1.
Calcite
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Calcite is a carbonate mineral and the most stable polymorph of calcium carbonate. The Mohs scale of hardness, based on scratch hardness comparison. Other polymorphs of calcium carbonate are the minerals aragonite and vaterite, aragonite will change to calcite at 380–470 °C, and vaterite is even less stable. Calcite is derived from the German Calcit, a term coined in the 19th century from the Latin word for lime and it is thus etymologically related to chalk. Calcite crystals are trigonal-rhombohedral, though actual calcite rhombohedra are rare as natural crystals, however, they show a remarkable variety of habits including acute to obtuse rhombohedra, tabular forms, prisms, or various scalenohedra. Calcite exhibits several twinning types adding to the variety of observed forms and it may occur as fibrous, granular, lamellar, or compact. Cleavage is usually in three directions parallel to the rhombohedron form and its fracture is conchoidal, but difficult to obtain. It has a defining Mohs hardness of 3, a gravity of 2.71. Color is white or none, though shades of gray, red, orange, yellow, green, blue, violet, brown, calcite is transparent to opaque and may occasionally show phosphorescence or fluorescence. A transparent variety called Iceland spar is used for optical purposes, acute scalenohedral crystals are sometimes referred to as dogtooth spar while the rhombohedral form is sometimes referred to as nailhead spar. Single calcite crystals display an optical property called birefringence and this strong birefringence causes objects viewed through a clear piece of calcite to appear doubled. The birefringent effect was first described by the Danish scientist Rasmus Bartholin in 1669, at a wavelength of ~590 nm calcite has ordinary and extraordinary refractive indices of 1.658 and 1.486, respectively. Between 190 and 1700 nm, the refractive index varies roughly between 1.9 and 1.5, while the extraordinary refractive index varies between 1.6 and 1.4. Calcite, like most carbonates, will dissolve with most forms of acid, calcite can be either dissolved by groundwater or precipitated by groundwater, depending on several factors including the water temperature, pH, and dissolved ion concentrations. Although calcite is fairly insoluble in water, acidity can cause dissolution of calcite. Ambient carbon dioxide, due to its acidity, has a slight solubilizing effect on calcite, calcite exhibits an unusual characteristic called retrograde solubility in which it becomes less soluble in water as the temperature increases. When conditions are right for precipitation, calcite forms mineral coatings that cement the existing rock grains together or it can fill fractures. On a landscape scale, continued dissolution of calcium carbonate-rich rocks can lead to the expansion and eventual collapse of cave systems, high-grade optical calcite was used in World War II for gun sights, specifically in bomb sights and anti-aircraft weaponry
2.
Optics
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Optics is the branch of physics which involves the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behaviour of visible, ultraviolet, and infrared light, because light is an electromagnetic wave, other forms of electromagnetic radiation such as X-rays, microwaves, and radio waves exhibit similar properties. Most optical phenomena can be accounted for using the classical description of light. Complete electromagnetic descriptions of light are, however, often difficult to apply in practice, practical optics is usually done using simplified models. The most common of these, geometric optics, treats light as a collection of rays that travel in straight lines, physical optics is a more comprehensive model of light, which includes wave effects such as diffraction and interference that cannot be accounted for in geometric optics. Historically, the model of light was developed first, followed by the wave model of light. Progress in electromagnetic theory in the 19th century led to the discovery that waves were in fact electromagnetic radiation. Some phenomena depend on the fact that light has both wave-like and particle-like properties, explanation of these effects requires quantum mechanics. When considering lights particle-like properties, the light is modelled as a collection of particles called photons, quantum optics deals with the application of quantum mechanics to optical systems. Optical science is relevant to and studied in many related disciplines including astronomy, various engineering fields, photography, practical applications of optics are found in a variety of technologies and everyday objects, including mirrors, lenses, telescopes, microscopes, lasers, and fibre optics. Optics began with the development of lenses by the ancient Egyptians and Mesopotamians, the earliest known lenses, made from polished crystal, often quartz, date from as early as 700 BC for Assyrian lenses such as the Layard/Nimrud lens. The ancient Romans and Greeks filled glass spheres with water to make lenses, the word optics comes from the ancient Greek word ὀπτική, meaning appearance, look. Greek philosophy on optics broke down into two opposing theories on how vision worked, the theory and the emission theory. The intro-mission approach saw vision as coming from objects casting off copies of themselves that were captured by the eye, plato first articulated the emission theory, the idea that visual perception is accomplished by rays emitted by the eyes. He also commented on the parity reversal of mirrors in Timaeus, some hundred years later, Euclid wrote a treatise entitled Optics where he linked vision to geometry, creating geometrical optics. Ptolemy, in his treatise Optics, held a theory of vision, the rays from the eye formed a cone, the vertex being within the eye. The rays were sensitive, and conveyed back to the observer’s intellect about the distance. He summarised much of Euclid and went on to describe a way to measure the angle of refraction, during the Middle Ages, Greek ideas about optics were resurrected and extended by writers in the Muslim world
3.
Refractive index
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In optics, the refractive index or index of refraction n of a material is a dimensionless number that describes how light propagates through that medium. It is defined as n = c v, where c is the speed of light in vacuum, for example, the refractive index of water is 1.333, meaning that light travels 1.333 times faster in a vacuum than it does in water. The refractive index determines how light is bent, or refracted. The refractive indices also determine the amount of light that is reflected when reaching the interface, as well as the angle for total internal reflection. This implies that vacuum has a index of 1. The refractive index varies with the wavelength of light and this is called dispersion and causes the splitting of white light into its constituent colors in prisms and rainbows, and chromatic aberration in lenses. Light propagation in absorbing materials can be described using a refractive index. The imaginary part then handles the attenuation, while the real part accounts for refraction, the concept of refractive index is widely used within the full electromagnetic spectrum, from X-rays to radio waves. It can also be used with wave phenomena such as sound, in this case the speed of sound is used instead of that of light and a reference medium other than vacuum must be chosen. Thomas Young was presumably the person who first used, and invented, 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, 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 the next years, others started using different symbols, n, m, and µ. 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, gases at atmospheric pressure have refractive indices close to 1 because of their low density. Almost all solids and liquids have refractive indices above 1.3, aerogel is a very low density solid that can be produced with refractive index in the range from 1.002 to 1.265. Moissanite lies at the 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, for infrared light refractive indices can be considerably higher
4.
Polarization (waves)
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Polarization is a parameter applying to transverse waves that specifies the geometrical orientation of the oscillations. In a transverse wave the direction of the oscillation is transverse to the direction of motion of the wave, a simple example of a polarized transverse wave is vibrations traveling along a taut string for example in a musical instrument like a guitar string. Depending on how the string is plucked, the vibrations can be in a direction, horizontal direction. Transverse waves that exhibit polarization include electromagnetic waves such as light and radio waves, gravitational waves, in some types of transverse waves the wave displacement is limited to a single direction, so these also dont exhibit polarization. For example, in waves in liquids the wave displacement of the particles is always in a vertical plane. In linear polarization the fields oscillate in a single direction, in circular or elliptical polarization the fields rotate at a constant rate in a plane as the wave travels. Polarized light can be produced by passing unpolarized light through a polarizing filter, some of these are used to make polarizing filters. Light is also partially polarized when it reflects from a surface, according to quantum mechanics, electromagnetic waves consist of particles called photons. When viewed in this way, the polarization of a wave is determined by a quantum mechanical property of photons called their spin. A photon has one of two spins, it can either spin in a right hand sense or a left hand sense about its direction of travel. Circularly polarized electromagnetic waves are composed of photons with one type of spin. Linearly polarized waves consist of numbers of right and left hand spinning photons. Polarization is an important parameter in areas of science dealing with transverse waves, such as optics, seismology, radio, especially impacted are technologies such as lasers, wireless and optical fiber telecommunications, and radar. And incoherent states can be modeled stochastically as a combination of such uncorrelated waves with some distribution of frequencies, phases. Considering a monochromatic wave of optical frequency f, let us take the direction of propagation as the z axis. Being a transverse wave the E and H fields must then contain components only in the x and y directions whereas Ez=Hz=0. Using complex notation, we understand the instantaneous electric and magnetic fields to be given by the real parts of the complex quantities occurring in the following equations. Here ex, ey, hx, and hy are complex numbers, in the second more compact form, as these equations are customarily expressed, these factors are described using the wavenumber k =2 π n / λ and angular frequency ω =2 π f
5.
Light
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Light is electromagnetic radiation within a certain portion of the electromagnetic spectrum. The word usually refers to light, which is visible to the human eye and is responsible for the sense of sight. Visible light is defined as having wavelengths in the range of 400–700 nanometres, or 4.00 × 10−7 to 7.00 × 10−7 m. This wavelength means a range of roughly 430–750 terahertz. The main source of light on Earth is the Sun, sunlight provides the energy that green plants use to create sugars mostly in the form of starches, which release energy into the living things that digest them. This process of photosynthesis provides virtually all the used by living things. Historically, another important source of light for humans has been fire, with the development of electric lights and power systems, electric lighting has effectively replaced firelight. Some species of animals generate their own light, a process called bioluminescence, for example, fireflies use light to locate mates, and vampire squids use it to hide themselves from prey. Visible light, as all types of electromagnetic radiation, is experimentally found to always move at this speed in a vacuum. In physics, the term sometimes refers to electromagnetic radiation of any wavelength. In this sense, gamma rays, X-rays, microwaves and radio waves are also light, like all types of light, visible light is emitted and absorbed in tiny packets called photons and exhibits properties of both waves and particles. This property is referred to as the wave–particle duality, the study of light, known as optics, is an important research area in modern physics. Generally, EM radiation, or EMR, is classified by wavelength into radio, microwave, infrared, the behavior of EMR depends on its wavelength. Higher frequencies have shorter wavelengths, and lower frequencies have longer wavelengths, when EMR interacts with single atoms and molecules, its behavior depends on the amount of energy per quantum it carries. There exist animals that are sensitive to various types of infrared, infrared sensing in snakes depends on a kind of natural thermal imaging, in which tiny packets of cellular water are raised in temperature by the infrared radiation. EMR in this range causes molecular vibration and heating effects, which is how these animals detect it, above the range of visible light, ultraviolet light becomes invisible to humans, mostly because it is absorbed by the cornea below 360 nanometers and the internal lens below 400. Furthermore, the rods and cones located in the retina of the eye cannot detect the very short ultraviolet wavelengths and are in fact damaged by ultraviolet. Many animals with eyes that do not require lenses are able to detect ultraviolet, by quantum photon-absorption mechanisms, various sources define visible light as narrowly as 420 to 680 to as broadly as 380 to 800 nm
6.
Anisotropy
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Anisotropy /ˌænaɪˈsɒtrəpi/ is the property of being directionally dependent, which implies different properties in different directions, as opposed to isotropy. It can be defined as a difference, when measured along different axes, another is wood, which is easier to split along its grain than against it. In the field of graphics, an anisotropic surface changes in appearance as it rotates about its geometric normal. Anisotropic filtering is a method of enhancing the quality of textures on surfaces that are far away. Older techniques, such as bilinear and trilinear filtering, do not take account the angle a surface is viewed from. By reducing detail in one more than another, these effects can be reduced. In NMR spectroscopy, the orientation of nuclei with respect to the magnetic field determines their chemical shift. In this context, anisotropic systems refer to the distribution of molecules with abnormally high electron density. This abnormal electron density affects the magnetic field and causes the observed chemical shift to change. Anisotropy measurements reveal the average displacement of the fluorophore that occurs between absorption and subsequent emission of a photon. Physicists from University of California, Berkeley reported about their detection of the anisotropy in cosmic microwave background radiation in 1977. Their experiment demonstrated the Doppler shift caused by the movement of the earth with respect to the early Universe matter, cosmic anisotropy has also been seen in the alignment of galaxies rotation axes and polarisation angles of quasars. Physicists use the term anisotropy to describe direction-dependent properties of materials, magnetic anisotropy, for example, may occur in a plasma, so that its magnetic field is oriented in a preferred direction. Plasmas may also show filamentation that is directional, liquid crystals are examples of anisotropic liquids. Some materials conduct heat in a way that is isotropic, that is independent of spatial orientation around the heat source, heat conduction is more commonly anisotropic, which implies that detailed geometric modeling of typically diverse materials being thermally managed is required. The materials used to transfer and reject heat from the source in electronics are often anisotropic. Many crystals are anisotropic to light, and exhibit such as birefringence. Crystal optics describes light propagation in these media, an axis of anisotropy is defined as the axis along which isotropy is broken
7.
Crystal
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A crystal or crystalline solid is a solid material whose constituents are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macroscopic single crystals are usually identifiable by their geometrical shape, the scientific study of crystals and crystal formation is known as crystallography. The process of crystal formation via mechanisms of crystal growth is called crystallization or solidification, the word crystal derives from the Ancient Greek word κρύσταλλος, meaning both ice and rock crystal, from κρύος, icy cold, frost. Examples of large crystals include snowflakes, diamonds, and table salt, most inorganic solids are not crystals but polycrystals, i. e. many microscopic crystals fused together into a single solid. Examples of polycrystals include most metals, rocks, ceramics, a third category of solids is amorphous solids, where the atoms have no periodic structure whatsoever. Examples of amorphous solids include glass, wax, and many plastics, Crystals are often used in pseudoscientific practices such as crystal therapy, and, along with gemstones, are sometimes associated with spellwork in Wiccan beliefs and related religious movements. The scientific definition of a crystal is based on the arrangement of atoms inside it. A crystal is a solid where the form a periodic arrangement. For example, when liquid water starts freezing, the change begins with small ice crystals that grow until they fuse. Most macroscopic inorganic solids are polycrystalline, including almost all metals, ceramics, ice, rocks, solids that are neither crystalline nor polycrystalline, such as glass, are called amorphous solids, also called glassy, vitreous, or noncrystalline. These have no periodic order, even microscopically, there are distinct differences between crystalline solids and amorphous solids, most notably, the process of forming a glass does not release the latent heat of fusion, but forming a crystal does. A crystal structure is characterized by its cell, a small imaginary box containing one or more atoms in a specific spatial arrangement. The unit cells are stacked in three-dimensional space to form the crystal, the symmetry of a crystal is constrained by the requirement that the unit cells stack perfectly with no gaps. There are 219 possible crystal symmetries, called space groups. These are grouped into 7 crystal systems, such as cubic crystal system or hexagonal crystal system, Crystals are commonly recognized by their shape, consisting of flat faces with sharp angles. Euhedral crystals are those with obvious, well-formed flat faces, anhedral crystals do not, usually because the crystal is one grain in a polycrystalline solid. The flat faces of a crystal are oriented in a specific way relative to the underlying atomic arrangement of the crystal. This occurs because some surface orientations are more stable than others, as a crystal grows, new atoms attach easily to the rougher and less stable parts of the surface, but less easily to the flat, stable surfaces
8.
Crystal structure
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In crystallography, crystal structure is a description of the ordered arrangement of atoms, ions or molecules in a crystalline material. Ordered structures occur from the nature of the constituent particles to form symmetric patterns that repeat along the principal directions of three-dimensional space in matter. The smallest group of particles in the material that constitutes the pattern is the unit cell of the structure. The unit cell completely defines the symmetry and structure of the crystal lattice. The repeating patterns are said to be located at the points of the Bravais lattice, the lengths of the principal axes, or edges, of the unit cell and the angles between them are the lattice constants, also called lattice parameters. The symmetry properties of the crystal are described by the concept of space groups, all possible symmetric arrangements of particles in three-dimensional space may be described by the 230 space groups. The crystal structure and symmetry play a role in determining many physical properties, such as cleavage, electronic band structure. The crystal structure of a material can be described in terms of its unit cell, the unit cell is a box containing one or more atoms arranged in three dimensions. The unit cells stacked in three-dimensional space describe the arrangement of atoms of the crystal. Commonly, atomic positions are represented in terms of fractional coordinates, the atom positions within the unit cell can be calculated through application of symmetry operations to the asymmetric unit. The asymmetric unit refers to the smallest possible occupation of space within the unit cell and this does not, however imply that the entirety of the asymmetric unit must lie within the boundaries of the unit cell. Symmetric transformations of atom positions are calculated from the group of the crystal structure. Vectors and planes in a lattice are described by the three-value Miller index notation. It uses the indices ℓ, m, and n as directional parameters, which are separated by 90°, by definition, the syntax denotes a plane that intercepts the three points a1/ℓ, a2/m, and a3/n, or some multiple thereof. That is, the Miller indices are proportional to the inverses of the intercepts of the plane with the unit cell, if one or more of the indices is zero, it means that the planes do not intersect that axis. A plane containing a coordinate axis is translated so that it no longer contains that axis before its Miller indices are determined, the Miller indices for a plane are integers with no common factors. Negative indices are indicated with horizontal bars, as in, in an orthogonal coordinate system for a cubic cell, the Miller indices of a plane are the Cartesian components of a vector normal to the plane. Likewise, the planes are geometric planes linking nodes
9.
Plastic
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Plastic is a material consisting of any of a wide range of synthetic or semi-synthetic organic compounds that are malleable and can be molded into solid objects. Plastics are typically organic polymers of high mass, but they often contain other substances. They are usually synthetic, most commonly derived from petrochemicals, due to their relatively low cost, ease of manufacture, versatility, and imperviousness to water, plastics are used in an enormous and expanding range of products, from paper clips to spaceships. They have already displaced many traditional materials, such as wood, stone, horn and bone, leather, paper, metal, glass, and ceramic, in most of their former uses. In developed countries, about a third of plastic is used in packaging, other uses include automobiles, furniture, and toys. In the developing world, the ratios may be different - for example, the worlds first fully synthetic plastic was bakelite, invented in New York in 1907 by Leo Baekeland who coined the term plastics. Toward the end of the century, one approach to this problem was met with wide efforts toward recycling, the word plastic is derived from the Greek πλαστικός meaning capable of being shaped or molded, from πλαστός meaning molded. The common word plastic should not be confused with the technical adjective plastic, used for insulating parts in electrical fixtures, paper laminated products, thermally insulation foams. Problems include the probability of moldings naturally being dark colors, One of the most expensive commercial polymers. It forms the basis of artistic and commercial acrylic paints when suspended in water with the use of other agents, polytetrafluoroethylene – Heat-resistant, low-friction coatings, used in things like non-stick surfaces for frying pans, plumbers tape and water slides. It is more known as Teflon. Urea-formaldehyde – One of the aminoplasts and used as an alternative to phenolics. Used as an adhesive and electrical switch housings. Early plastics were bio-derived materials such as egg and blood proteins, in 1600 BC, Mesoamericans used natural rubber for balls, bands, and figurines. Treated cattle horns were used as windows for lanterns in the Middle Ages, materials that mimicked the properties of horns were developed by treating milk-proteins with lye. In the 1800s, as industrial chemistry developed during the Industrial Revolution, the development of plastics also accelerated with Charles Goodyears discovery of vulcanization to thermoset materials derived from natural rubber. Parkesine is considered the first man-made plastic, the plastic material was patented by Alexander Parkes, In Birmingham, UK in 1856. It was unveiled at the 1862 Great International Exhibition in London, parkesine won a bronze medal at the 1862 Worlds fair in London
10.
Mechanical stress
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For example, when a solid vertical bar is supporting a weight, each particle in the bar pushes on the particles immediately below it. When a liquid is in a container under pressure, each particle gets pushed against by all the surrounding particles. The container walls and the pressure-inducing surface push against them in reaction and these macroscopic forces are actually the net result of a very large number of intermolecular forces and collisions between the particles in those molecules. Strain inside a material may arise by various mechanisms, such as stress as applied by external forces to the material or to its surface. Any strain of a material generates an internal elastic stress, analogous to the reaction force of a spring. In liquids and gases, only deformations that change the volume generate persistent elastic stress, however, if the deformation is gradually changing with time, even in fluids there will usually be some viscous stress, opposing that change. Elastic and viscous stresses are usually combined under the mechanical stress. Significant stress may exist even when deformation is negligible or non-existent, stress may exist in the absence of external forces, such built-in stress is important, for example, in prestressed concrete and tempered glass. Stress may also be imposed on a material without the application of net forces, for example by changes in temperature or chemical composition, stress that exceeds certain strength limits of the material will result in permanent deformation or even change its crystal structure and chemical composition. In some branches of engineering, the stress is occasionally used in a looser sense as a synonym of internal force. For example, in the analysis of trusses, it may refer to the total traction or compression force acting on a beam, since ancient times humans have been consciously aware of stress inside materials. Until the 17th century the understanding of stress was largely intuitive and empirical, with those tools, Augustin-Louis Cauchy was able to give the first rigorous and general mathematical model for stress in a homogeneous medium. Cauchy observed that the force across a surface was a linear function of its normal vector, and, moreover. The understanding of stress in liquids started with Newton, who provided a formula for friction forces in parallel laminar flow. Stress is defined as the force across a small boundary per unit area of that boundary, following the basic premises of continuum mechanics, stress is a macroscopic concept. In a fluid at rest the force is perpendicular to the surface, in a solid, or in a flow of viscous liquid, the force F may not be perpendicular to S, hence the stress across a surface must be regarded a vector quantity, not a scalar. Moreover, the direction and magnitude depend on the orientation of S. Thus the stress state of the material must be described by a tensor, called the stress tensor, with respect to any chosen coordinate system, the Cauchy stress tensor can be represented as a symmetric matrix of 3×3 real numbers
11.
Ray (optics)
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In optics a ray is an idealized model of light, obtained by choosing a line that is perpendicular to the wavefronts of the actual light, and that points in the direction of energy flow. This allows even very complex systems to be analyzed mathematically or simulated by computer. Ray theory does not describe phenomena such as interference and diffraction, a light ray is a line that is perpendicular to the lights wavefronts, its tangent is collinear with the wave vector. Light rays in homogeneous media are straight and they bend at the interface between two dissimilar media and may be curved in a medium in which the refractive index changes. Geometric optics describes how rays propagate through an optical system, objects to be imaged are treated as collections of independent point sources, each producing spherical wavefronts and corresponding outward rays. Rays from each point can be mathematically propagated to locate the corresponding point on the image. There are many special rays that are used in modelling to analyze an optical system. These are defined and described below, grouped by the type of system they are used to model, an incident ray is a ray of light that strikes a surface. The angle between this ray and the perpendicular or normal to the surface is the angle of incidence, the reflected ray corresponding to a given incident ray, is the ray that represents the light reflected by the surface. The angle between the normal and the reflected ray is known as the angle of reflection. The Law of Reflection says that for a surface, the angle of reflection always equals the angle of incidence. The refracted ray or transmitted ray corresponding to an incident ray represents the light that is transmitted through the surface. The angle between this ray and the normal is known as the angle of refraction, and it is given by Snells Law. Conservation of energy requires that the power in the incident ray must equal the sum of the power in the ray, the power in the reflected ray. If the material is birefringent, the ray may split into ordinary and extraordinary rays. A meridional ray or tangential ray is a ray that is confined to the containing the systems optical axis. A skew ray is a ray that does not propagate in a plane that contains both the point and the optical axis. Such rays do not cross the optical axis anywhere, and are not parallel to it
12.
Denmark
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The term Danish Realm refers to the relationship between Denmark proper, the Faroe Islands and Greenland—three countries constituting the Kingdom of Denmark. The legal nature of the Kingdom of Denmark is fundamentally one of a sovereign state. The Faroe Islands and Greenland have been part of the Crown of Denmark since 1397 when the Kalmar Union was ratified, legal matters in The Danish Realm are subject to the Danish Constitution. Beginning in 1953, state law issues within The Danish Realm has been governed by The Unity of the Realm, a less formal name for The Unity of the Realm is the Commonwealth of the Realm. In 1978, The Unity of The Realm was for the first time referred to as rigsfællesskabet. The name caught on and since the 1990s, both The Unity of The Realm and The Danish Realm itself has increasingly been referred to as simply rigsfællesskabet in daily parlance. The Danish Constitution stipulates that the foreign and security interests for all parts of the Danish Realm are the responsibility of the Danish government, the Faroes received home rule in 1948 and Greenland did so in 1979. In 2005, the Faroes received a self-government arrangement, and in 2009 Greenland received self rule, the Danish Realms unique state of internal affairs is acted out in the principle of The Unity of the Realm. This principle is derived from Article 1 of the Danish Constitution which specifies that constitutional law applies equally to all areas of the Danish Realm, the Constitutional Act specifies that sovereignty is to continue to be exclusively with the authorities of the Realm. The language of Denmark is Danish, and the Danish state authorities are based in Denmark, the Kingdom of Denmarks parliament, with its 179 members, is located in the capital, Copenhagen. Two of the members are elected in each of Greenland and the Faroe Islands. The Government ministries are located in Copenhagen, as is the highest court, in principle, the Danish Realm constitutes a unified sovereign state, with equal status between its constituent parts. Devolution differs from federalism in that the powers of the subnational authority ultimately reside in central government. The Self-Government Arrangements devolves political competence and responsibility from the Danish political authorities to the Faroese, the Faroese and Greenlandic authorities administer the tasks taken over from the state, enact legislation in these specific fields and have the economic responsibility for solving these tasks. The Danish government provides a grant to the Faroese and the Greenlandic authorities to cover the costs of these devolved areas. The 1948 Home Rule Act of the Faroe Islands sets out the terms of Faroese home rule, the Act states. the Faroe Islands shall constitute a self-governing community within the State of Denmark. It establishes the government of the Faroe Islands and the Faroese parliament. The Faroe Islands were previously administered as a Danish county, the Home Rule Act abolished the post of Amtmand and these powers were expanded in a 2005 Act, which named the Faroese home government as an equal partner with the Danish government
13.
Rasmus Bartholin
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Rasmus Bartholin was a Danish scientist, physician and grammarian. As part of his studies, he travelled in Europe for ten years, professor at the University of Copenhagen, first in Geometry, later in Medicine. He was a brother of Thomas Bartholin. He wrote, in Latin, the first grammar of the Danish language, rasmus Bartholin is remembered especially for his discovery of the double refraction of a light ray by Iceland spar. He published a description of the phenomenon, but since the physical nature of light was poorly understood at the time. It was only after Thomas Young proposed the theory of light. In Thomas Bartolin, De nivis usu medico observationes variae, accessit D. Erasmi Bartholini de figura nivis dissertatio, p. PA241, at Google Books. Copenhagen, P. Haubold,1661 OConnor, John J. Robertson, Edmund F. Erasmus Bartholin, MacTutor History of Mathematics archive, University of St Andrews
14.
Augustin-Jean Fresnel
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Augustin-Jean Fresnel, was a French engineer and physicist who contributed significantly to the establishment of the theory of wave optics. Fresnel studied the behaviour of light both theoretically and experimentally and he is perhaps best known as the inventor of the Fresnel lens, first adopted in lighthouses while he was a French commissioner of lighthouses, and found in many applications today. His Fresnel equations on waves and reflectivity also form the basis for many applications in computer graphics today — for instance, Fresnel was the son of an architect, born at Broglie. His early progress in learning was slow, and he still could not read when he was eight years old, at thirteen he entered the École Centrale in Caen, and at sixteen and a half the École Polytechnique, where he acquitted himself with distinction. From there he went to the École des Ponts et Chaussées and he received only scant public recognition during his lifetime for his labours in the cause of optical science. Some of his papers were not printed by the Académie des Sciences until many years after his death, but as he wrote to Young in 1824, in himself that sensibility, or that vanity, which people call love of glory had been blunted. Fresnel has been described as a man with interest in religious questions, as a form of consolation, he took religion very seriously especially during his illness. He spent much of his life in Paris, and died of tuberculosis at Ville-dAvray and his is one of the 72 names inscribed on the Eiffel Tower. The writer Prosper Mérimée was his first cousin and he served as an engineer successively in the departments of Vendée, Drôme and Ille-et-Vilaine, but having supported the Bourbons in 1814 he lost his appointment on Napoleons return to power. He appears to have begun his research in optics around 1814, in 1815, on the second restoration of the monarchy, he obtained a post as engineer in Paris. In 1818 he wrote a memoir on diffraction, for which he received the prize of the Académie des Sciences at Paris the following year and he was the first to construct a special type of lens, now called a Fresnel lens, as a substitute for mirrors in lighthouses. In 1819, he was nominated to be a commissioner of lighthouses, in 1823 he was unanimously elected a member of the academy. In 1825 he became a Fellow of the Royal Society of London, in 1827, the time of his last illness, the Royal Society of London awarded him the Rumford Medal. In 1818 he published his Memoir on the Diffraction of Light, in 1817, Young had proposed a small transverse component to light, while yet retaining a far larger longitudinal component. Fresnel, by the year 1821, was able to show by mathematical methods that polarization could be explained if light was entirely transverse. He proposed the aether drag hypothesis to explain a lack of variation in astronomical observations. His use of two plane mirrors of metal, forming with other a angle of nearly 180°, allowed him to avoid the diffraction effects caused in the experiment of F. M. Grimaldi on interference. This allowed him to account for the phenomenon of interference in accordance with the wave theory
15.
Index of refraction
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In optics, the refractive index or index of refraction n of a material is a dimensionless number that describes how light propagates through that medium. It is defined as n = c v, where c is the speed of light in vacuum, for example, the refractive index of water is 1.333, meaning that light travels 1.333 times faster in a vacuum than it does in water. The refractive index determines how light is bent, or refracted. The refractive indices also determine the amount of light that is reflected when reaching the interface, as well as the angle for total internal reflection. This implies that vacuum has a index of 1. The refractive index varies with the wavelength of light and this is called dispersion and causes the splitting of white light into its constituent colors in prisms and rainbows, and chromatic aberration in lenses. Light propagation in absorbing materials can be described using a refractive index. The imaginary part then handles the attenuation, while the real part accounts for refraction, the concept of refractive index is widely used within the full electromagnetic spectrum, from X-rays to radio waves. It can also be used with wave phenomena such as sound, in this case the speed of sound is used instead of that of light and a reference medium other than vacuum must be chosen. Thomas Young was presumably the person who first used, and invented, 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, 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 the next years, others started using different symbols, n, m, and µ. 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, gases at atmospheric pressure have refractive indices close to 1 because of their low density. Almost all solids and liquids have refractive indices above 1.3, aerogel is a very low density solid that can be produced with refractive index in the range from 1.002 to 1.265. Moissanite lies at the 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, for infrared light refractive indices can be considerably higher
16.
Snell's law
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In optics, the law is used in ray tracing to compute the angles of incidence or refraction, and in experimental optics to find the refractive index of a material. The law is also satisfied in metamaterials, which light to be bent backward at a negative angle of refraction with a negative refractive index. Although named after Dutch astronomer Willebrord Snellius, the law was first accurately described by the scientist Ibn Sahl at the Baghdad court in 984, in the manuscript On Burning Mirrors and Lenses, Sahl used the law to derive lens shapes that focus light with no geometric aberrations. The law follows from Fermats principle of least time, which in turn follows from the propagation of light as waves, ptolemy, a Greek living in Alexandria, Egypt, had found a relationship regarding refraction angles, but it was inaccurate for angles that were not small. Ptolemy was confident he had found an empirical law, partially as a result of fudging his data to fit theory. Alhazen, in his Book of Optics, came closer to discovering the law of refraction, although named after Dutch astronomer Willebrord Snellius, the law was first accurately described by the Persian scientist Ibn Sahl at the Baghdad court in 984. In the manuscript On Burning Mirrors and Lenses, Sahl used the law to derive lens shapes that focus light with no geometric aberrations. The law was rediscovered by Thomas Harriot in 1602, who however did not publish his results although he had corresponded with Kepler on this very subject, in 1621, Willebrord Snellius derived a mathematically equivalent form, that remained unpublished during his lifetime. René Descartes independently derived the law using heuristic momentum conservation arguments in terms of sines in his 1637 essay Dioptrics, rejecting Descartes solution, Pierre de Fermat arrived at the same solution based solely on his principle of least time. Interestingly, Descartes assumed the speed of light was infinite, yet in his derivation of Snells law he also assumed the denser the medium, the greater the speed of light. Fermat supported the assumptions, i. e. the speed of light is finite. Fermats derivation also utilized his invention of adequality, a mathematical equivalent to differential calculus, for finding maxima, minima. In his influential mathematics book Geometry, Descartes solves a problem that was worked on by Apollonius of Perga, given n lines L and a point P on each line, find the locus of points Q such that the lengths of the line segments QP satisfy certain conditions. For example, when n =4, given the lines a, b, c, and d and a point A on a, B on b, and so on, find the locus of points Q such that the product QA*QB equals the product QC*QD. When the lines are not all parallel, Pappus showed that the loci are conics, to show that the cubic curves were interesting, he showed that they arose naturally in optics from Snells law. According to Dijksterhuis, In De natura lucis et proprietate Isaac Vossius said that Descartes had seen Snells paper and we now know this charge to be undeserved but it has been adopted many times since. Both Fermat and Huygens repeated this accusation that Descartes had copied Snell, in French, Snells Law is called la loi de Descartes or loi de Snell-Descartes. As the development of optical and electromagnetic theory, the ancient Snells law was brought into a new stage
17.
Fresnel equations
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The Fresnel equations, deduced by Augustin-Jean Fresnel, describe the behaviour of light when moving between media of differing refractive indices. The reflection of light that the equations predict is known as Fresnel reflection, when light moves from a medium of a given refractive index, n1, into a second medium with refractive index, n2, both reflection and refraction of the light may occur. The Fresnel equations describe what fraction of the light is reflected and they also describe the phase shift of the reflected light. The equations assume the interface between the media is flat and that the media are homogeneous, the incident light is assumed to be a plane wave, and effects of edges are neglected. This plane is called the plane of incidence, it is the plane of the diagram below, the light is said to be s-polarized, from the German, senkrecht, meaning perpendicular. P-polarized The incident light is polarized with its electric field parallel to the plane of incidence, such light is described as p-polarized, from parallel. In the diagram on the right, an incident light ray, IO, part of the ray is reflected as ray, OR, and part refracted as ray, OT. The angles that the incident, reflected and refracted rays make to the normal of the interface are given as θi, θr and θt, respectively. The relationship between these angles is given by the law of reflection, θ i = θ r, for non-magnetic media, we have Z1 = Z0 n 1, Z2 = Z0 n 2. The second form of equation is derived from the first by eliminating θt using Snells law. If the incident light is unpolarised, the reflectance is R =12, for common glass, with n2 around 1.5, the reflectance at θi =0 is about 4%. Note that reflection by a window is from the front side as well as the side. The combined reflectance for this case is 2R/, when interference can be neglected, the discussion given here assumes that the permeability, μ, is equal to the vacuum permeability, μ0, in both media, embodying the assumption that the material is non-magnetic. This is approximately true for most dielectric materials, but not for other types of material. The completely general Fresnel equations are more complicated, for low-precision applications where polarization may be ignored, such as computer graphics, Schlicks approximation may be used. For the case of incidence, θ i = θ t =0. Thus, the reflectance simplifies to R = | n 1 − n 2 n 1 + n 2 |2, at one particular angle for a given n1 and n2, the value of Rp goes to zero and a p-polarised incident ray is purely refracted. This angle is known as Brewsters angle, and is around 56° for a medium in air or vacuum
18.
Poynting vector
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In physics, the Poynting vector represents the directional energy flux density of an electromagnetic field. The SI unit of the Poynting vector is the watt per square metre and it is named after its discoverer John Henry Poynting who first derived it in 1884. Oliver Heaviside and Nikolay Umov also independently discovered the Poynting vector and this expression is often called the Abraham form. The Poynting vector is denoted by S or N. In the microscopic version of Maxwells equations, this definition must be replaced by a definition in terms of the electric field E and the magnetic field B. It is also possible to combine the electric displacement field D with the magnetic field B to get the Minkowski form of the Poynting vector, or use D and H to construct yet another version. The choice has been controversial, Pfeifer et al. summarize, the Poynting vector represents the particular case of an energy flux vector for electromagnetic energy. However, any type of energy has its direction of movement in space, as well as its density, so energy flux vectors can be defined for types of energy as well. The Umov–Poynting vector discovered by Nikolay Umov in 1874 describes energy flux in liquid, in this definition, bound electrical currents are not included in this term, and instead contribute to S and u. For linear, nondispersive and isotropic materials, the relations can be written as D = ε E, H =1 μ B. Here ε and μ are scalar, real-valued constants independent of position, direction, in principle, this limits Poyntings theorem in this form to fields in vacuum and nondispersive linear materials. A generalization to dispersive materials is possible under certain circumstances at the cost of additional terms, the microscopic version of Maxwells equations admits only the fundamental fields E and B, without a built-in model of material media. Only the vacuum permittivity and permeability are used, and there is no D or H. When this model is used, the Poynting vector is defined as S =1 μ0 E × B and it can be derived directly from Maxwells equations in terms of total charge and current and the Lorentz force law only. The two alternative definitions of the Poynting vector are equal in vacuum or in non-magnetic materials, where B = μ0H and this is especially true for the electromagnetic energy density, in contrast to the macroscopic form E × H. The above form for the Poynting vector represents the power flow due to instantaneous electric and magnetic fields. More commonly, problems in electromagnetics are solved in terms of sinusoidally varying fields at a specified frequency, the results can then be applied more generally, for instance, by representing incoherent radiation as a superposition of such waves at different frequencies and with fluctuating amplitudes. We would thus not be considering the instantaneous E and H used above, note that these complex amplitude vectors are not functions of time, as they are understood to refer to oscillations over all time
19.
Wave vector
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In physics, a wave vector is a vector which helps describe a wave. In the context of relativity the wave vector can also be defined as a four-vector. There are two definitions of wave vector, which differ by a factor of 2π in their magnitudes. One definition is preferred in physics and related fields, while the definition is preferred in crystallography. For this article, they will be called the physics definition, a perfect one-dimensional traveling wave follows the equation, ψ = A cos where, x is position, t is time, ψ is the disturbance describing the wave. This wave travels in the +x direction with speed ω / k, in crystallography, the same waves are described using slightly different equations. In one and three respectively, ψ = A cos ψ = A cos The differences are. They are related by 2 π ν = ω and this substitution is not important for this article, but reflects common practice in crystallography. The wavenumber k and wave vector k are defined in a different way, here, k = | k | =1 / λ, while in the physics definition above, k = | k | =2 π / λ. The direction of k is discussed below, the direction in which the wave vector points must be distinguished from the direction of wave propagation. The direction of propagation is the direction of a waves energy flow. For light waves, this is also the direction of the Poynting vector, on the other hand, the wave vector points in the direction of phase velocity. In other words, the vector points in the normal direction to the surfaces of constant phase. In a lossless isotropic medium such as air, any gas, any liquid, or some solids, if the medium is lossy, the wave vector in general points in directions other than that of wave propagation. The condition for wave vector to point in the direction in which the wave propagates is that the wave has to be homogeneous. In a homogeneous wave, the surfaces of constant phase are also surfaces of constant amplitude, in case of inhomogeneous waves, these two species of surfaces differ in orientation. Wave vector is perpendicular to surfaces of constant phase. In solid-state physics, the wavevector of an electron or hole in a crystal is the wavevector of its quantum-mechanical wavefunction, see Bloch wave for further details
20.
Waveplate
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A waveplate or retarder is an optical device that alters the polarization state of a light wave travelling through it. A quarter-wave plate can be used to produce elliptical polarization as well, Waveplates are constructed out of a birefringent material, for which the index of refraction is different for different orientations of light passing through it. The behavior of a waveplate depends on the thickness of the crystal, the wavelength of light, a common use of waveplates—particularly the sensitive-tint and quarter-wave plates—is in optical mineralogy. This alignment can allow discrimination between minerals which otherwise appear similar in plane polarized and cross polarized light. A waveplate works by shifting the phase between two polarization components of the light wave. A typical waveplate is simply a birefringent crystal with a carefully chosen orientation, the crystal is cut into a plate, with the orientation of the cut chosen so that the optic axis of the crystal is parallel to the surfaces of the plate. This results in two axes in the plane of the cut, the axis, with index of refraction no. The ordinary axis is perpendicular to the optic axis, the extraordinary axis is parallel to the optic axis. This leads to a difference between the two components as they exit the crystal. When ne < no, as in calcite, the axis is called the fast axis. For ne > no the situation is reversed, depending on the thickness of the crystal, light with polarization components along both axes will emerge in a different polarization state. Waveplates are thus manufactured to work for a range of wavelengths. The phase variation can be minimized by stacking two waveplates that differ by an amount in thickness back-to-back, with the slow axis of one along the fast axis of the other. With this configuration, the relative phase imparted can be, for the case of a quarter-wave plate and this is called a zero-order waveplate. For a single waveplate changing the wavelength of the light introduces an error in the phase. Tilt of the waveplate enters via a factor of 1/cos θ into the path length, a polarization-independent phase shift of zero order needs a plate with thickness of one wavelength. For calcite the refractive index changes in the first decimal place, for quartz and magnesium fluoride the refractive index changes in the second decimal place and true zero order plates are common for wavelengths above 1 µm. For a half-wave plate, the relationship between L, Δn, and λ0 is chosen so that the shift between polarization components is Γ = π
21.
Circular polarization
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In electrodynamics the strength and direction of an electric field is defined by its electric field vector. In the case of a polarized wave, as seen in the accompanying animation. At any instant of time, the field vector of the wave describes a helix along the direction of propagation. Circular polarization is a case of the more general condition of elliptical polarization. The other special case is the linear polarization. The phenomenon of polarization arises as a consequence of the fact that light behaves as a transverse wave. On the right is an illustration of the electric field vectors of a circularly polarized electromagnetic wave, the electric field vectors have a constant magnitude but their direction changes in a rotary manner. Given that this is a wave, each vector represents the magnitude. Specifically, given that this is a circularly polarized plane wave, refer to these two images in the plane wave article to better appreciate this. This light is considered to be right-hand, clockwise circularly polarized if viewed by the receiver, as a result, the magnetic field vectors would trace out a second helix if displayed. Circular polarization is often encountered in the field of optics and in this section, refer to the second illustration on the right. The vertical component and its plane are illustrated in blue while the horizontal component. Notice that the horizontal component leads the vertical component by one quarter of a wavelength. The result of this alignment is that there are select vectors, corresponding to the helix, to appreciate how this quadrature phase shift corresponds to an electric field that rotates while maintaining a constant magnitude, imagine a dot traveling clockwise in a circle. Consider how the vertical and horizontal displacements of the dot, relative to the center of the circle, now referring again to the illustration, imagine the center of the circle just described, traveling along the axis from the front to the back. The circling dot will trace out a helix with the displacement toward our viewing left, the next pair of illustrations is that of left-handed, counter-clockwise circularly polarized light when viewed by the receiver. Because it is left-handed, the horizontal component is now lagging the vertical component by one quarter of a wavelength rather than leading it. To convert a given handedness of polarized light to the other one can use a half-wave plate
22.
Spheroid
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A spheroid, or ellipsoid of revolution, is a quadric surface obtained by rotating an ellipse about one of its principal axes, in other words, an ellipsoid with two equal semi-diameters. If the ellipse is rotated about its axis, the result is a prolate spheroid. If the ellipse is rotated about its axis, the result is an oblate spheroid. If the generating ellipse is a circle, the result is a sphere, because of the combined effects of gravity and rotation, the Earths shape is not quite a sphere but instead is slightly flattened in the direction of its axis of rotation. For that reason, in cartography the Earth is often approximated by an oblate spheroid instead of a sphere, the current World Geodetic System model uses a spheroid whose radius is 6,378.137 km at the equator and 6,356.752 km at the poles. The semi-major axis a is the radius of the spheroid. There are two cases, c < a, oblate spheroid c > a, prolate spheroid The case of a = c reduces to a sphere. An oblate spheroid with c < a has surface area S o b l a t e =2 π a 2 where e 2 =1 − c 2 a 2. The oblate spheroid is generated by rotation about the z-axis of an ellipse with semi-major axis a and semi-minor axis c, therefore e may be identified as the eccentricity. A prolate spheroid with c > a has surface area S p r o l a t e =2 π a 2 where e 2 =1 − a 2 c 2. The prolate spheroid is generated by rotation about the z-axis of an ellipse with semi-major axis c and semi-minor axis a and these formulas are identical in the sense that the formula for Soblate can be used to calculate the surface area of a prolate spheroid and vice versa. However, e then becomes imaginary and can no longer directly be identified with the eccentricity, both of these results may be cast into many other forms using standard mathematical identities and relations between parameters of the ellipse. The volume inside a spheroid is 4π/3a2c ≈4. 19a2c, if A = 2a is the equatorial diameter, and C = 2c is the polar diameter, the volume is π/6A2C ≈0. 523A2C. Both of these curvatures are always positive, so every point on a spheroid is elliptic. These are just two of different parameters used to define an ellipse and its solid body counterparts. The most common shapes for the density distribution of protons and neutrons in an atomic nucleus are spherical, prolate and oblate spheroidal, deformed nuclear shapes occur as a result of the competition between electromagnetic repulsion between protons, surface tension and quantum shell effects. An extreme example of a planet in science fiction is Mesklin, in Hal Clements novel Mission of Gravity. The prolate spheroid is the shape of the ball in several sports, several moons of the Solar system approximate prolate spheroids in shape, though they are actually triaxial ellipsoids
23.
Wollaston prism
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A Wollaston prism is an optical device, invented by William Hyde Wollaston, that manipulates polarized light. It separates randomly polarized or unpolarized light into two linearly polarized outgoing beams. The Wollaston prism consists of two orthogonal calcite prisms, cemented together on their base to two right triangle prisms with perpendicular optic axes. Outgoing light beams diverge from the prism, giving two polarized rays, with the angle of divergence determined by the wedge angle and the wavelength of the light. Commercial prisms are available with divergence angles from 15° to about 45°, nomarski prism Nicol prism Glan–Thompson prism Glan–Foucault prism Glan–Taylor prism Sénarmont prism Rochon prism Wollaston prism. Molecular Expressions Microscopy Primer, Specialized Microscopy Techniques - Wollaston Prisms, Interactive Java Tutorial
24.
Polarization density
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In classical electromagnetism, polarization density is the vector field that expresses the density of permanent or induced electric dipole moments in a dielectric material. When a dielectric is placed in an electric field, its molecules gain electric dipole moment. The electric dipole moment induced per unit volume of the material is called the electric polarization of the dielectric. It can be compared to magnetization, which is the measure of the response of a material to a magnetic field in magnetism. The SI unit of measure is coulombs per square meter, an external electric field that is applied to a dielectric material, causes a displacement of bound charged elements. These are elements which are bound to molecules and are not free to move around the material, positive charged elements are displaced in the direction of the field, and negative charged elements are displaced opposite to the direction of the field. The molecules may remain neutral in charge, yet an electric dipole moment forms and this definition of polarization as a dipole moment per unit volume is widely adopted, though in some cases it can bring to ambiguities and paradoxes. Let a volume dV be isolated inside the dielectric, due to polarization the positive bound charge d q b + will be displaced a distance d relative to the negative bound charge d q b −, giving rise to a dipole moment d p = d q b d. Note that in this case χ simplifies to a scalar, although generally it is a tensor. This is a case due to the isotropy of the dielectric. And since free charges can get as close to the dielectric as to its topmost surface, it follows that polarization only gives rise to surface bound charge density. σ b may be related to P by the following equation, the class of dielectrics where the polarization density and the electric field are not in the same direction are known as anisotropic materials. The case of a dielectric medium is described by the field of crystal optics. The polarizability of individual particles in the medium can be related to the average susceptibility, in general, the susceptibility is a function of the frequency ω of the applied field. When the field is a function of time t, the polarization is a convolution of the Fourier transform of χ with the E. This reflects the fact that the dipoles in the material cannot respond instantaneously to the applied field, if the polarization P is not linearly proportional to the electric field E, the medium is termed nonlinear and is described by the field of nonlinear optics. In ferroelectric materials, there is no correspondence between P and E at all because of hysteresis. The behavior of electric fields, magnetic fields, charge density, in terms of volume charge densities, the free charge density ρ f is given by ρ f = ρ − ρ b where ρ is the total charge density
25.
Electric field
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An electric field is a vector field that associates to each point in space the Coulomb force that would be experienced per unit of electric charge, by an infinitesimal test charge at that point. Electric fields are created by electric charges and can be induced by time-varying magnetic fields, the electric field combines with the magnetic field to form the electromagnetic field. The electric field, E, at a point is defined as the force, F. A particle of charge q would be subject to a force F = q E and its SI units are newtons per coulomb or, equivalently, volts per metre, which in terms of SI base units are kg⋅m⋅s−3⋅A−1. Electric fields are caused by electric charges or varying magnetic fields, in the special case of a steady state, the Maxwell-Faraday inductive effect disappears. The resulting two equations, taken together, are equivalent to Coulombs law, written as E =14 π ε0 ∫ d r ′ ρ r − r ′ | r − r ′ |3 for a charge density ρ. Notice that ε0, the permittivity of vacuum, must be substituted if charges are considered in non-empty media, the equations of electromagnetism are best described in a continuous description. A charge q located at r 0 can be described mathematically as a charge density ρ = q δ, conversely, a charge distribution can be approximated by many small point charges. Electric fields satisfy the principle, because Maxwells equations are linear. This principle is useful to calculate the field created by point charges. Q n are stationary in space at r 1, r 2, in that case, Coulombs law fully describes the field. If a system is static, such that magnetic fields are not time-varying, then by Faradays law, in this case, one can define an electric potential, that is, a function Φ such that E = − ∇ Φ. This is analogous to the gravitational potential, Coulombs law, which describes the interaction of electric charges, F = q = q E is similar to Newtons law of universal gravitation, F = m = m g. This suggests similarities between the electric field E and the gravitational field g, or their associated potentials, mass is sometimes called gravitational charge because of that similarity. Electrostatic and gravitational forces both are central, conservative and obey an inverse-square law, a uniform field is one in which the electric field is constant at every point. It can be approximated by placing two conducting plates parallel to other and maintaining a voltage between them, it is only an approximation because of boundary effects. Assuming infinite planes, the magnitude of the electric field E is, electrodynamic fields are E-fields which do change with time, for instance when charges are in motion. The electric field cannot be described independently of the field in that case
26.
Electromagnetic radiation
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In physics, electromagnetic radiation refers to the waves of the electromagnetic field, propagating through space carrying electromagnetic radiant energy. It includes radio waves, microwaves, infrared, light, ultraviolet, X-, classically, electromagnetic radiation consists of electromagnetic waves, which are synchronized oscillations of electric and magnetic fields that propagate at the speed of light through a vacuum. The oscillations of the two fields are perpendicular to other and perpendicular to the direction of energy and wave propagation. The wavefront of electromagnetic waves emitted from a point source is a sphere, the position of an electromagnetic wave within the electromagnetic spectrum can be characterized by either its frequency of oscillation or its wavelength. Electromagnetic waves are produced whenever charged particles are accelerated, and these waves can interact with other charged particles. EM waves carry energy, momentum and angular momentum away from their source particle, quanta of EM waves are called photons, whose rest mass is zero, but whose energy, or equivalent total mass, is not zero so they are still affected by gravity. Thus, EMR is sometimes referred to as the far field, in this language, the near field refers to EM fields near the charges and current that directly produced them, specifically, electromagnetic induction and electrostatic induction phenomena. In the quantum theory of electromagnetism, EMR consists of photons, 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 a photon is quantized and is greater for photons of higher frequency. This relationship is given by Plancks equation E = hν, where E is the energy per photon, ν is the frequency of the photon, a single gamma ray photon, for example, might carry ~100,000 times the energy of a single photon of visible light. The effects of EMR upon chemical compounds and biological organisms depend both upon the power and its frequency. EMR of visible or lower frequencies is called non-ionizing radiation, because its photons do not individually have enough energy to ionize atoms or molecules, the effects of these radiations on chemical systems and living tissue are caused primarily by heating effects from the combined energy transfer of many photons. In contrast, high ultraviolet, X-rays and gamma rays are called ionizing radiation since individual photons of high frequency have enough energy to ionize molecules or break chemical bonds. These radiations have the ability to cause chemical reactions and damage living cells beyond that resulting from simple heating, Maxwell derived 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 speed of light. Maxwell’s equations were confirmed by Heinrich Hertz through experiments with radio waves, according to Maxwells equations, a spatially varying electric field is always associated with a magnetic field that changes over time. Likewise, a varying magnetic field is associated with specific changes over time in the electric field. In an electromagnetic wave, the changes in the field are always accompanied by a wave in the magnetic field in one direction
27.
Isotropy
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Isotropy is uniformity in all orientations, it is derived from the Greek isos and tropos. Precise definitions depend on the subject area, exceptions, or inequalities, are frequently indicated by the prefix an, hence anisotropy. Anisotropy is also used to describe situations where properties vary systematically, Isotropic radiation has the same intensity regardless of the direction of measurement, and an isotropic field exerts the same action regardless of how the test particle is oriented. Within mathematics, isotropy has a few different meanings, Isotropic manifolds A manifold is isotropic if the geometry on the manifold is the same regardless of direction, a manifold can be homogeneous without being isotropic, but if it is inhomogeneous, it is necessarily anisotropic. Isotropic quadratic form A quadratic form q is said to be if there is a non-zero vector v such that q =0. In complex geometry, a line through the origin in the direction of a vector is an isotropic line. Isotropic coordinates Isotropic coordinates are coordinates on a chart for Lorentzian manifolds. Isotropy group An isotropy group is the group of isomorphisms from any object to itself in a groupoid, Isotropic position A probability distribution over a vector space is in isotropic position if its covariance matrix is the identity. This follows from invariance of the Hamiltonian, which in turn is guaranteed for a spherically symmetric potential. Kinetic theory of gases is also an example of isotropy and it is assumed that the molecules move in random directions and as a consequence, there is an equal probability of a molecule moving in any direction. Thus when there are molecules in the gas, with high probability there will be very similar numbers moving in one direction as any other hence demonstrating approximate isotropy. Fluid dynamics Fluid flow is isotropic if there is no directional preference, an example of anisotropy is in flows with a background density as gravity works in only one direction. The apparent surface separating two differing isotropic fluids would be referred to as an isotrope, thermal expansion A solid is said to be isotropic if the expansion of solid is equal in all directions when thermal energy is provided to the solid. Electromagnetics An isotropic medium is one such that the permittivity, ε, and permeability, μ, of the medium are uniform in all directions of the medium, optics Optical isotropy means having the same optical properties in all directions. The individual reflectance or transmittance of the domains is averaged if the macroscopic reflectance or transmittance is to be calculated, cosmology The Big Bang theory of the evolution of the observable universe assumes that space is isotropic. It also assumes that space is homogeneous and these two assumptions together are known as the Cosmological Principle. As of 2006, the observations suggest that, on scales much larger than galaxies, galaxy clusters are Great features. Here homogeneous means that the universe is the same everywhere and isotropic implies that there is no preferred direction, in the study of mechanical properties of materials, isotropic means having identical values of a property in all directions
28.
Optical rotation
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Optical rotation or optical activity is the rotation of the plane of polarization of linearly polarized light as it travels through certain materials. Optical activity occurs only in chiral materials, those lacking microscopic mirror symmetry, unlike other sources of birefringence which alter a beams state of polarization, optical activity can be observed in fluids. This can include gases or solutions of chiral molecules such as sugars, molecules with helical secondary structure such as some proteins and it can also be observed in chiral solids such as certain crystals with a rotation between adjacent crystal planes or metamaterials. The rotation of the plane of polarization may be either clockwise, to the right, for instance, sucrose and camphor are d-rotary whereas cholesterol is l-rotary. For a given substance, the angle by which the polarization of light of a wavelength is rotated is proportional to the path length through the material and proportional to its concentration. The rotation is not dependent on the direction of propagation, unlike the Faraday effect where the rotation is dependent on the direction of the applied magnetic field. Optical activity is measured using a source and polarimeter. Modulation of a liquid crystals optical activity, viewed between two polarizers, is the principle of operation of liquid-crystal displays. The rotation of the orientation of polarized light was first observed in 1811 in quartz by French physicist François Jean Dominique Arago. Jean Baptiste Biot also observed the rotation of the axis of polarization in certain liquids, simple polarimeters have been used since this time to measure the concentrations of simple sugars, such as glucose, in solution. In fact one name for D-glucose, is dextrose, referring to the fact that it causes linearly polarized light to rotate to the right or dexter side. In a similar manner, levulose, more known as fructose. Fructose is even more strongly levorotatory than glucose is dextrorotatory, in 1849, Louis Pasteur resolved a problem concerning the nature of tartaric acid. Pasteur noticed that the crystals come in two forms that are mirror images of one another. Sorting the crystals by hand gave two forms of the compound, Solutions of one form rotate polarized light clockwise, while the other form rotate light counterclockwise, an equal mix of the two has no polarizing effect on light. If the 4 neighbors are all different, then there are two possible orderings of the neighbors around the tetrahedron, which will be mirror images of each other and this led to a better understanding of the three-dimensional nature of molecules. Optical activity occurs due to molecules dissolved in a fluid or due to the fluid itself only if the molecules are one of two stereoisomers, this is known as an enantiomer, the structure of such a molecule is such that it is not identical to its mirror image. In mathematics, this property is known as chirality
29.
Enantiomeric excess
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Enantiomeric excess is a measurement of purity used for chiral substances. It reflects the degree to which a sample contains one enantiomer in greater amounts than the other, a racemic mixture has an ee of 0%, while a single completely pure enantiomer has an ee of 100%. A sample with 70% of one enantiomer and 30% of the other has an ee of 40%, E e = ×100 The enantiomeric excess can be determined in another way if we know the amount of each enantiomer produced. For mixtures of diastereomers, there are analogous definitions and uses for diastereomeric excess, as an example, a sample with 70% of R isomer and 30% of S will have an enantiomeric excess of 40%. This can also be thought of as a mixture of 40% pure R with 60% of a racemic mixture, a non-racemic mixture of two enantiomers will have a net optical rotation. It is possible to determine the rotation of the mixture and, with knowledge of the specific rotation of the pure enantiomer. This has led to use the two terms as interchangeable, especially because optical purity was the traditional way of measuring enantiomeric excess. However, other such as chiral column chromatography and NMR spectroscopy can now be used for measuring the amount of each enantiomer individually. The ideal equivalence between enantiomeric excess and optical purity does not always hold. d. in the succinic acid example the optical activity at 50% ee is lower than expected, the specific rotation of enantiopure 1-phenylethanol can be enhanced by the addition of achiral acetophenone as an impurity. The term enantiomeric excess was introduced in 1971 by Morrison and Mosher in their publication Asymmetric Organic Reactions, the use of enantiomeric excess has established itself because of its historic ties with optical rotation. The same arguments are valid for changing diastereomeric excess to diastereomeric ratio
30.
Stereoisomerism
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Stereoisomers are isomeric molecules that have the same molecular formula and sequence of bonded atoms, but differ in the three-dimensional orientations of their atoms in space. This contrasts with structural isomers, which share the same molecular formula, by definition, molecules that are stereoisomers of each other represent the same structural isomer. Enantiomers, also known as optical isomers, are two stereoisomers that are related to other by a reflection, They are mirror images of each other that are non-superimposable. Human hands are an analog of stereoisomerism. Every stereogenic center in one has the configuration in the other. As a result, different enantiomers of a compound may have different biological effects. Pure enantiomers also exhibit the phenomenon of optical activity and can be separated only with the use of a chiral agent, in nature, only one enantiomer of most chiral biological compounds, such as amino acids, is present. Diastereomers are stereoisomers not related through a reflection operation and they are not mirror images of each other. These include meso compounds, cis–trans isomers, and non-enantiomeric optical isomers, diastereomers seldom have the same physical properties. In the example shown below, the form of tartaric acid forms a diastereomeric pair with both levo and dextro tartaric acids, which form an enantiomeric pair. Please refer to Chirality for more regarding the D- and L- labels. Stereoisomerism about double bonds arises because rotation about the bond is restricted. The simplest examples of cis-trans isomerism are the 1, 2-disubstituted ethenes, molecule I is cis-1, 2-dichloroethene and molecule II is trans-1, 2-dichloroethene. Due to occasional ambiguity, IUPAC adopted a rigorous system wherein the substituents at each end of the double bond are assigned priority based on their atomic number. If the high-priority substituents are on the side of the bond. If they are on sides, it is E. Since chlorine has an atomic number than hydrogen, it is the highest-priority group. Using this notation to name the above pictured molecules, molecule I is -1, 2-dichloroethene and molecule II is -1 and it is not the case that Z and cis or E and trans are always interchangeable
31.
Metamaterial
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A metamaterial is a material engineered to have a property that is not found in nature. They are made from assemblies of multiple elements fashioned from materials such as metals or plastics. The materials are arranged in repeating patterns, at scales that are smaller than the wavelengths of the phenomena they influence. Metamaterials derive their properties not from the properties of the base materials, appropriately designed metamaterials can affect waves of electromagnetic radiation or sound in a manner not observed in bulk materials. Those that exhibit a negative index of refraction for particular wavelengths have attracted significant research and these materials are known as negative-index metamaterials. Metamaterials offer the potential to create superlenses, such a lens could allow imaging below the diffraction limit that is the minimum resolution that can be achieved by conventional glass lenses. A form of invisibility was demonstrated using gradient-index materials, acoustic and seismic metamaterials are also research areas. Explorations of artificial materials for manipulating electromagnetic waves began at the end of the 19th century, some of the earliest structures that may be considered metamaterials were studied by Jagadish Chandra Bose, who in 1898 researched substances with chiral properties. Karl Ferdinand Lindman studied wave interaction with metallic helices as artificial chiral media in the twentieth century. Winston E. Kock developed materials that had characteristics to metamaterials in the late 1940s. In the 1950s and 1960s, artificial dielectrics were studied for lightweight microwave antennas, microwave radar absorbers were researched in the 1980s and 1990s as applications for artificial chiral media. Negative-index materials were first described theoretically by Victor Veselago in 1967 and he proved that such materials could transmit light. He showed that the phase velocity could be made anti-parallel to the direction of Poynting vector and this is contrary to wave propagation in naturally occurring materials. John Pendry was the first to identify a practical way to make a left-handed metamaterial, such a material allows an electromagnetic wave to convey energy against its phase velocity. Pendrys idea was that metallic wires aligned along the direction of a wave could provide negative permittivity, natural materials display negative permittivity, the challenge was achieving negative permeability. In 1999 Pendry demonstrated that a ring with its axis placed along the direction of wave propagation could do so. In the same paper, he showed that an array of wires. Pendry also proposed a related negative-permeability design, the Swiss roll, in 2000, Smith et al. reported the experimental demonstration of functioning electromagnetic metamaterials by horizontally stacking, periodically, split-ring resonators and thin wire structures
32.
Nonlinear optics
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The nonlinearity is typically observed only at very high light intensities such as those provided by lasers. Above the Schwinger limit, the vacuum itself is expected to become nonlinear, in nonlinear optics, the superposition principle no longer holds. However, some effects were discovered before the development of the laser. The theoretical basis for many nonlinear processes were first described in Bloembergens monograph Nonlinear Optics, Nonlinear optics explains nonlinear response of properties such as frequency, polarization, phase or path of incident light. Third-harmonic generation, generation of light with a frequency, three photons are destroyed, creating a single photon at three times the frequency. High-harmonic generation, generation of light with much greater than the original. Sum-frequency generation, generation of light with a frequency that is the sum of two other frequencies, difference-frequency generation, generation of light with a frequency that is the difference between two other frequencies. Optical parametric amplification, amplification of an input in the presence of a higher-frequency pump wave. Optical parametric oscillation, generation of a signal and idler wave using an amplifier in a resonator. Optical parametric generation, like parametric oscillation but without a resonator, spontaneous parametric down-conversion, the amplification of the vacuum fluctuations in the low-gain regime. Optical rectification, generation of electric fields. Nonlinear light-matter interaction with electrons and plasmas. Optical Kerr effect, intensity-dependent refractive index, self-focusing, an effect due to the optical Kerr effect caused by the spatial variation in the intensity creating a spatial variation in the refractive index. Kerr-lens modelocking, the use of self-focusing as a mechanism to mode-lock laser, self-phase modulation, an effect due to the optical Kerr effect caused by the temporal variation in the intensity creating a temporal variation in the refractive index. Optical solitons, a solution for either an optical pulse or spatial mode that does not change during propagation due to a balance between dispersion and the Kerr effect. Cross-phase modulation, where one wavelength of light can affect the phase of another wavelength of light through the optical Kerr effect, four-wave mixing, can also arise from other nonlinearities. Cross-polarized wave generation, a χ effect in which a wave with polarization vector perpendicular to the one is generated. Stimulated Brillouin scattering, interaction of photons with acoustic phonons Multi-photon absorption, multiple photoionisation, near-simultaneous removal of many bound electrons by one photon
33.
Faraday effect
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In physics, the Faraday effect or Faraday rotation is a magneto-optical phenomenon—that is, an interaction between light and a magnetic field in a medium. The Faraday effect causes a rotation of the plane of polarization which is proportional to the component of the magnetic field in the direction of propagation. Formally, it is a case of gyroelectromagnetism obtained when the dielectric permittivity tensor is diagonal. Discovered by Michael Faraday in 1845, the Faraday effect was the first experimental evidence that light, the theoretical basis of electromagnetic radiation was completed by James Clerk Maxwell in the 1860s and 1870s. This effect occurs in most optically transparent dielectric materials under the influence of magnetic fields, the Faraday effect is caused by left and right circularly polarized waves propagating at slightly different speeds, a property known as circular birefringence. The Faraday effect has applications in measuring instruments, for instance, the Faraday effect has been used to measure optical rotatory power and for remote sensing of magnetic fields. The Faraday effect is used in research to study the polarization of electron spins in semiconductors. Faraday firmly believed that light was a phenomenon, and as such should be affected by electromagnetic forces. He spent considerable effort looking for evidence of electric forces affecting the polarization of light through what are now known as electro-optic effects, however, his experimental methods were not sensitive enough, and the effect was only measured thirty years later by John Kerr. Faraday then attempted to look for the effects of forces on light passing through various substances. After several unsuccessful trials, he happened to test a piece of glass, containing traces of lead. He was later able to reproduce the effect in several other solids, liquids, the discovery is well documented in Faradays daily notebook, which has since been published. On 13 Sept.1845, in paragraph #7504, under the rubric Heavy Glass, he wrote and we can look at the effects of each component separately, and see what effect this has on the result. In circularly polarized light the direction of the field rotates at the frequency of the light. In a material, this field causes a force on the charged particles comprising the material. The motion thus effected will be circular, and circularly moving charges will create their own field in addition to the magnetic field. This changes the dynamics of the interaction for each beam and one of the beams will be slowed down more than the other, causing a phase difference between the left- and right-polarized beam. When the two beams are added after this phase shift, the result is again a linearly polarized beam, the direction of polarization rotation depends on the properties of the material through which the light is shone
34.
Amphiphile
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Amphiphile is a term describing a chemical compound possessing both hydrophilic and lipophilic properties. Such a compound is called amphiphilic or amphipathic and this forms the basis for a number of areas of research in chemistry and biochemistry, notably that of lipid polymorphism. Organic compounds containing hydrophilic groups at both ends of a molecule are called bolaamphiphilic. Common amphiphilic substances are soaps, detergents and lipoproteins, the lipophilic group is typically a large hydrocarbon moiety, such as a long chain of the form CH3n, with n >4. The hydrophilic group falls into one of the categories, Charged groups Anionic. Examples, with the part of the molecule represented by an R, are, carboxylates, RCO2−, sulfates, RSO4−, sulfonates. Phosphates, The charged functionality in phospholipids, examples are alcohols with large R groups, such as diacyl glycerol, and oligoethyleneglycols with long alkyl chains. Often, amphiphilic species have several parts, several hydrophilic parts. Proteins and some block copolymers are such examples, amphiphilic compounds have lipophilic structures and hydrophilic polar functional groups. As a result of having both lipophilic and hydrophilic portions, some compounds may dissolve in water and to some extent in non-polar organic solvents. When placed in an immiscible biphasic system consisting of aqueous and organic solvents, the extent of the hydrophobic and hydrophilic portions determines the extent of partitioning. Phospholipids, a class of molecules, are the main components of biological membranes. The amphiphilic nature of these molecules defines the way in which they form membranes, there are several examples of molecules that present amphiphilic properties, Hydrocarbon based surfactants are an example group of amphiphilic compounds. Their polar region can be either ionic, or non-ionic, some typical members of this group are, sodium dodecyl sulfate, Benzalkonium chloride, Cocamidopropyl betaine and 1-octanol. Many biological compounds are amphiphilic, phospholipids, cholesterol, glycolipids, fatty acids, bile acids, saponins, local anaesthetics etc
35.
Lipid
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In biology, lipids comprise a group of naturally occurring molecules that include fats, waxes, sterols, fat-soluble vitamins, monoglycerides, diglycerides, triglycerides, phospholipids, and others. The main biological functions of lipids include storing energy, signaling, lipids have applications in the cosmetic and food industries as well as in nanotechnology. Biological lipids originate entirely or in part from two types of biochemical subunits or building-blocks, ketoacyl and isoprene groups. Although the term lipid is sometimes used as a synonym for fats, fats are a subgroup of lipids called triglycerides, lipids also encompass molecules such as fatty acids and their derivatives, as well as other sterol-containing metabolites such as cholesterol. Although humans and other mammals use various biosynthetic pathways both to break down and to synthesize lipids, some essential lipids cannot be made this way, the word lipid stems etymologically from the Greek lipos. The fatty acid structure is one of the most fundamental categories of biological lipids, the carbon chain, typically between four and 24 carbons long, may be saturated or unsaturated, and may be attached to functional groups containing oxygen, halogens, nitrogen, and sulfur. If a fatty acid contains a double bond, there is the possibility of either a cis or trans geometric isomerism, cis-double bonds cause the fatty acid chain to bend, an effect that is compounded with more double bonds in the chain. This in turn plays an important role in the structure and function of cell membranes, most naturally occurring fatty acids are of the cis configuration, although the trans form does exist in some natural and partially hydrogenated fats and oils. Examples of biologically important fatty acids include the eicosanoids, derived primarily from arachidonic acid and eicosapentaenoic acid, that include prostaglandins, leukotrienes, docosahexaenoic acid is also important in biological systems, particularly with respect to sight. Other major lipid classes in the fatty acid category are the fatty esters, fatty esters include important biochemical intermediates such as wax esters, fatty acid thioester coenzyme A derivatives, fatty acid thioester ACP derivatives and fatty acid carnitines. The fatty amides include N-acyl ethanolamines, such as the cannabinoid neurotransmitter anandamide, glycerolipids are composed of mono-, di-, and tri-substituted glycerols, the best-known being the fatty acid triesters of glycerol, called triglycerides. The word triacylglycerol is sometimes used synonymously with triglyceride, in these compounds, the three hydroxyl groups of glycerol are each esterified, typically by different fatty acids. Because they function as a store, these lipids comprise the bulk of storage fat in animal tissues. The hydrolysis of the bonds of triglycerides and the release of glycerol. Additional subclasses of glycerolipids are represented by glycosylglycerols, which are characterized by the presence of one or more sugar residues attached to glycerol via a glycosidic linkage, examples of structures in this category are the digalactosyldiacylglycerols found in plant membranes and seminolipid from mammalian sperm cells. Glycerophospholipids, usually referred to as phospholipids, are ubiquitous in nature and are key components of the bilayer of cells, as well as being involved in metabolism. Neural tissue contains high amounts of glycerophospholipids, and alterations in their composition has been implicated in various neurological disorders. Examples of glycerophospholipids found in biological membranes are phosphatidylcholine, phosphatidylethanolamine and phosphatidylserine, the major sphingoid base of mammals is commonly referred to as sphingosine
36.
Surfactants
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Surfactants are compounds that lower the surface tension between two liquids or between a liquid and a solid. Surfactants may act as detergents, wetting agents, emulsifiers, foaming agents, the term surfactant is a blend of surface active agent. In the United States National Library of Medicines Medical Subject Headings vocabulary, for the more general meaning, surface active agent/s is the heading. Surfactants are usually organic compounds that are amphiphilic, meaning they contain both hydrophobic groups and hydrophilic groups, therefore, a surfactant contains both a water-insoluble component and a water-soluble component. Surfactants will diffuse in water and adsorb at interfaces between air and water or at the interface between oil and water, in the case where water is mixed with oil. The water-insoluble hydrophobic group may extend out of the water phase, into the air or into the oil phase. World production of surfactants is estimated at 15 Mton/y, of which half are soaps. Other surfactants produced on a large scale are linear alkylbenzenesulfonates, lignin sulfonates, fatty alcohol ethoxylates. Other types of aggregates can also be formed, such as spherical or cylindrical micelles or lipid bilayers, the shape of the aggregates depends on the chemical structure of the surfactants, namely the balance in size between hydrophilic head and hydrophobic tail. A measure of this is the HLB, Hydrophilic-lipophilic balance, Surfactants reduce the surface tension of water by adsorbing at the liquid-air interface. The relation that links the surface tension and the excess is known as the Gibbs isotherm. The dynamics of adsorption depend on the coefficient of the surfactant. As the interface is created, the adsorption is limited by the diffusion of the surfactant to the interface, in some cases, there can exist an energetic barrier to adsorption or desorption of the surfactant. If such a barrier limits the rate, the dynamics are said to be ‘kinetically limited. Such energy barriers can be due to steric or electrostatic repulsions, the surface rheology of surfactant layers, including the elasticity and viscosity of the layer, play an important role in the stability of foams and emulsions. Interfacial and surface tension can be characterized by classical methods such as the -pendant or spinning drop method, surface rheology can be characterized by the oscillating drop method or shear surface rheometers such as double-cone, double-ring or magnetic rod shear surface rheometer. In solution, detergents help solubilize a variety of species by dissociating aggregates. Popular surfactants in the laboratory are SDS and CTAB
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Liquid crystal
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Liquid crystals are matter in a state which has properties between those of conventional liquids and those of solid crystals. For instance, a crystal may flow like a liquid. There are many different types of phases, which can be distinguished by their different optical properties. When viewed under a microscope using a light source, different liquid crystal phases will appear to have distinct textures. The contrasting areas in the textures correspond to domains where the molecules are oriented in different directions. Within a domain, however, the molecules are well ordered, LC materials may not always be in a liquid-crystal phase. Liquid crystals can be divided into thermotropic, lyotropic and metallotropic phases, thermotropic and lyotropic liquid crystals consist mostly of organic molecules, although a few minerals are also known. Thermotropic LCs exhibit a phase transition into the phase as temperature is changed. Lyotropic LCs exhibit phase transitions as a function of temperature and concentration of the liquid-crystal molecules in a solvent. Examples of liquid crystals can be 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 also 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, and some clays. Previously, other researchers had observed distinct color effects when cooling cholesterol derivatives just above the freezing point, 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 manner as other compounds. At 145.5 °C it melts into a liquid, and at 178.5 °C it melts again. Seeking help from a physicist, on March 14,1888, he wrote to Otto Lehmann, Lehmann examined the intermediate cloudy fluid, and reported seeing crystallites. Reinitzers Viennese colleague von Zepharovich also indicated that the 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
38.
Cellophane
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Cellophane is a thin, transparent sheet made of regenerated cellulose. Its low permeability to air, oils, greases, bacteria, Cellophane is in many countries a registered trade mark of Innovia Films Ltd based in Wigton, Cumbria, United Kingdom. The film is passed through several more baths, one to remove sulfur, one to bleach the film. A similar process, using a hole instead of a slit, is used to make a fibre called rayon, chemically, cellophane, rayon and cellulose are polymers of glucose and contain the chemical elements carbon, hydrogen and oxygen. Cellophane was invented by Swiss chemist Jacques E. Brandenberger while employed by Blanchisserie et Teinturerie de Thaon, in 1900, inspired by seeing a wine spill on a restaurants tablecloth, he decided to create a cloth that could repel liquids rather than absorb them. His first step was to spray a waterproof coating onto fabric, the resultant coated fabric was far too stiff, but the clear film easily separated from the backing cloth, and he abandoned his original idea as the possibilities of the new material became apparent. It took ten years for Brandenberger to perfect his film, his chief improvement over earlier work with films being to add glycerin to soften the material. By 1912 he had constructed a machine to manufacture the film, the following year, the company Comptoir des Textiles Artificiels bought the Thaon firms interest in Cellophane and established Brandenberger in a new company, La Cellophane SA. Whitmans candy company initiated use of cellophane for candy wrapping in the United States in 1912 for their Whitmans Sampler and they remained the largest user of imported cellophane from France until nearly 1924, when DuPont built the first cellophane manufacturing plant in the US. Cellophane saw limited sales in the US at first since while it was waterproof and this meant that it was unsuited to packaging products that required moisture proofing. DuPont hired chemist William Hale Charch, who spent three years developing a nitrocellulose lacquer that, when applied to Cellophane, made it moisture proof. Following the introduction of moisture-proof Cellophane in 1927, the materials sales tripled between 1928 and 1930, and in 1938, Cellophane accounted for 10% of DuPonts sales and 25% of its profits. The British textile company Courtaulds viscose technology had allowed it to diversify in 1930 into viscose film, however, competition with Cellophane was an obstacle to its sales, and in 1935 it founded British Cellophane Limited in conjunction with the Cellophane Company and its French parent company CTA. A major production facility was constructed at Bridgwater, Somerset, England, from 1935 to 1937, BCL subsequently constructed plants in Cornwall, Ontario, as an adjunct to the existing Courtaulds viscose rayon plant there, and in 1957 at Barrow-in-Furness, Cumbria. Those last two plants were closed in the 1990s, cellulose film has been manufactured continuously since the mid-1930s and is still used today. In the UK and in other countries, cellophane is a registered trademark. Cellophane sales have dwindled since the 1960s, due to alternative packaging options, when placed between two plane polarizing filters, cellophane produces prismatic colours due to its birefringent nature. Artists have used this effect to create stained glass-like creations that are kinetic and interactive
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Polarizer
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A polarizer or polariser is an optical filter that lets light waves of a specific polarization pass and blocks light waves of other polarizations. It can convert a beam of light of undefined or mixed polarization into a beam of well-defined polarization, the common types of polarizers are linear polarizers and circular polarizers. Polarizers are used in many techniques and instruments, and polarizing filters find applications in photography. Polarizers can also be made for other types of electromagnetic waves besides light, such as waves, microwaves. The simplest linear polarizer is the wire-grid polarizer, which consists of many fine parallel wires that are placed in a plane perpendicular to the incident beam. Electromagnetic waves which have a component of their electric fields aligned parallel to the wires will induce the movement of electrons along the length of the wires, for waves with electric fields perpendicular to the wires, the electrons cannot move very far across 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 wave to be linearly polarized with an electric field that is completely perpendicular to the wires. The hypothesis that the waves slip through the gaps between the wires is incorrect, for practical purposes, the separation between wires must be less than the wavelength of the incident radiation. In addition, the width of each wires should be compared to the spacing between wires. Therefore, it is easy to construct wire-grid polarizers for microwaves, far-infrared. In addition, advanced techniques can also build very tight pitch metallic grids. Since the degree of polarization depends little on wavelength and angle of incidence, certain crystals, due to the effects described by crystal optics, show dichroism, preferential absorption of light which 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 used as a polarizer, since the dichroic effect is strongly wavelength dependent. 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 the wire-grid polarizer. It was originally made of microscopic herapathite crystals and 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
40.
Polystyrene
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Polystyrene /ˌpɒliˈstaɪriːn/ is a synthetic aromatic polymer made from the monomer styrene. Polystyrene can be solid or foamed, general-purpose polystyrene is clear, hard, and rather brittle. It is an inexpensive resin per unit weight and it is a rather poor barrier to oxygen and water vapor and has a relatively low melting point. Polystyrene is one of the most widely used plastics, the scale of its production being several million tonnes per year, Polystyrene can be naturally transparent, but can be colored with colorants. Uses include protective packaging, containers, lids, bottles, trays, tumblers, as a thermoplastic polymer, polystyrene is in a solid state at room temperature but flows if heated above about 100 °C, its glass transition temperature. It becomes rigid again when cooled and this temperature behavior is exploited for extrusion and also for molding and vacuum forming, since it can be cast into molds with fine detail. Polystyrene is very slow to biodegrade and is therefore a focus of controversy among environmentalists, Polystyrene was discovered in 1839 by Eduard Simon, an apothecary from Berlin. From storax, the resin of the American sweetgum tree Liquidambar styraciflua, he distilled an oily substance, several days later, Simon found that the styrol had thickened into a jelly he dubbed styrol oxide because he presumed an oxidation. By 1845 Jamaican-born chemist John Buddle Blyth and German chemist August Wilhelm von Hofmann showed that the transformation of styrol took place in the absence of oxygen. They called the product metastyrol, analysis showed that it was identical to Simons Styroloxyd. In 1866 Marcelin Berthelot correctly identified the formation of metastyrol/Styroloxyd from styrol as a polymerization process, about 80 years later it was realized that heating of styrol starts a chain reaction that produces macromolecules, following the thesis of German organic chemist Hermann Staudinger. This eventually led to the substance receiving its present name, polystyrene, the company I. G. Farben began manufacturing polystyrene in Ludwigshafen, about 1931, hoping it would be a suitable replacement for die-cast zinc in many applications. Success was achieved when they developed a reactor vessel that extruded polystyrene through a tube and cutter. In 1941, Dow Chemical invented a Styrofoam process, before 1949, the chemical engineer Fritz Stastny developed pre-expanded PS beads by incorporating aliphatic hydrocarbons, such as pentane. These beads are the raw material for moulding parts or extruding sheets, BASF and Stastny applied for a patent that was issued in 1949. The moulding process was demonstrated at the Kunststoff Messe 1952 in Düsseldorf, the crystal structure of isotactic polystyrene was reported by Giulio Natta. In 1954, the Koppers Company in Pittsburgh, Pennsylvania, developed expanded polystyrene foam under the trade name Dylite, in 1960, Dart Container, the largest manufacturer of foam cups, shipped their first order. In 1988, the first U. S. ban of general polystyrene foam was enacted in Berkeley, in chemical terms, polystyrene is a long chain hydrocarbon wherein alternating carbon centers are attached to phenyl groups
41.
Polycarbonate
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Polycarbonates are a group of thermoplastic polymers containing carbonate groups in their chemical structures. Polycarbonates used in engineering are strong, tough materials, and some grades are optically transparent and they are easily worked, molded, and thermoformed. Because of these properties, polycarbonates find many applications, Polycarbonates do not have a unique resin identification code and are identified as Other,7 on the RIC list. Products made from polycarbonate can contain the precursor monomer bisphenol A. Polycarbonates received their name because they are polymers containing carbonate groups, a balance of useful features, including temperature resistance, impact resistance and optical properties, positions polycarbonates between commodity plastics and engineering plastics. The main polycarbonate material is produced by the reaction of bisphenol A, the net reaction from the diphenoxide is, Na22CMe2 + COCl2 → 1/n n +2 NaCl In this way, approximately one billion kilograms of polycarbonate is produced annually. Many other diols have been tested in place of bisphenol A, e. g.1, the cyclohexane is used as a comonomer to suppress crystallisation tendency of the BPA-derived product. Tetrabromobisphenol A is used to enhance fire resistance, tetramethylcyclobutanediol has been developed as a replacement for BPA. Although it has high impact-resistance, it has low scratch-resistance, therefore, a hard coating is applied to polycarbonate eyewear lenses and polycarbonate exterior automotive components. The characteristics of polycarbonate compare to those of polymethyl methacrylate, but polycarbonate is stronger, Polycarbonate is highly transparent to visible light, with better light transmission than many kinds of glass. Polycarbonate has a transition temperature of about 147 °C, so it softens gradually above this point. Tools must be held at high temperatures, generally above 80 °C to make strain-free and stress-free products, low molecular mass grades are easier to mold than higher grades, but their strength is lower as a result. The toughest grades have the highest molecular mass, but are more difficult to process. Unlike most thermoplastics, polycarbonate can undergo plastic deformations without cracking or breaking. As a result, it can be processed and formed at room temperature using sheet metal techniques, even for sharp angle bends with a tight radius, heating may not be necessary. This makes it valuable in prototyping applications where transparent or electrically non-conductive parts are needed, pMMA/Acrylic, which is similar in appearance to polycarbonate, is brittle and cannot be bent at room temperature. Due to its chemical properties it is not conducive to laser-cutting, Injection molding into ready articles Polycarbonate may become brittle when exposed to ionizing radiation above 25 kGy. Polycarbonate is mainly used for applications that capitalize on its collective safety features. Being a good insulator and having heat-resistant and flame-retardant properties, it is used in various products associated with electrical
42.
Cotton
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Cotton is a soft, fluffy staple fiber that grows in a boll, or protective case, around the seeds of the cotton plants of the genus Gossypium in the family of Malvaceae. The fiber is almost pure cellulose, under natural conditions, the cotton bolls will tend to increase the dispersal of the seeds. The plant is a native to tropical and subtropical regions around the world, including the Americas, Africa. The greatest diversity of wild species is found in Mexico, followed by Australia. Cotton was independently domesticated in the Old and New Worlds, the fiber is most often spun into yarn or thread and used to make a soft, breathable textile. Current estimates for world production are about 25 million tonnes or 110 million bales annually, China is the worlds largest producer of cotton, but most of this is used domestically. The United States has been the largest exporter for many years, in the United States, cotton is usually measured in bales, which measure approximately 0.48 cubic meters and weigh 226.8 kilograms. Cotton cultivation in the region is dated to the Indus Valley Civilization, the Indus cotton industry was well-developed and some methods used in cotton spinning and fabrication continued to be used until the industrialization of India. Between 2000 and 1000 BC cotton became widespread across much of India, for example, it has been found at the site of Hallus in Karnataka dating from around 1000 BC. Cotton fabrics discovered in a cave near Tehuacán, Mexico have been dated to around 5800 BC, the domestication of Gossypium hirsutum in Mexico is dated between 3400 and 2300 BC. Cotton was grown upriver, made into nets, and traded with fishing villages along the coast for supplies of fish. The Spanish who came to Mexico and Peru in the early 16th century found the people growing cotton and this may be a reference to tree cotton, Gossypium arboreum, which is a native of the Indian subcontinent. According to the Columbia Encyclopedia, Cotton has been spun, woven and it clothed the people of ancient India, Egypt, and China. Hundreds of years before the Christian era, cotton textiles were woven in India with matchless skill, in Iran, the history of cotton dates back to the Achaemenid era, however, there are few sources about the planting of cotton in pre-Islamic Iran. The planting of cotton was common in Merv, Ray and Pars of Iran, in Persian poets poems, especially Ferdowsis Shahname, there are references to cotton. Marco Polo refers to the products of Persia, including cotton. John Chardin, a French traveler of the 17th century who visited the Safavid Persia, during the Han dynasty, cotton was grown by Chinese peoples in the southern Chinese province of Yunnan. Mohamed Ali Pasha accepted the proposition and granted himself the monopoly on the sale and export of cotton in Egypt, and later dictated cotton should be grown in preference to other crops
43.
Optical fiber
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An optical fiber or optical fibre is a flexible, transparent fiber made by drawing glass or plastic to a diameter slightly thicker than that of a human hair. Fibers are also used for illumination, and are wrapped in bundles so that they may be used to carry images, thus allowing viewing in confined spaces, as in the case of a fiberscope. Specially designed fibers are used for a variety of other applications, some of them being fiber optic sensors. Optical fibers typically include a transparent core surrounded by a transparent cladding material with an index of refraction. Light is kept in the core by the phenomenon of internal reflection which causes the fiber to act as a waveguide. Fibers that support many propagation paths or transverse modes are called multi-mode fibers, multi-mode fibers generally have a wider core diameter and are used for short-distance communication links and for applications where high power must be transmitted. Single-mode fibers are used for most communication links longer than 1,000 meters, being able to join optical fibers with low loss is important in fiber optic communication. This is more complex than joining electrical wire or cable and involves careful cleaving of the fibers, precise alignment of the cores. For applications that demand a permanent connection a fusion splice is common, in this technique, an electric arc is used to melt the ends of the fibers together. Another common technique is a splice, where the ends of the fibers are held in contact by mechanical force. Temporary or semi-permanent connections are made by means of specialized optical fiber connectors, the field of applied science and engineering concerned with the design and application of optical fibers is known as fiber optics. The term was coined by Indian physicist Narinder Singh Kapany who is acknowledged as the father of fiber optics. Guiding of light by refraction, the principle that makes fiber optics possible, was first demonstrated by Daniel Colladon, John Tyndall included a demonstration of it in his public lectures in London,12 years later. When the ray passes from water to air it is bent from the perpendicular. If the angle which the ray in water encloses with the perpendicular to the surface be greater than 48 degrees, the angle which marks the limit where total reflection begins is called the limiting angle of the medium. For water this angle is 48°27′, for flint glass it is 38°41′, unpigmented human hairs have also been shown to act as an optical fiber. Practical applications, such as close internal illumination during dentistry, appeared early in the twentieth century, image transmission through tubes was demonstrated independently by the radio experimenter Clarence Hansell and the television pioneer John Logie Baird in the 1920s. The principle was first used for medical examinations by Heinrich Lamm in the following decade
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Fiber-optic communication
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Fiber-optic communication is a method of transmitting information from one place to another by sending pulses of light through an optical fiber. The light forms a carrier wave that is modulated to carry information. Fiber is preferred over electrical cabling when high bandwidth, long distance, optical fiber is used by many telecommunications companies to transmit telephone signals, Internet communication, and cable television signals. Researchers at Bell Labs have reached speeds of over 100 petabit×kilometer per second using fiber-optic communication. First developed in the 1970s, fiber-optics have revolutionized the industry and have played a major role in the advent of the Information Age. Because of its advantages over electrical transmission, optical fibers have largely replaced copper wire communications in core networks in the developed world, due to much lower attenuation and interference, optical fiber has large advantages over existing copper wire in long-distance and high-demand applications. However, infrastructure development within cities was difficult and time-consuming. Since 2000, the prices for fiber-optic communications have dropped considerably, the price for rolling out fiber to the home has currently become more cost-effective than that of rolling out a copper based network. Prices have dropped to $850 per subscriber in the US and lower in countries like The Netherlands, since 1990, when optical-amplification systems became commercially available, the telecommunications industry has laid a vast network of intercity and transoceanic fiber communication lines. Bell considered it his most important invention, the device allowed for the transmission of sound on a beam of light. On June 3,1880, Bell conducted the worlds first wireless transmission between two buildings, some 213 meters apart. Due to its use of a transmission medium, the Photophone would not prove practical until advances in laser. The Photophones first practical use came in military communication systems many decades later, in 1954 Harold Hopkins and Narinder Singh Kapany showed that rolled fiber glass allowed light to be transmitted. Initially it was considered that the light can traverse in only straight medium, after a period of research starting from 1975, the first commercial fiber-optic communications system was developed, which operated at a wavelength around 0.8 µm and used GaAs semiconductor lasers. This first-generation system operated at a bit rate of 45 Mbit/s with repeater spacing of up to 10 km, soon on 22 April 1977, General Telephone and Electronics sent the first live telephone traffic through fiber optics at a 6 Mbit/s throughput in Long Beach, California. The second generation of fiber-optic communication was developed for use in the early 1980s, operated at 1.3 µm. In 1984, they had developed a fiber optic cable that would help further their progress toward making fiber optic cables that would circle the globe. Canadian service provider SaskTel had completed construction of what was then the world’s longest commercial fiberoptic network, by 1987, these systems were operating at bit rates of up to 1.7 Gb/s with repeater spacing up to 50 km
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Polarization-maintaining optical fiber
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Such fiber is used in special applications where preserving polarization is essential. In an ordinary fiber, two polarization modes have the nominal phase velocity due to the fibers circular symmetry. However tiny amounts of birefringence in such a fiber, or bending in the fiber. The beat length Lb of such a fiber is the distance over which the wave in one mode will experience a delay of one wavelength compared to the other polarization mode. Thus a length Lb /2 of such fiber is equivalent to a half-wave plate, now consider that there might be a random coupling between the two polarization states over a significant length of such fiber. At point 0 along the fiber, the wave in polarization mode 1 induces an amplitude into mode 2 at some phase, at point Lb along the fiber the coupling is again in the original phase, but at 3/2 Lb it is again out of phase and so on. The possibility of coherent addition of wave amplitudes through crosstalk over distances much larger than Lb is thus eliminated, most of the waves power remains in the original polarization mode, and exits the fiber in that modes polarization as it is oriented at the fiber end. Optical fiber connectors used for PM fibers are specially keyed so that the two modes are aligned and exit in a specific orientation. Note that a polarization-maintaining fiber does not polarize light as a polarizer does, rather, PM fiber maintains the linear polarization of linearly polarized light provided that it is launched into the fiber aligned with one of the fibers polarization modes. Launching linearly polarized light into the fiber at a different angle will excite both polarization modes, conducting the same wave at a different phase velocities. At most points along the fiber the net polarization will be an elliptically polarized state, several different designs are used to create birefringence in a fiber. The fiber may be geometrically asymmetric or have a refractive index profile which is such as the design using an elliptical cladding as shown in the diagram. Alternatively, stress induced in the fiber will produce stress birefringence. Several different shapes of rod are used, and the fiber is sold under brand names such as Panda. It is possible to create a circularly birefringent optical fiber just using an ordinary single-mode fiber and twisting it and that causes the phase velocity of right and left hand circular polarizations to significantly differ. They are also used in telecommunications for the connection between a source laser and a modulator, since the modulator requires polarized light as input. They are rarely used for transmission, because PM fiber is expensive and has higher attenuation than singlemode fiber. The output of a PM fiber is typically characterized by its polarization extinction ratio —the ratio of correctly to incorrectly polarized light, the quality of PM patchcords and pigtails can be characterized with a PER meter
. PMID 6536274.
