Circular polarization
In electrodynamics, circular polarization of an electromagnetic wave is a polarization state in which, at each point, the electric field of the wave has a constant magnitude but its direction rotates with time at a steady rate in a plane perpendicular to the direction of the wave. In electrodynamics the strength and direction of an electric field is defined by its electric field vector. In the case of a circularly polarized wave, as seen in the accompanying animation, the tip of the electric field vector, at a given point in space, describes a circle as time progresses. At any instant of time, the electric field vector of the wave describes a helix along the direction of propagation. A circularly polarized wave can be in one of two possible states, right circular polarization in which the electric field vector rotates in a right-hand sense with respect to the direction of propagation, left circular polarization in which the vector rotates in a left-hand sense. Circular polarization is a limiting case of the more general condition of elliptical polarization.
The other special case is the easier-to-understand linear polarization. The phenomenon of polarization arises as a consequence of the fact that light behaves as a two-dimensional 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 plane wave, each vector represents the magnitude and direction of the electric field for an entire plane, perpendicular to the axis. Given that this is a circularly polarized plane wave, these vectors indicate that the electric field, from plane to plane, has a constant strength while its direction rotates. 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. Since this is an electromagnetic wave each electric field vector has a corresponding, but not illustrated, magnetic field vector, at a right angle to the electric field vector and proportional in magnitude to it.
As a result, the magnetic field vectors would trace out a second helix. Circular polarization is encountered in the field of optics and in this section, the electromagnetic wave will be referred to as light; the nature of circular polarization and its relationship to other polarizations is understood by thinking of the electric field as being divided into two components which are at right angles to each other. Refer to the second illustration on the right; the vertical component and its corresponding plane are illustrated in blue while the horizontal component and its corresponding plane are illustrated in green. Notice that the rightward horizontal component leads the vertical component by one quarter of a wavelength, it is this quadrature phase relationship which creates the helix and causes the points of maximum magnitude of the vertical component to correspond with the points of zero magnitude of the horizontal component, vice versa. The result of this alignment is that there are select vectors, corresponding to the helix, which match the maxima of the vertical and horizontal components.
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, vary sinusoidally in time and are out of phase by one quarter of a cycle; the displacements are said to be out of phase by one quarter of a cycle because the horizontal maximum displacement is reached one quarter of a cycle before the vertical maximum displacement is reached. 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, leading the vertical displacement. Just as the horizontal and vertical displacements of the rotating dot are out of phase by one quarter of a cycle in time, the magnitude of the horizontal and vertical components of the electric field are out of phase by one quarter of a wavelength.
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 rightward 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 handedness one can use a half-waveplate. A half-waveplate shifts a given linear component of light one half of a wavelength relative to its orthogonal linear component; the handedness of polarized light is reversed when it is reflected off a surface at normal incidence. Upon such reflection, the rotation of the plane of polarization of the reflected light is identical to that of the incident field. However, with propagation now in the opposite direction, the same rotation direction that would be described as "right handed" for the incident beam, is "left-handed" for propagation in the reverse direction, vice versa. Aside from the reversal of handedness, the ellipticity of polarization is preserved.
Note that this principle only holds for light reflected at normal incidence. For instance, right circularly polarized light reflected from a dielectric surface at grazing incidence will st
Optics
Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics describes the behaviour of visible and infrared light; because light is an electromagnetic wave, other forms of electromagnetic radiation such as X-rays and radio waves exhibit similar properties. Most optical phenomena can be accounted for using the classical electromagnetic description of light. Complete electromagnetic descriptions of light are, however difficult to apply in practice. Practical optics is done using simplified models; the most common of these, geometric optics, treats light as a collection of rays that travel in straight lines and bend when they pass through or reflect from surfaces. 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; the ray-based 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 light waves were in fact electromagnetic radiation. Some phenomena depend on the fact that light has both particle-like properties. Explanation of these effects requires quantum mechanics; when considering light's 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 and medicine. Practical applications of optics are found in a variety of technologies and everyday objects, including mirrors, telescopes, microscopes and fibre optics. Optics began with the development of lenses by Mesopotamians; the earliest known lenses, made from polished crystal 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.
These practical developments were followed by the development of theories of light and vision by ancient Greek and Indian philosophers, the development of geometrical optics in the Greco-Roman world. 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 "intromission 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. With many propagators including Democritus, Epicurus and their followers, this theory seems to have some contact with modern theories of what vision is, but it remained only speculation lacking any experimental foundation. Plato first articulated the emission theory, the idea that visual perception is accomplished by rays emitted by the eyes, he commented on the parity reversal of mirrors in Timaeus. Some hundred years Euclid wrote a treatise entitled Optics where he linked vision to geometry, creating geometrical optics.
He based his work on Plato's emission theory wherein he described the mathematical rules of perspective and described the effects of refraction qualitatively, although he questioned that a beam of light from the eye could instantaneously light up the stars every time someone blinked. Ptolemy, in his treatise Optics, held an extramission-intromission theory of vision: the rays from the eye formed a cone, the vertex being within the eye, the base defining the visual field; the rays were sensitive, conveyed information back to the observer's intellect about the distance and orientation of surfaces. He summarised much of Euclid and went on to describe a way to measure the angle of refraction, though he failed to notice the empirical relationship between it and the angle of incidence. During the Middle Ages, Greek ideas about optics were resurrected and extended by writers in the Muslim world. One of the earliest of these was Al-Kindi who wrote on the merits of Aristotelian and Euclidean ideas of optics, favouring the emission theory since it could better quantify optical phenomena.
In 984, the Persian mathematician Ibn Sahl wrote the treatise "On burning mirrors and lenses" describing a law of refraction equivalent to Snell's law. He used this law to compute optimum shapes for curved mirrors. In the early 11th century, Alhazen wrote the Book of Optics in which he explored reflection and refraction and proposed a new system for explaining vision and light based on observation and experiment, he rejected the "emission theory" of Ptolemaic optics with its rays being emitted by the eye, instead put forward the idea that light reflected in all directions in straight lines from all points of the objects being viewed and entered the eye, although he was unable to explain how the eye captured the rays. Alhazen's work was ignored in the Arabic world but it was anonymously translated into Latin around 1200 A. D. and further summarised and expanded on by the Polish monk Witelo making it a standard text on optics in Europe for the next 400 years. In the 13th century in medieval Europe, English bishop Robert Grosseteste wrote on a wide range of scientific topics, discussed light from four different perspectives: an epistemology of light, a metaphysics or cosmogony of light, an etiology or physics of light, a theology of light, basing it on the works Aristotle and Platonism.
Grosseteste's most famous disciple, Roger Bacon, wrote w
Light
Light is electromagnetic radiation within a certain portion of the electromagnetic spectrum. The word refers to visible light, the visible spectrum, 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, between the infrared and the ultraviolet. This wavelength means a frequency range of 430–750 terahertz; the main source of light on Earth is the Sun. Sunlight provides the energy that green plants use to create sugars in the form of starches, which release energy into the living things that digest them; this process of photosynthesis provides all the energy used by living things. Another important source of light for humans has been fire, from ancient campfires to modern kerosene lamps. With the development of electric lights and power systems, electric lighting has replaced firelight; some species of animals generate their own light, a process called bioluminescence.
For example, fireflies use light to locate mates, vampire squids use it to hide themselves from prey. The primary properties of visible light are intensity, propagation direction, frequency or wavelength spectrum, polarization, while its speed in a vacuum, 299,792,458 metres per second, is one of the fundamental constants of nature. Visible light, as with all types of electromagnetic radiation, is experimentally found to always move at this speed in a vacuum. In physics, the term light sometimes refers to electromagnetic radiation of any wavelength, whether visible or not. In this sense, gamma rays, X-rays and radio waves are light. Like all types of EM radiation, visible light propagates as waves. However, the energy imparted by the waves is absorbed at single locations the way particles are absorbed; the absorbed energy of the EM waves is called a photon, represents the quanta of light. When a wave of light is transformed and absorbed as a photon, the energy of the wave collapses to a single location, this location is where the photon "arrives."
This is. This dual wave-like and particle-like nature of light is known as the wave–particle duality; the study of light, known as optics, is an important research area in modern physics. EM radiation, or EMR, is classified by wavelength into radio waves, infrared, the visible spectrum that we perceive as light, ultraviolet, X-rays, gamma rays; the behavior of EMR depends on its wavelength. Higher frequencies have shorter wavelengths, 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. EMR in the visible light region consists of quanta that are at the lower end of the energies that are capable of causing electronic excitation within molecules, which leads to changes in the bonding or chemistry of the molecule. At the lower end of the visible light spectrum, EMR becomes invisible to humans because its photons no longer have enough individual energy to cause a lasting molecular change in the visual molecule retinal in the human retina, which change triggers the sensation of vision.
There exist animals that are sensitive to various types of infrared, but not by means of quantum-absorption. 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, how these animals detect it. Above the range of visible light, ultraviolet light becomes invisible to humans because it is absorbed by the cornea below 360 nm and the internal lens below 400 nm. Furthermore, the rods and cones located in the retina of the human eye cannot detect the 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, in much the same chemical way that humans detect visible light. Various sources define visible light as narrowly as 420–680 nm to as broadly as 380–800 nm. Under ideal laboratory conditions, people can see infrared up to at least 1050 nm.
Plant growth is affected by the color spectrum of light, a process known as photomorphogenesis. The speed of light in a vacuum is defined to be 299,792,458 m/s; the fixed value of the speed of light in SI units results from the fact that the metre is now defined in terms of the speed of light. All forms of electromagnetic radiation move at this same speed in vacuum. Different physicists have attempted to measure the speed of light throughout history. Galileo attempted to measure the speed of light in the seventeenth century. An early experiment to measure the speed of light was conducted by Ole Rømer, a Danish physicist, in 1676. Using a telescope, Rømer observed one of its moons, Io. Noting discrepancies in the apparent period of Io's orbit, he calculated that light takes about 22 minutes to traverse the diameter of Earth's orbit. However, its size was not known at that time. If Rømer had known the diameter of the Earth's orbit, he would have calculated a speed of 227,000,000 m/s. Another, more accurate, measurement of the speed of light was performed in Europe by Hippolyte Fizeau in 1849.
Fizeau dire
Birefringence
Birefringence is the optical property of a material having a refractive index that depends on the polarization and propagation direction of light. These optically anisotropic materials are said to be birefringent; the birefringence is quantified as the maximum difference between refractive indices exhibited by the material. Crystals with non-cubic crystal structures are birefringent, as are plastics under mechanical stress. Birefringence is responsible for the phenomenon of double refraction whereby a ray of light, when incident upon a birefringent material, is split by polarization into two rays taking different paths; this effect was first described by the Danish scientist Rasmus Bartholin in 1669, who observed it in calcite, a crystal having one of the strongest birefringences. However it was not until the 19th century that Augustin-Jean Fresnel described the phenomenon in terms of polarization, understanding light as a wave with field components in transverse polarizations. A mathematical description of wave propagation in a birefringent medium is presented below.
Following is a qualitative explanation of the phenomenon. The simplest type of birefringence is described as uniaxial, meaning that there is a single direction governing the optical anisotropy whereas all directions perpendicular to it are optically equivalent, thus rotating the material around this axis does not change its optical behavior. This special direction is known as the optic axis of the material. Light propagating parallel to the optic axis is governed by a refractive index no. Light whose polarization is in the direction of the optic axis sees an optical index ne. For any ray direction there is a linear polarization direction perpendicular to the optic axis, this is called an ordinary ray. However, for ray directions not parallel to the optic axis, the polarization direction perpendicular to the ordinary ray's polarization will be in the direction of the optic axis, this is called an extraordinary ray. I.e. when unpolarized light enters an uniaxial birefringent material it is split into two beams travelling different directions.
The ordinary ray will always experience a refractive index of no, whereas the refractive index of the extraordinary ray will be in between no and ne, depending on the ray direction as described by the index ellipsoid. The magnitude of the difference is quantified by the birefringence: Δ n = n e − n o; the propagation of the ordinary ray is described by no as if there were no birefringence involved. However the extraordinary ray, as its name suggests, propagates unlike any wave in a homogenous optical material, its refraction at a surface can be understood using the effective refractive index. However it is in fact an inhomogeneous wave whose power flow is not in the direction of the wave vector; this causes an additional shift in that beam when launched at normal incidence, as is popularly observed using a crystal of calcite as photographed above. Rotating the calcite crystal will cause one of the two images, that of the extraordinary ray, to rotate around that of the ordinary ray, which remains fixed.
When the light propagates either along or orthogonal to the optic axis, such a lateral shift does not occur. In the first case, both polarizations see the same effective refractive index, so there is no extraordinary ray. In the second case the extraordinary ray propagates at a different phase velocity but is not an inhomogeneous wave. A crystal with its optic axis in this orientation, parallel to the optical surface, may be used to create a waveplate, in which there is no distortion of the image but an intentional modification of the state of polarization of the incident wave. For instance, a quarter-wave plate is used to create circular polarization from a linearly polarized source; the case of so-called biaxial crystals is more complex. These are characterized by three refractive indices corresponding to three principal axes of the crystal. For most ray directions, both polarizations would be classified as extraordinary rays but with different effective refractive indices. Being extraordinary waves, the direction of power flow is not identical to the direction of the wave vector in either case.
The two refractive indices can be determined using the index ellipsoids for given directions of the polarization. Note that for biaxial crystals the index ellipsoid will not be an ellipsoid of revolution but is described by three unequal principle refractive indices nα, nβ and nγ, thus there is no axis. Although there is no axis of symmetry, there are two optical axes or binormals which are defined as directions along which light may propagate without birefringence, i.e. directions along which the wavelength is independent of polarization. For this reason, birefringent materials with three distinct refractive indices are called biaxial. Additionally, there are two distinct axes known as optical ray axes or biradials along which the group velocity of the light is independent of polarization; when an arbitrary beam of light strikes the surface of a b
Mica
The mica group of sheet silicate minerals includes several related materials having nearly perfect basal cleavage. All are monoclinic, with a tendency towards pseudohexagonal crystals, are similar in chemical composition; the nearly perfect cleavage, the most prominent characteristic of mica, is explained by the hexagonal sheet-like arrangement of its atoms. The word mica is derived from the Latin word mica, meaning a crumb, influenced by micare, to glitter. Chemically, micas can be given the general formula X2Y4–6Z8O204,in which X is K, Na, or Ca or less Ba, Rb, or Cs. Structurally, micas can be classed as trioctahedral. If the X ion is K or Na, the mica is a common mica, whereas if the X ion is Ca, the mica is classed as a brittle mica. Muscovite Common micas: Biotite Lepidolite Phlogopite ZinnwalditeBrittle micas: Clintonite Very fine-grained micas, which show more variation in ion and water content, are informally termed "clay micas", they include: Hydro-muscovite with H3O+ along with K in the X site.
Mica is distributed and occurs in igneous and sedimentary regimes. Large crystals of mica used for various applications are mined from granitic pegmatites; until the 19th century, large crystals of mica were quite rare and expensive as a result of the limited supply in Europe. However, their price dropped when large reserves were found and mined in Africa and South America during the early 19th century; the largest documented single crystal of mica was found in Lacey Mine, Canada. Similar-sized crystals were found in Karelia, Russia; the British Geological Survey reported that as of 2005, Koderma district in Jharkhand state in India had the largest deposits of mica in the world. China was the top producer of mica with a third of the global share followed by the US, South Korea and Canada. Large deposits of sheet mica were mined in New England from the 19th century to the 1970s. Large mines existed in Connecticut, New Hampshire, Maine. Scrap and flake mica is produced all over the world. In 2010, the major producers were Russia, United States, South Korea and Canada.
The total global production was 350,000 t. Most sheet mica was produced in Russia. Flake mica comes from several sources: the metamorphic rock called schist as a byproduct of processing feldspar and kaolin resources, from placer deposits, from pegmatites. Sheet mica is less abundant than flake and scrap mica, is recovered from mining scrap and flake mica; the most important sources of sheet mica are pegmatite deposits. Sheet mica prices vary with grade and can range from less than $1 per kilogram for low-quality mica to more than $2,000 per kilogram for the highest quality; the mica group represents 37 phyllosilicate minerals that have a platy texture. The commercially important micas are muscovite and phlogopite, which are used in a variety of applications. Mica’s value is based on several of its unique physical properties; the crystalline structure of mica forms layers that can be split or delaminated into thin sheets causing foliation in rocks. These sheets are chemically inert, elastic, hydrophilic, lightweight, reflective, refractive and range in opacity from transparent to opaque.
Mica is stable when exposed to electricity, light and extreme temperatures. It has superior electrical properties as an insulator and as a dielectric, can support an electrostatic field while dissipating minimal energy in the form of heat. Muscovite, the principal mica used by the electrical industry, is used in capacitors that are ideal for high frequency and radio frequency. Phlogopite mica remains stable at higher temperatures and is used in applications in which a combination of high-heat stability and electrical properties is required. Muscovite and phlogopite are used in ground forms; the leading use of dry-ground mica in the US is in the joint compound for filling and finishing seams and blemishes in gypsum wallboard. The mica acts as a filler and extender, provides a smooth consistency, improves the workability of the compound, provides resistance to cracking. In 2008, joint compound accounted for 54% of dry-ground mica consumption. In the paint industry, ground mica is used as a pigment extender that facilitates suspension, reduces chalking, prevents shrinking and shearing of the paint film, increases the resistance of the paint film to water penetration and weathering and brightens the tone of colored pigments.
Mica promotes paint adhesion in aqueous and oleoresinous formulations. Consumption of dry-ground mica in paint, the second-ranked use, accounted for 22% of the dry-ground mica used in 2008. Ground mica is used in the well-drilling industry as an additive to drilling fluids; the coarsely ground mica flakes help prevent the loss of circulation by sealing po
Thin section
In optical mineralogy and petrography, a thin section is a laboratory preparation of a rock, soil, bones, or metal sample for use with a polarizing petrographic microscope, electron microscope and electron microprobe. A thin sliver of rock is cut from the sample with a diamond ground optically flat, it is mounted on a glass slide and ground smooth using progressively finer abrasive grit until the sample is only 30 μm thick. The method involved using the Michel-Lévy interference colour chart. Quartz is used as the gauge to determine thickness as it is one of the most abundant minerals; when placed between two polarizing filters set at right angles to each other, the optical properties of the minerals in the thin section alter the colour and intensity of the light as seen by the viewer. As different minerals have different optical properties, most rock forming minerals can be identified. Plagioclase for example can be seen in the photo on the right as a clear mineral with multiple parallel twinning planes.
The large blue-green minerals are clinopyroxene with some exsolution of orthopyroxene. Thin sections are prepared in order to investigate the optical properties of the minerals in the rock; this work helps to reveal the origin and evolution of the parent rock. A photograph of a rock in thin section is referred to as a photomicrograph. Under thin section, in plane polarized light, quartz is colorless with no cleavage, its habit is either equant or anhedral if it infills around other minerals as a cement. Under cross polarized light quartz displays low interference colors and is the defining mineral used to determine if the thin section is at standardized thickness of 30 microns as quartz will only display up to a pale yellow interference color and no further at that thickness, it is common in most rocks so it will be available to judge the thickness. In thin section, quartz grain provenance in a sedimentary rock can be estimated. In crossed polarized light, the quartz grain can go extinct all at once, called monocrystalline quartz, or in waves, called polycrystalline quartz.
The extinction in waves is called undulose extinction and indicates dislocation walls in mineral grains. Dislocation walls are where dislocations, intracrystalline deformation via movement of a dislocation front within a plane, organize themselves into planes of sufficient quantity, they change the crystallographic orientation across the walls, so for example in quartz, the two sides of the wall will have different extinction angles and thus result in undulose extinction. Since undulose extinction requires dislocation walls to have developed, these occur more at higher pressures and temperatures, quartz grains with undulose extinction indicate metamorphic rock provenance for that grain; those grains that are monocrystalline quartz are more to have been formed by igneous processes. Differing sources suggest the extent; some note the trend for immature sandstones to have less polycrystalline quartz grains compared to mature sandstones, which have grains that have passed through many sedimentary cycles.
Quartz grains derived from previous sedimentary sources are determined by looking for authigenic, or grown in place, overgrowths of silica cement over the grain. The above descriptions of quartz in thin section is enough to identify it. Minerals with similar appearance may include plagioclase, although it can be distinguished by the distinctive twinning in crossed polarized light and cleavage in plane polarized light, cordierite, although it can be distinguished by twinning or inclusions in the grain. However, for certainty, other distinguishing features of quartz include the fact that it is uniaxial, it has a positive optic sign, length-slow sign of elongation, zero degree extinction angle. Fine-grained rocks those containing minerals of high birefringence, such as calcite, are sometimes prepared as ultra-thin sections. An ordinary 30 μm thin section is prepared as described above but the slice of rock is attached to the glass slide using a soluble cement such as Canada balsam to allow both sides to be worked on.
The section is polished on both sides using a fine diamond paste until it has a thickness in the range of 2-12 μm. This technique has been used to study the microstructure of fine-grained carbonates such as the Lochseitenkalk mylonite in which the matrix grains are less than 5 μm in size; this method is sometimes used in the preparation of mineral and rock specimens for transmission electron microscopy and allows greater accuracy in comparing features using both optical and electron imaging. Ceramography: thin sections of ceramics Shelley, D. Optical Mineralogy, Second Edition. University of Canterbury, New Zealand. Thin sections of soils. Collection of Prof. Kubiëna
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