In optics, the refractive index or index of refraction of a material is a dimensionless number that describes how fast light propagates through the material. It is defined as n = c v, where c is the speed of light in vacuum and v is the phase velocity of light in the medium. For example, the refractive index of water is 1.333, meaning that light travels 1.333 times as fast in vacuum as in water. The refractive index determines how much the path of light is bent, or refracted, when entering a material; this is described by Snell's law of refraction, n1 sinθ1 = n2 sinθ2, where θ1 and θ2 are the angles of incidence and refraction of a ray crossing the interface between two media with refractive indices n1 and n2. The refractive indices determine the amount of light, reflected when reaching the interface, as well as the critical angle for total internal reflection and Brewster's angle; the refractive index can be seen as the factor by which the speed and the wavelength of the radiation are reduced with respect to their vacuum values: the speed of light in a medium is v = c/n, the wavelength in that medium is λ = λ0/n, where λ0 is the wavelength of that light in vacuum.
This implies that vacuum has a refractive index of 1, that the frequency of the wave is not affected by the refractive index. As a result, the energy of the photon, therefore the perceived color of the refracted light to a human eye which depends on photon energy, is not affected by the refraction or the refractive index of the medium. While the refractive index affects wavelength, it depends on photon frequency and energy so the resulting difference in the bending angle causes white light to split into its constituent colors; this is called dispersion. It can be observed in prisms and rainbows, chromatic aberration in lenses. Light propagation in absorbing materials can be described using a complex-valued refractive index; the imaginary part handles the attenuation, while the real part accounts for refraction. The concept of refractive index applies within the full electromagnetic spectrum, from X-rays to radio waves, it can be applied to wave phenomena such as sound. In this case the speed of sound is used instead of that of light, a reference medium other than vacuum must be chosen.
The refractive index n of an optical medium is defined as the ratio of the speed of light in vacuum, c = 299792458 m/s, the phase velocity v of light in the medium, n = c v. The phase velocity is the speed at which the crests or the phase of the wave moves, which may be different from the group velocity, the speed at which the pulse of light or the envelope of the wave moves; the definition above is sometimes referred to as the absolute refractive index or the absolute index of refraction to distinguish it from definitions where the speed of light in other reference media than vacuum is used. Air at a standardized pressure and temperature has been common as a reference medium. Thomas Young was the person who first used, invented, the name "index of refraction", in 1807. At the same time he changed this value of refractive power into a single number, instead of the traditional ratio of two numbers; the ratio had the disadvantage of different appearances. Newton, who called it the "proportion of the sines of incidence and refraction", wrote it as a ratio of two numbers, like "529 to 396".
Hauksbee, who called it the "ratio of refraction", wrote it as a ratio with a fixed numerator, like "10000 to 7451.9". Hutton wrote it as a ratio with a fixed denominator, like 1.3358 to 1. Young did not use a symbol for the index of refraction, in 1807. In the next years, others started using different symbols: n, m, µ; the symbol n prevailed. For visible light most transparent media have refractive indices between 1 and 2. A few examples are given in the adjacent table; these values are measured at the yellow doublet D-line of sodium, with a wavelength of 589 nanometers, as is conventionally done. Gases at atmospheric pressure have refractive indices close to 1 because of their low density. All solids and liquids have refractive indices above 1.3, with aerogel as the clear exception. Aerogel is a low density solid that can be produced with refractive index in the range from 1.002 to 1.265. Moissanite lies at the other end of the range with a refractive index as high as 2.65. Most plastics have refractive indices in the range from 1.3 to 1.7, but some high-refractive-index polymers can have values as high as 1.76.
For infrared light refractive indices can be higher. Germanium is transparent in the wavelength region from 2 to 14 µm and has a refractive index of about 4. A type of new materials, called topological insulator, was found holding higher refractive index of up to 6 in near to mid infrared frequency range. Moreover, topological insulator material are transparent; these excellent properties make them a type of significant materials for infrared optics. According to the theory of relativity, no information can travel faster than the speed of light in vacuum, but this does not mean that the refractive index cannot be lower than 1; the refractive index measures the phase velocity of light. The phase velocity is the speed at which the crests of the wave move and can be faster than the speed of light in vacuum, thereby give a refractive index below 1; this can occur close to resonance frequencies, for absorbing media, in plasmas, for X-rays. In the X-ray regime the refractive indices are
Specific gravity is the ratio of the density of a substance to the density of a reference substance. Apparent specific gravity is the ratio of the weight of a volume of the substance to the weight of an equal volume of the reference substance; the reference substance for liquids is nearly always water at its densest. Nonetheless, the temperature and pressure must be specified for the reference. Pressure is nearly always 1 atm. Temperatures for both sample and reference vary from industry to industry. In British beer brewing, the practice for specific gravity as specified above is to multiply it by 1,000. Specific gravity is used in industry as a simple means of obtaining information about the concentration of solutions of various materials such as brines, antifreeze coolants, sugar solutions and acids. Being a ratio of densities, specific gravity is a dimensionless quantity; the reason for the specific gravity being dimensionless is to provide a global consistency between the U. S. and Metric Systems, since various units for density may be used such as pounds per cubic feet or grams per cubic centimeter, etc.
Specific gravity varies with pressure. Substances with a specific gravity of 1 are neutrally buoyant in water; those with SG greater than 1 are denser than water and will, disregarding surface tension effects, sink in it. Those with an SG less than 1 will float on it. In scientific work, the relationship of mass to volume is expressed directly in terms of the density of the substance under study, it is in industry where specific gravity finds wide application for historical reasons. True specific gravity can be expressed mathematically as: S G true = ρ sample ρ H 2 O where ρsample is the density of the sample and ρH2O is the density of water; the apparent specific gravity is the ratio of the weights of equal volumes of sample and water in air: S G apparent = W A, sample W A, H 2 O where WA,sample represents the weight of the sample measured in air and WA,H2O the weight of water measured in air. It can be shown that true specific gravity can be computed from different properties: S G true = ρ sample ρ H 2 O = m sample V m H 2 O V = m sample m H 2 O g g = W V, sample W V, H 2 O where g is the local acceleration due to gravity, V is the volume of the sample and of water, ρsample is the density of the sample, ρH2O is the density of water and WV represents a weight obtained in vacuum.
The density of water varies with pressure as does the density of the sample. So it is necessary to specify the temperatures and pressures at which the densities or weights were determined, it is nearly always the case. But as specific gravity refers to incompressible aqueous solutions or other incompressible substances, variations in density caused by pressure are neglected at least where apparent specific gravity is being measured. For true specific gravity calculations, air pressure must be considered. Temperatures are specified by the notation, with Ts representing the temperature at which the sample's density was determined and Tr the temperature at which the reference density is specified. For example, SG would be understood to mean that the density of the sample was determined at 20 °C and of the water at 4 °C. Taking into account different sample and reference temperatures, we note that, while SGH2O = 1.000000, it is the case that SGH2O = 0.998203⁄0.999840 = 0.998363. Here, temperature is being specified using the current ITS-90 scale and the densities used here and in the rest of this article are based on that scale.
On the previous IPTS-68 scale, the densities at 20 °C and 4 °C are 0.9982071 and 0.9999720 respective
A botryoidal texture or mineral habit is one in which the mineral has a globular external form resembling a bunch of grapes as derived from the Greek botruoeidēs. This is a common form for many minerals hematite, the classically recognized shape, it is a common form of goethite, smithsonite and malachite. This includes chrysocolla; each sphere in a botryoidal mineral is smaller than that of a reniform mineral, much smaller than that of a mamillary mineral. Botryoidal minerals form when many nearby nuclei, specks of sand, dust, or other particles, are present. Acicular or fibrous crystals grow radially around the nuclei at the same rate; these spheres abut or overlap with those that are nearby. These nearby spheres are fused together to form the botryoidal cluster. Klein and Cornelius S. Hurlbut, Jr..
Mineralogy is a subject of geology specializing in the scientific study of the chemistry, crystal structure, physical properties of minerals and mineralized artifacts. Specific studies within mineralogy include the processes of mineral origin and formation, classification of minerals, their geographical distribution, as well as their utilization. Early writing on mineralogy on gemstones, comes from ancient Babylonia, the ancient Greco-Roman world and medieval China, Sanskrit texts from ancient India and the ancient Islamic World. Books on the subject included the Naturalis Historia of Pliny the Elder, which not only described many different minerals but explained many of their properties, Kitab al Jawahir by Persian scientist Al-Biruni; the German Renaissance specialist Georgius Agricola wrote works such as De re metallica and De Natura Fossilium which began the scientific approach to the subject. Systematic scientific studies of minerals and rocks developed in post-Renaissance Europe; the modern study of mineralogy was founded on the principles of crystallography and to the microscopic study of rock sections with the invention of the microscope in the 17th century.
Nicholas Steno first observed the law of constancy of interfacial angles in quartz crystals in 1669. This was generalized and established experimentally by Jean-Baptiste L. Romé de l'Islee in 1783. René Just Haüy, the "father of modern crystallography", showed that crystals are periodic and established that the orientations of crystal faces can be expressed in terms of rational numbers, as encoded in the Miller indices. In 1814, Jöns Jacob Berzelius introduced a classification of minerals based on their chemistry rather than their crystal structure. William Nicol developed the Nicol prism, which polarizes light, in 1827–1828 while studying fossilized wood. James D. Dana published his first edition of A System of Mineralogy in 1837, in a edition introduced a chemical classification, still the standard. X-ray diffraction was demonstrated by Max von Laue in 1912, developed into a tool for analyzing the crystal structure of minerals by the father/son team of William Henry Bragg and William Lawrence Bragg.
More driven by advances in experimental technique and available computational power, the latter of which has enabled accurate atomic-scale simulations of the behaviour of crystals, the science has branched out to consider more general problems in the fields of inorganic chemistry and solid-state physics. It, retains a focus on the crystal structures encountered in rock-forming minerals. In particular, the field has made great advances in the understanding of the relationship between the atomic-scale structure of minerals and their function. To this end, in their focus on the connection between atomic-scale phenomena and macroscopic properties, the mineral sciences display more of an overlap with materials science than any other discipline. An initial step in identifying a mineral is to examine its physical properties, many of which can be measured on a hand sample; these can be classified into density. Hardness is determined by comparison with other minerals. In the Mohs scale, a standard set of minerals are numbered in order of increasing hardness from 1 to 10.
A harder mineral will scratch a softer, so an unknown mineral can be placed in this scale by which minerals it scratches and which scratch it. A few minerals such as calcite and kyanite have a hardness that depends on direction. Hardness can be measured on an absolute scale using a sclerometer. Tenacity refers to the way a mineral behaves when it is broken, bent or torn. A mineral can be brittle, sectile, flexible or elastic. An important influence on tenacity is the type of chemical bond. Of the other measures of mechanical cohesion, cleavage is the tendency to break along certain crystallographic planes, it is described by the orientation of the plane in crystallographic nomenclature. Parting is the tendency to break along planes of weakness due to twinning or exsolution. Where these two kinds of break do not occur, fracture is a less orderly form that may be conchoidal, splintery, hackly, or uneven. If the mineral is well crystallized, it will have a distinctive crystal habit that reflects the crystal structure or internal arrangement of atoms.
It is affected by crystal defects and twinning. Many crystals are polymorphic, having more than
The Czech Republic known by its short-form name, Czechia, is a landlocked country in Central Europe bordered by Germany to the west, Austria to the south, Slovakia to the east and Poland to the northeast. The Czech Republic covers an area of 78,866 square kilometres with a temperate continental climate and oceanic climate, it is a unitary parliamentary republic, with 10.6 million inhabitants. Other major cities are Brno, Ostrava and Pilsen; the Czech Republic is a member of the European Union, NATO, the OECD, the United Nations, the OSCE, the Council of Europe. It is a developed country with an advanced, high income export-oriented social market economy based in services and innovation; the UNDP ranks the country 14th in inequality-adjusted human development. The Czech Republic is a welfare state with a "continental" European social model, a universal health care system, tuition-free university education and is ranked 14th in the Human Capital Index, it ranks as the 6th safest or most peaceful country and is one of the most non-religious countries in the world, while achieving strong performance in democratic governance.
The Czech Republic includes the historical territories of Bohemia and Czech Silesia. The Czech state was formed in the late 9th century as the Duchy of Bohemia under the Great Moravian Empire. After the fall of the Empire in 907, the centre of power transferred from Moravia to Bohemia under the Přemyslid dynasty. In 1002, the duchy was formally recognized as an Imperial State of the Holy Roman Empire along with the Kingdom of Germany, the Kingdom of Burgundy, the Kingdom of Italy, numerous other territories, becoming the Kingdom of Bohemia in 1198 and reaching its greatest territorial extent in the 14th century. Beside Bohemia itself, the King of Bohemia ruled the lands of the Bohemian Crown, holding a vote in the election of the Holy Roman Emperor. In the Hussite Wars of the 15th century driven by the Protestant Bohemian Reformation, the kingdom faced economic embargoes and defeated five consecutive crusades proclaimed by the leaders of the Catholic Church. Following the Battle of Mohács in 1526, the whole Crown of Bohemia was integrated into the Habsburg Monarchy alongside the Archduchy of Austria and the Kingdom of Hungary.
The Protestant Bohemian Revolt against the Catholic Habsburgs led to the Thirty Years' War. After the Battle of the White Mountain, the Habsburgs consolidated their rule, eradicated Protestantism and reimposed Catholicism, adopted a policy of gradual Germanization; this contributed to the anti-Habsburg sentiment. A long history of resentment of the Catholic Church followed and still continues. With the dissolution of the Holy Roman Empire in 1806, the Bohemian Kingdom became part of the German Confederation 1815-1866 as part of Austrian Empire and the Czech language experienced a revival as a consequence of widespread romantic nationalism. In the 19th century, the Czech lands became the industrial powerhouse of the monarchy and were subsequently the core of the Republic of Czechoslovakia, formed in 1918 following the collapse of the Austro-Hungarian Empire after World War I. Czechoslovakia remained the only democracy in this part of Europe in the interwar period. However, the Czech part of Czechoslovakia was occupied by Germany in World War II, while the Slovak region became the Slovak Republic.
Most of the three millions of the German-speaking minority were expelled following the war. The Communist Party of Czechoslovakia won the 1946 elections and after the 1948 coup d'état, Czechoslovakia became a one-party communist state under Soviet influence. In 1968, increasing dissatisfaction with the regime culminated in a reform movement known as the Prague Spring, which ended in a Soviet-led invasion. Czechoslovakia remained occupied until the 1989 Velvet Revolution, when the communist regime collapsed and market economy was reintroduced. On 1 January 1993, Czechoslovakia peacefully dissolved, with its constituent states becoming the independent states of the Czech Republic and Slovakia; the Czech Republic joined NATO in 1999 and the EU in 2004. The traditional English name "Bohemia" derives from Latin "Boiohaemum", which means "home of the Boii"; the current English name comes from the Polish ethnonym associated with the area, which comes from the Czech word Čech. The name comes from the Slavic tribe and, according to legend, their leader Čech, who brought them to Bohemia, to settle on Říp Mountain.
The etymology of the word Čech can be traced back to the Proto-Slavic root *čel-, meaning "member of the people. The country has been traditionally divided into three lands, namely Bohemia in the west, Moravia in the east, Czech Silesia in the northeast. Known as the lands of the Bohemian Crown since the 14th century, a number of other names for the country have been used, including Czech/Bohemian lands, Bohemian Crown and the lands of the Crown of Saint Wenceslas; when the country regained its independence after the dissolution of the Austro-Hungarian empire in 1918, the new name of Czechoslovakia was coined to reflect the union of the Czech and Slovak nations within the one country. After Czechoslovakia dissolved in 1992, the Czech part lac
Calcium is a chemical element with symbol Ca and atomic number 20. As an alkaline earth metal, calcium is a reactive metal that forms a dark oxide-nitride layer when exposed to air, its physical and chemical properties are most similar to its heavier homologues strontium and barium. It is the fifth most abundant element in Earth's crust and the third most abundant metal, after iron and aluminium; the most common calcium compound on Earth is calcium carbonate, found in limestone and the fossilised remnants of early sea life. The name derives from Latin calx "lime", obtained from heating limestone; some calcium compounds were known to the ancients, though their chemistry was unknown until the seventeenth century. Pure calcium was isolated in 1808 via electrolysis of its oxide by Humphry Davy, who named the element. Calcium compounds are used in many industries: in foods and pharmaceuticals for calcium supplementation, in the paper industry as bleaches, as components in cement and electrical insulators, in the manufacture of soaps.
On the other hand, the metal in pure form has few applications due to its high reactivity. Calcium is the fifth-most abundant element in the human body; as electrolytes, calcium ions play a vital role in the physiological and biochemical processes of organisms and cells: in signal transduction pathways where they act as a second messenger. Calcium ions outside cells are important for maintaining the potential difference across excitable cell membranes as well as proper bone formation. Calcium is a ductile silvery metal whose properties are similar to the heavier elements in its group, strontium and radium. A calcium atom has twenty electrons, arranged in the electron configuration 4s2. Like the other elements placed in group 2 of the periodic table, calcium has two valence electrons in the outermost s-orbital, which are easily lost in chemical reactions to form a dipositive ion with the stable electron configuration of a noble gas, in this case argon. Hence, calcium is always divalent in its compounds, which are ionic.
Hypothetical univalent salts of calcium would be stable with respect to their elements, but not to disproportionation to the divalent salts and calcium metal, because the enthalpy of formation of MX2 is much higher than those of the hypothetical MX. This occurs because of the much greater lattice energy afforded by the more charged Ca2+ cation compared to the hypothetical Ca+ cation. Calcium, strontium and radium are always considered to be alkaline earth metals. Beryllium and magnesium are different from the other members of the group in their physical and chemical behaviour: they behave more like aluminium and zinc and have some of the weaker metallic character of the post-transition metals, why the traditional definition of the term "alkaline earth metal" excludes them; this classification is obsolete in English-language sources, but is still used in other countries such as Japan. As a result, comparisons with strontium and barium are more germane to calcium chemistry than comparisons with magnesium.
Calcium metal melts at 842 °C and boils at 1494 °C. It crystallises in the face-centered cubic arrangement like strontium, its density of 1.55 g/cm3 is the lowest in its group. Calcium can be cut with a knife with effort. While calcium is a poorer conductor of electricity than copper or aluminium by volume, it is a better conductor by mass than both due to its low density. While calcium is infeasible as a conductor for most terrestrial applications as it reacts with atmospheric oxygen, its use as such in space has been considered; the chemistry of calcium is that of a typical heavy alkaline earth metal. For example, calcium spontaneously reacts with water more than magnesium and less than strontium to produce calcium hydroxide and hydrogen gas, it reacts with the oxygen and nitrogen in the air to form a mixture of calcium oxide and calcium nitride. When finely divided, it spontaneously burns in air to produce the nitride. In bulk, calcium is less reactive: it forms a hydration coating in moist air, but below 30% relative humidity it may be stored indefinitely at room temperature.
Besides the simple oxide CaO, the peroxide CaO2 can be made by direct oxidation of calcium metal under a high pressure of oxygen, there is some evidence for a yellow superoxide Ca2. Calcium hydroxide, Ca2, is a strong base, though it is not as strong as the hydroxides of strontium, barium or the alkali metals. All four dihalides of calcium are known. Calcium carbonate and calcium sulfate are abundant minerals. Like strontium and barium, as well as the alkali metals and the divalent lanthanides europium and ytterbium, calcium metal dissolves directly in liquid ammonia to give a dark blue solution. Due to the large size of the Ca2+ ion, high coordination numbers are common, up to 24 in some intermetallic compounds such as CaZn13. Calcium is complexed by oxygen chelates such as EDTA and polyphosphates, which are useful in an