Mars is the fourth planet from the Sun and the second-smallest planet in the Solar System after Mercury. In English, Mars carries a name of the Roman god of war, is referred to as the "Red Planet" because the reddish iron oxide prevalent on its surface gives it a reddish appearance, distinctive among the astronomical bodies visible to the naked eye. Mars is a terrestrial planet with a thin atmosphere, having surface features reminiscent both of the impact craters of the Moon and the valleys and polar ice caps of Earth; the days and seasons are comparable to those of Earth, because the rotational period as well as the tilt of the rotational axis relative to the ecliptic plane are similar. Mars is the site of Olympus Mons, the largest volcano and second-highest known mountain in the Solar System, of Valles Marineris, one of the largest canyons in the Solar System; the smooth Borealis basin in the northern hemisphere covers 40% of the planet and may be a giant impact feature. Mars has two moons and Deimos, which are small and irregularly shaped.
These may be captured asteroids, similar to a Mars trojan. There are ongoing investigations assessing the past habitability potential of Mars, as well as the possibility of extant life. Future astrobiology missions are planned, including the Mars 2020 and ExoMars rovers. Liquid water cannot exist on the surface of Mars due to low atmospheric pressure, less than 1% of the Earth's, except at the lowest elevations for short periods; the two polar ice caps appear to be made of water. The volume of water ice in the south polar ice cap, if melted, would be sufficient to cover the entire planetary surface to a depth of 11 meters. In November 2016, NASA reported finding a large amount of underground ice in the Utopia Planitia region of Mars; the volume of water detected has been estimated to be equivalent to the volume of water in Lake Superior. Mars can be seen from Earth with the naked eye, as can its reddish coloring, its apparent magnitude reaches −2.94, surpassed only by Jupiter, the Moon, the Sun.
Optical ground-based telescopes are limited to resolving features about 300 kilometers across when Earth and Mars are closest because of Earth's atmosphere. Mars is half the diameter of Earth with a surface area only less than the total area of Earth's dry land. Mars is less dense than Earth, having about 15% of Earth's volume and 11% of Earth's mass, resulting in about 38% of Earth's surface gravity; the red-orange appearance of the Martian surface is caused by rust. It can look like butterscotch. Like Earth, Mars has differentiated into a dense metallic core overlaid by less dense materials. Current models of its interior imply a core with a radius of about 1,794 ± 65 kilometers, consisting of iron and nickel with about 16–17% sulfur; this iron sulfide core is thought to be twice as rich in lighter elements as Earth's. The core is surrounded by a silicate mantle that formed many of the tectonic and volcanic features on the planet, but it appears to be dormant. Besides silicon and oxygen, the most abundant elements in the Martian crust are iron, aluminum and potassium.
The average thickness of the planet's crust is about 50 km, with a maximum thickness of 125 km. Earth's crust averages 40 km. Mars is a terrestrial planet that consists of minerals containing silicon and oxygen and other elements that make up rock; the surface of Mars is composed of tholeiitic basalt, although parts are more silica-rich than typical basalt and may be similar to andesitic rocks on Earth or silica glass. Regions of low albedo suggest concentrations of plagioclase feldspar, with northern low albedo regions displaying higher than normal concentrations of sheet silicates and high-silicon glass. Parts of the southern highlands include detectable amounts of high-calcium pyroxenes. Localized concentrations of hematite and olivine have been found. Much of the surface is covered by finely grained iron oxide dust. Although Mars has no evidence of a structured global magnetic field, observations show that parts of the planet's crust have been magnetized, suggesting that alternating polarity reversals of its dipole field have occurred in the past.
This paleomagnetism of magnetically susceptible minerals is similar to the alternating bands found on Earth's ocean floors. One theory, published in 1999 and re-examined in October 2005, is that these bands suggest plate tectonic activity on Mars four billion years ago, before the planetary dynamo ceased to function and the planet's magnetic field faded, it is thought that, during the Solar System's formation, Mars was created as the result of a stochastic process of run-away accretion of material from the protoplanetary disk that orbited the Sun. Mars has many distinctive chemical features caused by its position in the Solar System. Elements with comparatively low boiling points, such as chlorine and sulphur, are much more common on Mars than Earth. After the formation of the planets, all were subjected to the so-called "Late Heavy Bombardment". About 60% of the surface of Mars shows a record of impacts from that era, whereas much of the remaining surface is underlain by immense impact basins caused by those events.
There is evidence of an enormous impact basin in the northern hemisphere of Mars, spanning 10,600 by 8,500 km, or four times the size of the Moon's South Pole – Aitk
Halite known as rock salt, is a type of salt, the mineral form of sodium chloride. Halite forms isometric crystals; the mineral is colorless or white, but may be light blue, dark blue, pink, orange, yellow or gray depending on inclusion of other materials and structural or isotopic abnormalities in the crystals. It occurs with other evaporite deposit minerals such as several of the sulfates and borates; the name halite is derived from the Ancient Greek word for salt, ἅλς. Halite occurs in vast beds of sedimentary evaporite minerals that result from the drying up of enclosed lakes and seas. Salt beds may underlie broad areas. In the United States and Canada extensive underground beds extend from the Appalachian basin of western New York through parts of Ontario and under much of the Michigan Basin. Other deposits are in Ohio, New Mexico, Nova Scotia and Saskatchewan; the Khewra salt mine is a massive deposit of halite near Pakistan. Salt domes are vertical diapirs or pipe-like masses of salt that have been "squeezed up" from underlying salt beds by mobilization due to the weight of overlying rock.
Salt domes contain anhydrite and native sulfur, in addition to halite and sylvite. They are common along the Gulf coasts of Texas and Louisiana and are associated with petroleum deposits. Germany, the Netherlands and Iran have salt domes. Salt glaciers exist in arid Iran where the salt has broken through the surface at high elevation and flows downhill. In all of these cases, halite is said to be behaving in the manner of a rheid. Unusual, fibrous vein filling halite is found in France and a few other localities. Halite crystals termed hopper crystals appear to be "skeletons" of the typical cubes, with the edges present and stairstep depressions on, or rather in, each crystal face. In a crystallizing environment, the edges of the cubes grow faster than the centers. Halite crystals form quickly in some evaporating lakes resulting in modern artifacts with a coating or encrustation of halite crystals. Halite flowers are rare stalactites of curling fibers of halite that are found in certain arid caves of Australia's Nullarbor Plain.
Halite stalactites and encrustations are reported in the Quincy native copper mine of Hancock, Michigan. The worlds largest underground salt mine is the Sifto Salt Mine, it uses the Room and Pillar Mining Method. It is located half a kilometre under Lake Huron in Canada. In the United Kingdom there are three mines. Salt is used extensively in cooking as a flavor enhancer, to cure a wide variety of foods such as bacon and fish, it is used in food preservation methods across various cultures. Larger pieces dusted over food from a shaker as finishing salt. Halite is often used both residentially and municipally for managing ice; because brine has a lower freezing point than pure water, putting salt or saltwater on ice, below 0 °C will cause it to melt. It is common for homeowners in cold climates to spread salt on their sidewalks and driveways after a snow storm to melt the ice, it is not necessary to use so much salt that the ice is melted. Many cities will spread a mixture of sand and salt on roads during and after a snowstorm to improve traction.
Using Salt Brine is more effective than spreading dry salt because moisture is necessary for the freezing-point depression to work and wet salt sticks to the roads better. Otherwise the salt can be wiped away by traffic. In addition to de-icing, rock salt is used in agriculture. An example of this would be inducing salt stress to suppress the growth of annual meadow grass in turf production. Other examples involve exposing weeds to salt water to dehydrate and kill them preventing them from affecting other plants. Salt is used as a household cleaning product, its coarse nature allows for its use in various cleaning scenarios including grease/oil removal, stain removal, dries out and hardens sticky spills for an easier clean. Some cultures in Africa and Brazil, prefer a wide variety of different rock salts for different dishes. Pure salt is avoided. Many recipes call for particular kinds of rock salt, imported pure salt has impurities added to adapt to local tastes. Salt was used as a form of currency in barter systems and was exlcusively controlled by authorities and their appointees.
In some ancient civilizations the practice of Salting The Earth was done to make conquered land of an enemy infertile and inhospitable as an act of domination. This act is known as Salting The Earth. We see biblical reference to this practice in Judges 9:45: “he killed the people in it, pulled the wall down and sowed the site with salt.”. Salt Coarse salt Salt tectonics
New Mexico is a state in the Southwestern region of the United States of America. It is one of the Mountain States and shares the Four Corners region with Utah and Arizona. With a population around two million, New Mexico is the 36th state by population. With a total area of 121,592 sq mi, it is the fifth-largest and sixth-least densely populated of the 50 states. Due to their geographic locations and eastern New Mexico exhibit a colder, alpine climate, while western and southern New Mexico exhibit a warmer, arid climate; the economy of New Mexico is dependent on oil drilling, mineral extraction, dryland farming, cattle ranching, lumber milling, retail trade. As of 2016–2017, its total gross domestic product was $95 billion with a GDP per capita of $45,465. New Mexico's status as a tax haven yields low to moderate personal income taxes on residents and military personnel, gives tax credits and exemptions to favorable industries; because of this, its film industry contributed $1.23 billion to its overall economy.
Due to its large area and economic climate, New Mexico has a large U. S. military presence marked notably with the White Sands Missile Range. Various U. S. national security agencies base their research and testing arms in New Mexico such as the Sandia and Los Alamos National Laboratories. During the 1940s, Project Y of the Manhattan Project developed and built the country's first atomic bomb and nuclear test, Trinity. Inhabited by Native Americans for many thousands of years before European exploration, it was colonized by the Spanish in 1598 as part of the Imperial Spanish viceroyalty of New Spain. In 1563, it was named Nuevo México after the Aztec Valley of Mexico by Spanish settlers, more than 250 years before the establishment and naming of the present-day country of Mexico. After Mexican independence in 1824, New Mexico became a Mexican territory with considerable autonomy; this autonomy was threatened, however, by the centralizing tendencies of the Mexican government from the 1830s onward, with rising tensions leading to the Revolt of 1837.
At the same time, the region became more economically dependent on the United States. At the conclusion of the Mexican–American War in 1848, the United States annexed New Mexico as the U. S. New Mexico Territory, it was admitted to the Union as the 47th state on January 6, 1912. Its history has given New Mexico the highest percentage of Hispanic and Latino Americans, the second-highest percentage of Native Americans as a population proportion. New Mexico is home to part of the Navajo Nation, 19 federally recognized Pueblo communities of Puebloan peoples, three different federally recognized Apache tribes. In prehistoric times, the area was home to Ancestral Puebloans and the modern extant Comanche and Utes inhabited the state; the largest Hispanic and Latino groups represented include the Hispanos of New Mexico and Mexican Americans. The flag of New Mexico features the state's Spanish origins with the same scarlet and gold coloration as Spain's Cross of Burgundy, along with the ancient sun symbol of the Zia, a Puebloan tribe.
These indigenous, Mexican and American frontier roots are reflected in the eponymous New Mexican cuisine and the New Mexico music genre. New Mexico received its name long before the present-day nation of Mexico won independence from Spain and adopted that name in 1821. Though the name “Mexico” itself derives from Nahuatl, in that language it referred to the heartland of the Empire of the Mexicas in the Valley of Mexico far from the area of New Mexico, Spanish explorers used the term “Mexico” to name the region of New Mexico in 1563. In 1581, the Chamuscado and Rodríguez Expedition named the region north of the Rio Grande "San Felipe del Nuevo México"; the Spaniards had hoped to find wealthy indigenous Mexica cultures there similar to those of the Aztec Empire of the Valley of Mexico. The indigenous cultures of New Mexico, proved to be unrelated to the Mexicas, they were not wealthy, but the name persisted. Before statehood, the name "New Mexico" was applied to various configurations of the U.
S. territory, to a Mexican state, to a province of New Spain, all in the same general area, but of varying extensions. With a total area of 121,699 square miles, the state is the fifth-largest state of the US, larger than British Isles. New Mexico's eastern border lies along 103°W longitude with the state of Oklahoma, 2.2 miles west of 103°W longitude with Texas. On the southern border, Texas makes up the eastern two-thirds, while the Mexican states of Chihuahua and Sonora make up the western third, with Chihuahua making up about 90% of that; the western border with Arizona runs along the 109° 03'W longitude. The southwestern corner of the state is known as the Bootheel; the 37°N parallel forms the northern boundary with Colorado. The states of New Mexico, Colorado and Utah come together at the Four Corners in New Mexico's northwestern corner. New Mexico has no natural water sources
In optics, dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency. Media having this common property may be termed dispersive media. Sometimes the term chromatic dispersion is used for specificity. Although the term is used in the field of optics to describe light and other electromagnetic waves, dispersion in the same sense can apply to any sort of wave motion such as acoustic dispersion in the case of sound and seismic waves, in gravity waves, for telecommunication signals along transmission lines or optical fiber. In optics, one important and familiar consequence of dispersion is the change in the angle of refraction of different colors of light, as seen in the spectrum produced by a dispersive prism and in chromatic aberration of lenses. Design of compound achromatic lenses, in which chromatic aberration is cancelled, uses a quantification of a glass's dispersion given by its Abbe number V, where lower Abbe numbers correspond to greater dispersion over the visible spectrum.
In some applications such as telecommunications, the absolute phase of a wave is not important but only the propagation of wave packets or "pulses". The most familiar example of dispersion is a rainbow, in which dispersion causes the spatial separation of a white light into components of different wavelengths. However, dispersion has an effect in many other circumstances: for example, group velocity dispersion causes pulses to spread in optical fibers, degrading signals over long distances. Most chromatic dispersion refers to bulk material dispersion, that is, the change in refractive index with optical frequency. However, in a waveguide there is the phenomenon of waveguide dispersion, in which case a wave's phase velocity in a structure depends on its frequency due to the structure's geometry. More "waveguide" dispersion can occur for waves propagating through any inhomogeneous structure, whether or not the waves are confined to some region. In a waveguide, both types of dispersion will be present, although they are not additive.
For example, in fiber optics the material and waveguide dispersion can cancel each other out to produce a zero-dispersion wavelength, important for fast fiber-optic communication. Material dispersion can be a desirable or undesirable effect in optical applications; the dispersion of light by glass prisms is used to construct spectrometers and spectroradiometers. Holographic gratings are used, as they allow more accurate discrimination of wavelengths. However, in lenses, dispersion causes chromatic aberration, an undesired effect that may degrade images in microscopes and photographic objectives; the phase velocity, v, of a wave in a given uniform medium is given by v = c n where c is the speed of light in a vacuum and n is the refractive index of the medium. In general, the refractive index is some function of the frequency f of the light, thus n = n, or alternatively, with respect to the wave's wavelength n = n; the wavelength dependence of a material's refractive index is quantified by its Abbe number or its coefficients in an empirical formula such as the Cauchy or Sellmeier equations.
Because of the Kramers–Kronig relations, the wavelength dependence of the real part of the refractive index is related to the material absorption, described by the imaginary part of the refractive index. In particular, for non-magnetic materials, the susceptibility χ that appears in the Kramers–Kronig relations is the electric susceptibility χe = n2 − 1; the most seen consequence of dispersion in optics is the separation of white light into a color spectrum by a prism. From Snell's law it can be seen that the angle of refraction of light in a prism depends on the refractive index of the prism material. Since that refractive index varies with wavelength, it follows that the angle that the light is refracted by will vary with wavelength, causing an angular separation of the colors known as angular dispersion. For visible light, refraction indices n of most transparent materials decrease with increasing wavelength λ: 1 < n < n < n, or alternatively: d n d λ < 0. In this case, the medium is said to have normal dispersion.
Whereas, if the index increases with increasing wavelength, the medium is said to have anomalous dispersion. At the interface of such a material with air or vacuum, Snell's law predicts that light incident at an angle θ to the normal will be refracted at an angle arcsin. Thus, blue light, with a higher refractive index, will be bent more than red light, resulting in the well-known rainbow pattern. Another consequence of dispersion manifests itself as a temporal effect; the formula v = c/n calculates the
Anhydrite, or anhydrous calcium sulfate, is a mineral with the chemical formula CaSO4. It is in the orthorhombic crystal system, with three directions of perfect cleavage parallel to the three planes of symmetry, it is not isomorphous with the orthorhombic barium and strontium sulfates, as might be expected from the chemical formulas. Distinctly developed crystals are somewhat rare, the mineral presenting the form of cleavage masses; the Mohs hardness is 3.5, the specific gravity is 2.9. The color is sometimes greyish, bluish, or purple. On the best developed of the three cleavages, the lustre is pearly; when exposed to water, anhydrite transforms to the more occurring gypsum, by the absorption of water. This transformation is reversible, with gypsum or calcium sulfate hemihydrate forming anhydrite by heating to around 200 °C under normal atmospheric conditions. Anhydrite is associated with calcite and sulfides such as galena, chalcopyrite and pyrite in vein deposits. Anhydrite is most found in evaporite deposits with gypsum.
In this occurrence, depth is critical since nearer the surface anhydrite has been altered to gypsum by absorption of circulating ground water. From an aqueous solution, calcium sulfate is deposited as crystals of gypsum, but when the solution contains an excess of sodium or potassium chloride, anhydrite is deposited if the temperature is above 40 °C; this is one of the several methods by which the mineral has been prepared artificially and is identical with its mode of origin in nature. The mineral is common in salt basins. Anhydrite occurs in a tidal flat environment in the Persian Gulf sabkhas as massive diagenetic replacement nodules. Cross sections of these nodular masses have a netted appearance and have been referred to as chicken-wire anhydrite. Nodular anhydrite occurs as replacement of gypsum in a variety of sedimentary depositional environments. Massive amounts of anhydrite occur. Anhydrite is 1–3% of the minerals in salt domes and is left as a cap at the top of the salt when the halite is removed by pore waters.
The typical cap rock is a salt, topped by a layer of anhydrite, topped by patches of gypsum, topped by a layer of calcite. Interaction with oil can reduce SO4 creating calcite and hydrogen sulfide. Anhydrite has been found in some igneous rocks, for example in the intrusive dioritic pluton of El Teniente, Chile and in trachyandesite pumice erupted by El Chichón volcano, Mexico; the name anhydrite was given by A. G. Werner in 1804, because of the absence of water of crystallization, as contrasted with the presence of water in gypsum; some obsolete names for the species are karstenite. A peculiar variety occurring as contorted concretionary masses is known as tripe-stone, a scaly granular variety, from Volpino, near Bergamo, in Lombardy, as vulpinite. A semi-transparent light blue-grey variety from Peru is referred to by the trade name angelite; the Catalyst Science Discovery Centre in Widnes, has a relief carving of an anhydrite kiln, made from a piece of anhydrite, for the United Sulphuric Acid Corporation.
Spencer, Leonard James. Anhydrite. 1911 Encyclopædia Britannica Mineralgalleries.com Minerals.net
Potassium is a chemical element with symbol K and atomic number 19. It was first isolated from the ashes of plants, from which its name derives. In the periodic table, potassium is one of the alkali metals. All of the alkali metals have a single valence electron in the outer electron shell, removed to create an ion with a positive charge – a cation, which combines with anions to form salts. Potassium in nature occurs only in ionic salts. Elemental potassium is a soft silvery-white alkali metal that oxidizes in air and reacts vigorously with water, generating sufficient heat to ignite hydrogen emitted in the reaction, burning with a lilac-colored flame, it is found dissolved in sea water, is part of many minerals. Potassium is chemically similar to sodium, the previous element in group 1 of the periodic table, they have a similar first ionization energy, which allows for each atom to give up its sole outer electron. That they are different elements that combine with the same anions to make similar salts was suspected in 1702, was proven in 1807 using electrolysis.
Occurring potassium is composed of three isotopes, of which 40K is radioactive. Traces of 40K are found in all potassium, it is the most common radioisotope in the human body. Potassium ions are vital for the functioning of all living cells; the transfer of potassium ions across nerve cell membranes is necessary for normal nerve transmission. Fresh fruits and vegetables are good dietary sources of potassium; the body responds to the influx of dietary potassium, which raises serum potassium levels, with a shift of potassium from outside to inside cells and an increase in potassium excretion by the kidneys. Most industrial applications of potassium exploit the high solubility in water of potassium compounds, such as potassium soaps. Heavy crop production depletes the soil of potassium, this can be remedied with agricultural fertilizers containing potassium, accounting for 95% of global potassium chemical production; the English name for the element potassium comes from the word "potash", which refers to an early method of extracting various potassium salts: placing in a pot the ash of burnt wood or tree leaves, adding water and evaporating the solution.
When Humphry Davy first isolated the pure element using electrolysis in 1807, he named it potassium, which he derived from the word potash. The symbol "K" stems from kali, itself from the root word alkali, which in turn comes from Arabic: القَلْيَه al-qalyah "plant ashes". In 1797, the German chemist Martin Klaproth discovered "potash" in the minerals leucite and lepidolite, realized that "potash" was not a product of plant growth but contained a new element, which he proposed to call kali. In 1807, Humphry Davy produced the element via electrolysis: in 1809, Ludwig Wilhelm Gilbert proposed the name Kalium for Davy's "potassium". In 1814, the Swedish chemist Berzelius advocated the name kalium for potassium, with the chemical symbol "K"; the English and French speaking countries adopted Davy and Gay-Lussac/Thénard's name Potassium, while the Germanic countries adopted Gilbert/Klaproth's name Kalium. The "Gold Book" of the International Union of Physical and Applied Chemistry has designated the official chemical symbol as K.
Potassium is the second least dense metal after lithium. It is a soft solid with a low melting point, can be cut with a knife. Freshly cut potassium is silvery in appearance, but it begins to tarnish toward gray on exposure to air. In a flame test and its compounds emit a lilac color with a peak emission wavelength of 766.5 nanometers. Neutral potassium atoms have 19 electrons, one more than the stable configuration of the noble gas argon; because of this and its low first ionization energy of 418.8 kJ/mol, the potassium atom is much more to lose the last electron and acquire a positive charge than to gain one and acquire a negative charge. This process requires so little energy that potassium is oxidized by atmospheric oxygen. In contrast, the second ionization energy is high, because removal of two electrons breaks the stable noble gas electronic configuration. Potassium therefore does not form compounds with the oxidation state of higher. Potassium is an active metal that reacts violently with oxygen in water and air.
With oxygen it forms potassium peroxide, with water potassium forms potassium hydroxide. The reaction of potassium with water is dangerous because of its violent exothermic character and the production of hydrogen gas. Hydrogen reacts again with atmospheric oxygen, producing water, which reacts with the remaining potassium; this reaction requires only traces of water. Because of the sensitivity of potassium to water and air, reactions with other elements are possible only in an inert atmosphere such as argon gas using air-free techniques. Potassium does not react with most hydrocarbons such as mineral kerosene, it dissolves in liquid ammonia, up to 480 g per 1000 g of ammonia at 0 °C. Depending on the concentration, the ammonia solutions are blue to yellow, their electrical conductivity is similar to that of liquid metals. In a pure solution, potassium reacts with ammonia to form KNH2, but this reaction is accelerated by minute amounts of transition metal s
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