In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is thus the inverse of the spatial frequency. Wavelength is determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings and is a characteristic of both traveling waves and standing waves, as well as other spatial wave patterns. Wavelength is designated by the Greek letter lambda; the term wavelength is sometimes applied to modulated waves, to the sinusoidal envelopes of modulated waves or waves formed by interference of several sinusoids. Assuming a sinusoidal wave moving at a fixed wave speed, wavelength is inversely proportional to frequency of the wave: waves with higher frequencies have shorter wavelengths, lower frequencies have longer wavelengths. Wavelength depends on the medium. Examples of wave-like phenomena are sound waves, water waves and periodic electrical signals in a conductor.
A sound wave is a variation in air pressure, while in light and other electromagnetic radiation the strength of the electric and the magnetic field vary. Water waves are variations in the height of a body of water. In a crystal lattice vibration, atomic positions vary. Wavelength is a measure of the distance between repetitions of a shape feature such as peaks, valleys, or zero-crossings, not a measure of how far any given particle moves. For example, in sinusoidal waves over deep water a particle near the water's surface moves in a circle of the same diameter as the wave height, unrelated to wavelength; the range of wavelengths or frequencies for wave phenomena is called a spectrum. The name originated with the visible light spectrum but now can be applied to the entire electromagnetic spectrum as well as to a sound spectrum or vibration spectrum. In linear media, any wave pattern can be described in terms of the independent propagation of sinusoidal components; the wavelength λ of a sinusoidal waveform traveling at constant speed v is given by λ = v f, where v is called the phase speed of the wave and f is the wave's frequency.
In a dispersive medium, the phase speed itself depends upon the frequency of the wave, making the relationship between wavelength and frequency nonlinear. In the case of electromagnetic radiation—such as light—in free space, the phase speed is the speed of light, about 3×108 m/s, thus the wavelength of a 100 MHz electromagnetic wave is about: 3×108 m/s divided by 108 Hz = 3 metres. The wavelength of visible light ranges from deep red 700 nm, to violet 400 nm. For sound waves in air, the speed of sound is 343 m/s; the wavelengths of sound frequencies audible to the human ear are thus between 17 m and 17 mm, respectively. Note that the wavelengths in audible sound are much longer than those in visible light. A standing wave is an undulatory motion. A sinusoidal standing wave includes stationary points of no motion, called nodes, the wavelength is twice the distance between nodes; the upper figure shows three standing waves in a box. The walls of the box are considered to require the wave to have nodes at the walls of the box determining which wavelengths are allowed.
For example, for an electromagnetic wave, if the box has ideal metal walls, the condition for nodes at the walls results because the metal walls cannot support a tangential electric field, forcing the wave to have zero amplitude at the wall. The stationary wave can be viewed as the sum of two traveling sinusoidal waves of oppositely directed velocities. Wavelength and wave velocity are related just as for a traveling wave. For example, the speed of light can be determined from observation of standing waves in a metal box containing an ideal vacuum. Traveling sinusoidal waves are represented mathematically in terms of their velocity v, frequency f and wavelength λ as: y = A cos = A cos where y is the value of the wave at any position x and time t, A is the amplitude of the wave, they are commonly expressed in terms of wavenumber k and angular frequency ω as: y = A cos = A cos in which wavelength and wavenumber are related to velocity and frequency as: k = 2 π λ = 2 π f v = ω
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
General Services Administration
The General Services Administration, an independent agency of the United States government, was established in 1949 to help manage and support the basic functioning of federal agencies. GSA supplies products and communications for U. S. government offices, provides transportation and office space to federal employees, develops government-wide cost-minimizing policies and other management tasks. GSA employs about 12,000 federal workers and has an annual operating budget of $20.9 billion. GSA oversees $66 billion of procurement annually, it contributes to the management of about $500 billion in U. S. federal property, divided chiefly among 8,700 owned and leased buildings and a 215,000 vehicle motor pool. Among the real estate assets managed by GSA are the Ronald Reagan Building and International Trade Center in Washington, D. C. – the largest U. S. federal building after the Pentagon – and the Hart-Dole-Inouye Federal Center. GSA's business lines include the Federal Acquisition Service and the Public Buildings Service, as well as several Staff Offices including the Office of Government-wide Policy, the Office of Small Business Utilization, the Office of Mission Assurance.
As part of FAS, GSA's Technology Transformation Services helps federal agencies improve delivery of information and services to the public. Key initiatives include FedRAMP, Cloud.gov, the USAGov platform, Data.gov, Performance.gov, Challenge.gov. GSA is a member of the Procurement G6, an informal group leading the use of framework agreements and e-procurement instruments in public procurement. In 1947 President Harry Truman asked former President Herbert Hoover to lead what became known as the Hoover Commission to make recommendations to reorganize the operations of the federal government. One of the recommendations of the commission was the establishment of an "Office of the General Services." This proposed office would combine the responsibilities of the following organizations: U. S. Treasury Department's Bureau of Federal Supply U. S. Treasury Department's Office of Contract Settlement National Archives Establishment All functions of the Federal Works Agency, including the Public Buildings Administration and the Public Roads Administration War Assets AdministrationGSA became an independent agency on July 1, 1949, after the passage of the Federal Property and Administrative Services Act.
General Jess Larson, Administrator of the War Assets Administration, was named GSA's first Administrator. The first job awaiting Administrator Larson and the newly formed GSA was a complete renovation of the White House; the structure had fallen into such a state of disrepair by 1949 that one inspector of the time said the historic structure was standing "purely from habit." Larson explained the nature of the total renovation in depth by saying, "In order to make the White House structurally sound, it was necessary to dismantle, I mean dismantle, everything from the White House except the four walls, which were constructed of stone. Everything, except the four walls without a roof, was stripped down, that's where the work started." GSA worked with President Truman and First Lady Bess Truman to ensure that the new agency's first major project would be a success. GSA completed the renovation in 1952. In 1986 GSA headquarters, U. S. General Services Administration Building, located at Eighteenth and F Streets, NW, was listed on the National Register of Historic Places, at the time serving as Interior Department offices.
In 1960 GSA created the Federal Telecommunications System, a government-wide intercity telephone system. In 1962 the Ad Hoc Committee on Federal Office Space created a new building program to address obsolete office buildings in Washington, D. C. resulting in the construction of many of the offices that now line Independence Avenue. In 1970 the Nixon administration created the Consumer Product Information Coordinating Center, now part of USAGov. In 1974 the Federal Buildings Fund was initiated, allowing GSA to issue rent bills to federal agencies. In 1972 GSA established the Automated Data and Telecommunications Service, which became the Office of Information Resources Management. In 1973 GSA created the Office of Federal Management Policy. GSA's Office of Acquisition Policy centralized procurement policy in 1978. GSA was responsible for emergency preparedness and stockpiling strategic materials to be used in wartime until these functions were transferred to the newly-created Federal Emergency Management Agency in 1979.
In 1984 GSA introduced the federal government to the use of charge cards, known as the GMA SmartPay system. The National Archives and Records Administration was spun off into an independent agency in 1985; the same year, GSA began to provide governmentwide policy oversight and guidance for federal real property management as a result of an Executive Order signed by President Ronald Reagan. In 2003 the Federal Protective Service was moved to the Department of Homeland Security. In 2005 GSA reorganized to merge the Federal Supply Service and Federal Technology Service business lines into the Federal Acquisition Service. On April 3, 2009, President Barack Obama nominated Martha N. Johnson to serve as GSA Administrator. After a nine-month delay, the United States Senate confirmed her nomination on February 4, 2010. On April 2, 2012, Johnson resigned in the wake of a management-deficiency report that detailed improper payments for a 2010 "Western Regions" training conference put on by the Public Buildings Service in Las Vegas.
In July 1991 GSA contractors began the excavation of what is now the Ted Weiss Federal Building in New York City. The planning for that buildin
An optical fiber is a flexible, transparent fiber made by drawing glass or plastic to a diameter thicker than that of a human hair. Optical fibers are used most as a means to transmit light between the two ends of the fiber and find wide usage in fiber-optic communications, where they permit transmission over longer distances and at higher bandwidths than electrical cables. Fibers are used instead of metal wires. Fibers are used for illumination and imaging, are wrapped in bundles so they may be used to carry light into, or images out of 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 and fiber lasers. Optical fibers include a core surrounded by a transparent cladding material with a lower index of refraction. Light is kept in the core by the phenomenon of total 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, while those that support a single mode are called single-mode fibers.
Multi-mode fibers 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 fiber cores, the coupling of these aligned 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 mechanical 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, 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 and Jacques Babinet in Paris in the early 1840s. John Tyndall included a demonstration of it in his public lectures in London, 12 years later. Tyndall wrote about the property of total internal reflection in an introductory book about the nature of light in 1870:When the light passes from air into water, the refracted ray is bent towards the perpendicular... 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 ray will not quit the water at all: it will be reflected at the surface.... 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′, while for diamond it is 23°42′.
In the late 19th and early 20th centuries, light was guided through bent glass rods to illuminate body cavities. 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. In the 1930s, Heinrich Lamm showed that one could transmit images through a bundle of unclad optical fibers and used it for internal medical examinations, but his work was forgotten. In 1953, Dutch scientist Bram van Heel first demonstrated image transmission through bundles of optical fibers with a transparent cladding; that same year, Harold Hopkins and Narinder Singh Kapany at Imperial College in London succeeded in making image-transmitting bundles with over 10,000 fibers, subsequently achieved image transmission through a 75 cm long bundle which combined several thousand fibers. Their article titled "A flexible fibrescope, using static scanning" was published in the journal Nature in 1954.
The first practical fiber optic semi-flexible gastroscope was patented by Basil Hirschowitz, C. Wilbur Peters, Lawrence E. Curtiss, researchers at the University of Michigan, in 1956. In the process of developing the gastroscope, Curtiss produced the first glass-clad fibers. A variety of other image transmission applications soon followed. Kapany coined the term fiber optics, wrote a 1960 article in Scientific American that introduced the topic to a wide audience, wrote the first book about the new field; the first working fiber-optical data transmission system was demonstrated by German physicist Manfred Börner at Telefunken Research Labs in Ulm in 1965, followed by the first patent application for this technology in 1966. NASA used fiber optics in the television cameras. At the time, the use in the cameras was classified confidential, employees handling the cameras had to be supervised by someone with an appropriate security clearance. Charles K. Kao and George A. Hockham of the British company Standard Telephones and Cables were the first, in 1965, to promote the idea that the attenuation in optical fibers could be reduced below 20 decibels per kilometer, making fibers a practical communication medium.
They proposed th
The kilometre, or kilometer is a unit of length in the metric system, equal to one thousand metres. It is now the measurement unit used for expressing distances between geographical places on land in most of the world. K is used in some English-speaking countries as an alternative for the word kilometre in colloquial writing and speech. A slang term for the kilometre in the US and UK military is klick. There are two common pronunciations for the word; the former follows a pattern in English whereby metric units are pronounced with the stress on the first syllable and the pronunciation of the actual base unit does not change irrespective of the prefix. It is preferred by the British Broadcasting Corporation and the Australian Broadcasting Corporation. Many scientists and other users in countries where the metric system is not used, use the pronunciation with stress on the second syllable; the latter pronunciation follows the stress pattern used for the names of measuring instruments. The problem with this reasoning, however, is that the word meter in those usages refers to a measuring device, not a unit of length.
The contrast is more obvious in countries using the British rather than American spelling of the word metre. When Australia introduced the metric system in 1975, the first pronunciation was declared official by the government's Metric Conversion Board. However, the Australian prime minister at the time, Gough Whitlam, insisted that the second pronunciation was the correct one because of the Greek origins of the two parts of the word. By the 8 May 1790 decree, the Constituent assembly ordered the French Academy of Sciences to develop a new measurement system. In August 1793, the French National Convention decreed the metre as the sole length measurement system in the French Republic; the first name of the kilometre was "Millaire". Although the metre was formally defined in 1799, the myriametre was preferred to the "kilometre" for everyday use; the term "myriamètre" appeared a number of times in the text of Develey's book Physique d'Emile: ou, Principes de la science de la nature, while the term kilometre only appeared in an appendix.
French maps published in 1835 had scales showing myriametres and "lieues de Poste". The Dutch gave it the local name of the mijl, it was only in 1867 that the term "kilometer" became the only official unit of measure in the Netherlands to represent 1000 metres. Two German textbooks dated 1842 and 1848 give a snapshot of the use of the kilometre across Europe - the kilometre was in use in the Netherlands and in Italy and the myriametre was in use in France. In 1935, the International Committee for Weights and Measures abolished the prefix "myria-" and with it the "myriametre", leaving the kilometre as the recognised unit of length for measurements of that magnitude. In the United Kingdom, road signs show distances in miles and location marker posts that are used for reference purposes by road engineers and emergency services show distance references in unspecified units which are kilometre-based; the advent of the mobile phone has been instrumental in the British Department for Transport authorising the use of driver location signs to convey the distance reference information of location marker posts to road users should they need to contact the emergency services.
In the US, the National Highway System Designation Act of 1995 prohibits the use of federal-aid highway funds to convert existing signs or purchase new signs with metric units. The Executive Director of the US Federal Highway Administration, Jeffrey Paniati, wrote in a 2008 memo: "Section 205 of the National Highway System Designation Act of 1995 prohibited us from requiring any State DOT to use the metric system during project development activities. Although the State DOT's had the option of using metric measurements or dual units, all of them abandoned metric measurements and reverted to sole use of inch-pound values." The Manual on Uniform Traffic Control Devices since 2000 is published in both metric and American Customary Units. Some sporting disciplines feature 1000 m races in major events, but in other disciplines though world records are catalogued, the one kilometre event remains a minority event; the world records for various sporting disciplines are: Conversion of units, for comparison with other units of length Cubic metre Metric prefix Mileage Odometer Orders of magnitude Square kilometre Media related to Distance indicators at Wikimedia Commons
The micrometre or micrometer commonly known by the previous name micron, is an SI derived unit of length equalling 1×10−6 metre. The micrometre is a common unit of measurement for wavelengths of infrared radiation as well as sizes of biological cells and bacteria, for grading wool by the diameter of the fibres; the width of a single human hair ranges from 10 to 200 μm. The longest human chromosome is 10 μm in length. Between 1 μm and 10 μm: 1–10 μm – length of a typical bacterium 10 μm – Size of fungal hyphae 5 μm – length of a typical human spermatozoon's head 3–8 μm – width of strand of spider web silk about 10 μm – size of a fog, mist, or cloud water droplet Between 10 μm and 100 μm about 10–12 μm – thickness of plastic wrap 10 to 55 μm – width of wool fibre 17 to 181 μm – diameter of human hair 70 to 180 μm – thickness of paper The term micron and the symbol μ were accepted for use in isolation to denote the micrometre in 1879, but revoked by the International System of Units in 1967; this became necessary because the older usage was incompatible with the official adoption of the unit prefix micro-, denoted μ, during the creation of the SI in 1960.
In the SI, the systematic name micrometre became the official name of the unit, μm became the official unit symbol. In practice, "micron" remains a used term in preference to "micrometre" in many English-speaking countries, both in academic science and in applied science and industry. Additionally, in American English, the use of "micron" helps differentiate the unit from the micrometer, a measuring device, because the unit's name in mainstream American spelling is a homograph of the device's name. In spoken English, they may be distinguished by pronunciation, as the name of the measuring device is invariably stressed on the second syllable, whereas the systematic pronunciation of the unit name, in accordance with the convention for pronouncing SI units in English, places the stress on the first syllable; the plural of micron is "microns", though "micra" was used before 1950. The official symbol for the SI prefix micro- is a Greek lowercase mu. In Unicode, there is a micro sign with the code point U+00B5, distinct from the code point U+03BC of the Greek letter lowercase mu.
According to the Unicode Consortium, the Greek letter character is preferred, but implementations must recognize the micro sign as well. Most fonts use the same glyph for the two characters. Metric prefix Metric system Orders of magnitude Wool measurement The dictionary definition of micrometre at Wiktionary