meters of wood were harvested. Dominant uses were for building construction. A 2011 discovery in the Canadian province of New Brunswick yielded the earliest known plants to have grown wood 395 to 400 million years ago. Wood can be dated by carbon dating and in some species by dendrochronology to determine when a wooden object was created. People have used wood for thousands of years for many purposes, including as a fuel or as a construction material for making houses, weapons, packaging and paper. Known constructions using wood date back ten thousand years. Buildings like the European Neolithic long house were made of wood. Recent use of wood has been enhanced by the addition of bronze into construction; the year-to-year variation in tree-ring widths and isotopic abundances gives clues to the prevailing climate at the time a tree was cut.
Wood, in the strict sense, is yielded by trees, which increase in diameter by the formation, between the existing wood and the inner bark, of new woody layers which envelop the entire stem, living branches, roots. This process is known as secondary growth; these cells go on to form thickened secondary cell walls, composed of cellulose and lignin. Where the differences between the four seasons are distinct, e.g. New Zealand, growth can occur in a discrete annual or seasonal pattern, leading to growth rings. If the distinctiveness between seasons is annual, these growth rings are referred to as annual rings. Where there is little seasonal difference growth rings are to be indistinct or absent. If the bark of the tree has been removed in a particular area, the rings will be deformed as the plant overgrows the scar. If there are differences within a growth ring the part of a growth ring nearest the center of the tree, formed early in the growing season when growth is rapid, is composed of wider elements.
It is lighter in color than that near the outer portion of the ring, is known as earlywood or springwood. The outer portion formed in the season is known as the latewood or summerwood. However, there are major differences, depending on the kind of wood; as a tree grows, lower branches die, their bases may become overgrown and enclosed by subsequent layers of trunk wood, forming a type of imperfection known as a knot. The dead branch may not be attached to the trunk wood except at its base, can drop out after the tree has been sawn into boards. Knots affect the technical properties of the wood reducing the local strength and increasing the tendency for splitting along the wood grain, but may be exploited for visual effect. In a longitudinally sawn plank, a knot will appear as a circular "solid" piece of wood around which the grain of the rest of the wood "flows". Within a knot, the direction of the wood is up to 90 degrees different from the grain direction of the regular wood. In the tree a knot is either the base of a dormant bud.
A knot is conical in shape with the inner tip at the point in stem diameter at which the plant's vascular cambium was located when the branch formed as a bud. In grading lumber and structural timber, knots are classified according to their form, size and the firmness with which they are held in place; this firmness is affected by, among other factors, the length of time for which the branch was dead while the attaching stem continued to grow. Knots materially affect cracking and warping, ease in working, cleavability of timber, they are defects which weaken timber and lower its value for structural purposes where strength is an important consideration. The weakening effect is much more serious when timber is subjected to forces perpendicular to the grain and/or tension than when under load along the grain and/or compression; the extent to which knots affect the strength of a beam depends upon their position, size and condition. A knot on the upper side is compressed. If there is a season check
Electrical resistivity and conductivity
Electrical resistivity and its converse, electrical conductivity, is a fundamental property of a material that quantifies how it resists or conducts the flow of electric current. A low resistivity indicates a material that allows the flow of electric current. Resistivity is represented by the Greek letter ρ; the SI unit of electrical resistivity is the ohm-metre. For example, if a 1 m × 1 m × 1 m solid cube of material has sheet contacts on two opposite faces, the resistance between these contacts is 1 Ω the resistivity of the material is 1 Ω⋅m. Electrical conductivity or specific conductance is the reciprocal of electrical resistivity, it represents a material's ability to conduct electric current. It is signified by the Greek letter σ, but κ and γ are sometimes used; the SI unit of electrical conductivity is siemens per metre. In an ideal case, cross-section and physical composition of the examined material are uniform across the sample, the electric field and current density are both parallel and constant everywhere.
Many resistors and conductors do in fact have a uniform cross section with a uniform flow of electric current, are made of a single material, so that this is a good model. When this is the case, the electrical resistivity ρ can be calculated by: ρ = R A ℓ, where R is the electrical resistance of a uniform specimen of the material ℓ is the length of the specimen A is the cross-sectional area of the specimenBoth resistance and resistivity describe how difficult it is to make electrical current flow through a material, but unlike resistance, resistivity is an intrinsic property; this means that all pure copper wires, irrespective of their shape and size, have the same resistivity, but a long, thin copper wire has a much larger resistance than a thick, short copper wire. Every material has its own characteristic resistivity. For example, rubber has a far larger resistivity than copper. In a hydraulic analogy, passing current through a high-resistivity material is like pushing water through a pipe full of sand—while passing current through a low-resistivity material is like pushing water through an empty pipe.
If the pipes are the same size and shape, the pipe full of sand has higher resistance to flow. Resistance, however, is not determined by the presence or absence of sand, it depends on the length and width of the pipe: short or wide pipes have lower resistance than narrow or long pipes. The above equation can be transposed to get Pouillet's law: R = ρ ℓ A; the resistance of a given material is proportional to the length, but inversely proportional to the cross-sectional area. Thus resistivity can be expressed using the SI unit "ohm metre" (i.e ohms divided by metres and multiplied by square metres }. For example, if A = 1 m2 ℓ = 1 m the resistance of this element in ohms is numerically equal to the resistivity of the material it is made of in Ω⋅m. Conductivity, σ, is the inverse of resistivity: σ = 1 ρ. Conductivity has SI units of "siemens per metre". For less ideal cases, such as more complicated geometry, or when the current and electric field vary in different parts of the material, it is necessary to use a more general expression in which the resistivity at a particular point is defined as the ratio of the electric field to the density of the current it creates at that point: ρ = E J, where ρ is the resistivity of the conductor material, E is the magnitude of the electric field, J is the magnitude of the current density,in which E and J are inside the conductor.
Conductivity is the inverse of resistivity. Here, it is given by: σ = 1 ρ = J E. For example, rubber is a material with large ρ and small σ—because a large electric field in rubber makes no current flow through it. On the other hand, copper is a material with small ρ and large σ—because a small electric field pulls a lot of current through it; as shown below, this expression simplifies to a single number when the electric field and current density are constant in the material. When the resistivity of a material has a directional component, the most general definition of resistivity must be used, it starts from the tensor-vector form of Ohm's law which relates the electric field inside a material to the electric current flow. This equation is general, meaning it is valid in all cases, including those mentioned above. However, this definition is the most complicated, so it is only directly used in anisotropic cases, where the more simple definitions cannot be applied. If the material is not anisotropic
Liquid crystals are a state of matter which has properties between those of conventional liquids and those of solid crystals. For instance, a liquid crystal may flow like a liquid, but its molecules may be oriented in a crystal-like way. There are many different types of liquid-crystal phases, which can be distinguished by their different optical properties; the contrasting areas in the textures correspond to domains where the liquid-crystal molecules are oriented in different directions. Within a domain, the molecules are well ordered. LC materials may not always be in a liquid-crystal phase. Liquid crystals can be divided into thermotropic and metallotropic phases. Thermotropic and lyotropic liquid crystals consist of organic molecules, although a few minerals are known. Thermotropic LCs exhibit a phase transition into the liquid-crystal phase. Lyotropic LCs exhibit phase transitions as a function of both temperature and concentration of the liquid-crystal molecules in a solvent. Metallotropic LCs are composed of both inorganic molecules.
Examples of liquid crystals can be found both in the natural world and in technological applications. Most contemporary electronic displays use liquid crystals. Lyotropic liquid-crystalline phases are abundant in living systems but can be found in the mineral world. For example, many proteins and cell membranes are liquid crystals. Other well-known examples of liquid crystals are solutions of soap and various related detergents, as well as the tobacco mosaic virus, some clays. In 1888, Austrian botanical physiologist Friedrich Reinitzer, working at the Karl-Ferdinands-Universität, examined the physico-chemical properties of various derivatives of cholesterol which now belong to the class of materials known as cholesteric liquid crystals. Other researchers had observed distinct color effects when cooling cholesterol derivatives just above the freezing point, but had not associated it with a new phenomenon. Reinitzer perceived that color changes in a derivative cholesteryl benzoate were not the most peculiar feature.
He found that cholesteryl benzoate does not melt in the same manner as other compounds, but has two melting points. At 145.5 °C it melts into a cloudy liquid, at 178.5 °C it melts again and the cloudy liquid becomes clear. The phenomenon is reversible. Seeking help from a physicist, on March 14, 1888, he wrote to Otto Lehmann, at that time a Privatdozent in Aachen, they exchanged samples. Lehmann examined the intermediate cloudy fluid, reported seeing crystallites. Reinitzer's Viennese colleague von Zepharovich indicated that the intermediate "fluid" was crystalline; the exchange of letters with Lehmann ended on April 24, with many questions unanswered. Reinitzer presented his results, with credits to Lehmann and von Zepharovich, at a meeting of the Vienna Chemical Society on May 3, 1888. By that time, Reinitzer had discovered and described three important features of cholesteric liquid crystals: the existence of two melting points, the reflection of circularly polarized light, the ability to rotate the polarization direction of light.
After his accidental discovery, Reinitzer did not pursue studying liquid crystals further. The research was continued by Lehmann, who realized that he had encountered a new phenomenon and was in a position to investigate it: In his postdoctoral years he had acquired expertise in crystallography and microscopy. Lehmann started a systematic study, first of cholesteryl benzoate, of related compounds which exhibited the double-melting phenomenon, he was able to make observations in polarized light, his microscope was equipped with a hot stage enabling high temperature observations. The intermediate cloudy phase sustained flow, but other features the signature under a microscope, convinced Lehmann that he was dealing with a solid. By the end of August 1889 he had published his results in the Zeitschrift für Physikalische Chemie. Lehmann's work was continued and expanded by the German chemist Daniel Vorländer, who from the beginning of 20th century until his retirement in 1935, had synthesized most of the liquid crystals known.
However, liquid crystals were not popular among scientists and the material remained a pure scientific curiosity for about 80 years. After World War II work on the synthesis of liquid crystals was restarted at university research laboratories in Europe. George William Gray, a prominent researcher of liquid crystals, began investigating these materials in England in the late 1940s, his group synthesized many new materials that exhibited the liquid crystalline state and developed a better understanding of how to design molecules that exhibit the state. His book Molecular Structure and the Properties of Liquid Crystals became a guidebook on the subject. One of the first U. S. chemists to study liquid crystals was Glenn H. Brown, starting in 1953 at the University of Cincinnati and at Kent State University. In 1965, he organized the first international conference on liquid crystals, in Kent, with about 100 of the world's top liquid crystal scientists in attendance; this conference marked the beginning of a worldwide effort to perform research in this field, which soon led to the development of practical applications for these unique materials.
Liquid crystal materials became a focus of research in the development of flat panel electronic displays beginning in 1962 at RCA Laboratories. When physical che
In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is thus the inverse of the spatial frequency. Wavelength is determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings and is a characteristic of both traveling waves and standing waves, as well as other spatial wave patterns. Wavelength is designated by the Greek letter lambda; the term wavelength is sometimes applied to modulated waves, to the sinusoidal envelopes of modulated waves or waves formed by interference of several sinusoids. Assuming a sinusoidal wave moving at a fixed wave speed, wavelength is inversely proportional to frequency of the wave: waves with higher frequencies have shorter wavelengths, lower frequencies have longer wavelengths. Wavelength depends on the medium. Examples of wave-like phenomena are sound waves, water waves and periodic electrical signals in a conductor.
A sound wave is a variation in air pressure, while in light and other electromagnetic radiation the strength of the electric and the magnetic field vary. Water waves are variations in the height of a body of water. In a crystal lattice vibration, atomic positions vary. Wavelength is a measure of the distance between repetitions of a shape feature such as peaks, valleys, or zero-crossings, not a measure of how far any given particle moves. For example, in sinusoidal waves over deep water a particle near the water's surface moves in a circle of the same diameter as the wave height, unrelated to wavelength; the range of wavelengths or frequencies for wave phenomena is called a spectrum. The name originated with the visible light spectrum but now can be applied to the entire electromagnetic spectrum as well as to a sound spectrum or vibration spectrum. In linear media, any wave pattern can be described in terms of the independent propagation of sinusoidal components; the wavelength λ of a sinusoidal waveform traveling at constant speed v is given by λ = v f, where v is called the phase speed of the wave and f is the wave's frequency.
In a dispersive medium, the phase speed itself depends upon the frequency of the wave, making the relationship between wavelength and frequency nonlinear. In the case of electromagnetic radiation—such as light—in free space, the phase speed is the speed of light, about 3×108 m/s, thus the wavelength of a 100 MHz electromagnetic wave is about: 3×108 m/s divided by 108 Hz = 3 metres. The wavelength of visible light ranges from deep red 700 nm, to violet 400 nm. For sound waves in air, the speed of sound is 343 m/s; the wavelengths of sound frequencies audible to the human ear are thus between 17 m and 17 mm, respectively. Note that the wavelengths in audible sound are much longer than those in visible light. A standing wave is an undulatory motion. A sinusoidal standing wave includes stationary points of no motion, called nodes, the wavelength is twice the distance between nodes; the upper figure shows three standing waves in a box. The walls of the box are considered to require the wave to have nodes at the walls of the box determining which wavelengths are allowed.
For example, for an electromagnetic wave, if the box has ideal metal walls, the condition for nodes at the walls results because the metal walls cannot support a tangential electric field, forcing the wave to have zero amplitude at the wall. The stationary wave can be viewed as the sum of two traveling sinusoidal waves of oppositely directed velocities. Wavelength and wave velocity are related just as for a traveling wave. For example, the speed of light can be determined from observation of standing waves in a metal box containing an ideal vacuum. Traveling sinusoidal waves are represented mathematically in terms of their velocity v, frequency f and wavelength λ as: y = A cos = A cos where y is the value of the wave at any position x and time t, A is the amplitude of the wave, they are commonly expressed in terms of wavenumber k and angular frequency ω as: y = A cos = A cos in which wavelength and wavenumber are related to velocity and frequency as: k = 2 π λ = 2 π f v = ω