An optical telescope is a telescope that gathers and focuses light from the visible part of the electromagnetic spectrum, to create a magnified image for direct view, or to make a photograph, or to collect data through electronic image sensors. There are three primary types of optical telescope: refractors, which use lenses reflectors, which use mirrors catadioptric telescopes, which combine lenses and mirrorsA telescope's light gathering power and ability to resolve small detail is directly related to the diameter of its objective; the larger the objective, the more light the telescope collects and the finer detail it resolves. People use telescopes and binoculars for activities such as observational astronomy, ornithology and reconnaissance, watching sports or performance arts; the telescope is more a discovery of optical craftsmen than an invention of a scientist. The lens and the properties of refracting and reflecting light had been known since antiquity and theory on how they worked were developed by ancient Greek philosophers and expanded on in the medieval Islamic world, had reached a advanced state by the time of the telescope's invention in early modern Europe.
But the most significant step cited in the invention of the telescope was the development of lens manufacture for spectacles, first in Venice and Florence in the thirteenth century, in the spectacle making centers in both the Netherlands and Germany. It is in the Netherlands in 1608; the invention is credited to the spectacle makers Hans Lippershey and Zacharias Janssen in Middelburg, the instrument-maker and optician Jacob Metius of Alkmaar. Galileo improved on these designs the following year, is credited as the first to use a telescope for astronomy. Galileo's telescope used Hans Lippershey's design of a convex objective lens and a concave eye lens, this design is now called a Galilean telescope. Johannes Kepler proposed an improvement on the design that used a convex eyepiece called the Keplerian Telescope; the next big step in the development of refractors was the advent of the Achromatic lens in the early 18th century, which corrected the chromatic aberration in Keplerian telescopes up to that time—allowing for much shorter instruments with much larger objectives.
For reflecting telescopes, which use a curved mirror in place of the objective lens, theory preceded practice. The theoretical basis for curved mirrors behaving similar to lenses was established by Alhazen, whose theories had been disseminated in Latin translations of his work. Soon after the invention of the refracting telescope Galileo, Giovanni Francesco Sagredo, others, spurred on by their knowledge that curved mirrors had similar properties as lenses, discussed the idea of building a telescope using a mirror as the image forming objective; the potential advantages of using parabolic mirrors led to several proposed designs for reflecting telescopes, the most notable of, published in 1663 by James Gregory and came to be called the Gregorian telescope, but no working models were built. Isaac Newton has been credited with constructing the first practical reflecting telescopes, the Newtonian telescope, in 1668 although due to their difficulty of construction and the poor performance of the speculum metal mirrors used it took over 100 years for reflectors to become popular.
Many of the advances in reflecting telescopes included the perfection of parabolic mirror fabrication in the 18th century, silver coated glass mirrors in the 19th century, long-lasting aluminum coatings in the 20th century, segmented mirrors to allow larger diameters, active optics to compensate for gravitational deformation. A mid-20th century innovation was catadioptric telescopes such as the Schmidt camera, which uses both a lens and mirror as primary optical elements used for wide field imaging without spherical aberration; the late 20th century has seen the development of adaptive optics and space telescopes to overcome the problems of astronomical seeing The basic scheme is that the primary light-gathering element the objective, focuses that light from the distant object to a focal plane where it forms a real image. This image may be viewed through an eyepiece, which acts like a magnifying glass; the eye sees an inverted magnified virtual image of the object. Most telescope designs produce an inverted image at the focal plane.
In fact, the image is both turned upside down and reversed left to right, so that altogether it is rotated by 180 degrees from the object orientation. In astronomical telescopes the rotated view is not corrected, since it does not affect how the telescope is used. However, a mirror diagonal is used to place the eyepiece in a more convenient viewing location, in that case the image is erect, but still reversed left to right. In terrestrial telescopes such as spotting scopes and binoculars, prisms or a relay lens between objective and eyepiece are used to correct the image orientation. There are telescope designs that do not present an inverted image such as the Galilean refractor and the Gregorian reflector; these are referred to as erecting telescopes. Many types of telescope divert the optical path with secondary or tertiary mirrors; these may be integral part of the optical design (Newtonian telescope, Cassegrain r
Atacama Large Millimeter Array
The Atacama Large Millimeter/submillimeter Array is an astronomical interferometer of 66 radio telescopes in the Atacama Desert of northern Chile, which observe electromagnetic radiation at millimeter and submillimeter wavelengths. The array has been constructed on the 5,000 m elevation Chajnantor plateau - near the Llano de Chajnantor Observatory and the Atacama Pathfinder Experiment; this location was chosen for its high elevation and low humidity, factors which are crucial to reduce noise and decrease signal attenuation due to Earth's atmosphere. ALMA is expected to provide insight on star birth during the early Stelliferous era and detailed imaging of local star and planet formation. ALMA is an international partnership among Europe, the United States, Japan, South Korea and Chile. Costing about US$1.4 billion, it is the most expensive ground-based telescope in operation. ALMA began scientific observations in the second half of 2011 and the first images were released to the press on 3 October 2011.
The array has been operational since March 2013. The initial ALMA array is composed of 66 high-precision antennas, operates at wavelengths of 9.6 to 0.3 millimeters. The array has much higher sensitivity and higher resolution than earlier submillimeter telescopes such as the single-dish James Clerk Maxwell Telescope or existing interferometer networks such as the Submillimeter Array or the Institut de Radio Astronomie Millimétrique Plateau de Bure facility; the antennas can be moved across the desert plateau over distances from 150 m to 16 km, which will give ALMA a powerful variable "zoom", similar in its concept to that employed at the centimetre-wavelength Very Large Array site in New Mexico, United States. The high sensitivity is achieved through the large numbers of antenna dishes that will make up the array; the telescopes were provided by the European, North American and East Asian partners of ALMA. The American and European partners each provided twenty-five 12-meter diameter antennas, that compose the main array.
The participating East Asian countries are contributing 16 antennas in the form of the Atacama Compact Array, part of the enhanced ALMA. By using smaller antennas than the main ALMA array, larger fields of view can be imaged at a given frequency using ACA. Placing the antennas closer together enables the imaging of sources of larger angular extent; the ACA works together with the main array in order to enhance the latter's wide-field imaging capability. ALMA has its conceptual roots in three astronomical projects — the Millimeter Array of the United States, the Large Southern Array of Europe, the Large Millimeter Array of Japan; the first step toward the creation of what would become ALMA came in 1997, when the National Radio Astronomy Observatory and the European Southern Observatory agreed to pursue a common project that merged the MMA and LSA. The merged array combined the sensitivity of the LSA with the frequency coverage and superior site of the MMA. ESO and NRAO worked together in technical and management groups to define and organize a joint project between the two observatories with participation by Canada and Spain.
A series of resolutions and agreements led to the choice of "Atacama Large Millimeter Array", or ALMA, as the name of the new array in March 1999 and the signing of the ALMA Agreement on 25 February 2003, between the North American and European parties. Following mutual discussions over several years, the ALMA Project received a proposal from the National Astronomical Observatory of Japan whereby Japan would provide the ACA and three additional receiver bands for the large array, to form Enhanced ALMA. Further discussions between ALMA and NAOJ led to the signing of a high-level agreement on 14 September 2004 that makes Japan an official participant in Enhanced ALMA, to be known as the Atacama Large Millimeter/submillimeter Array. A groundbreaking ceremony was held on November 6, 2003 and the ALMA logo was unveiled. During an early stage of the planning of ALMA, it was decided to employ ALMA antennas designed and constructed by known companies in North America and Japan, rather than using one single design.
This was for political reasons. Although different approaches have been chosen by the providers, each of the antenna designs appears to be able to meet ALMA's stringent requirements; the components designed and manufactured across Europe were transported by specialist aerospace and astrospace logistics company Route To Space Alliance, 26 in total which were delivered to Antwerp for onward shipment to Chile. ALMA was a 50-50 collaboration between the National Radio Astronomy Observatory and European Southern Observatory and extended with the help of the other Japanese and Chilean partners. ALMA is the largest and most expensive ground-based astronomical project, costing between US$1.4 and 1.5 billion.. PartnersEuropean Southern Observatory and the European Regional Support Centre National Science Foundation via the National Radio Astronomy Observatory and the North American ALMA Science Center National Research Council of Canada National Astronomical Observatory of Japan under the National Institutes of Natural Sciences ALMA-Taiwan at the Academia Sinica Institute of Astronomy & Astrophysics Republic of Chile The complex was built by European, U.
S. Japanese, Canadian co
Submillimetre astronomy or submillimeter astronomy is the branch of observational astronomy, conducted at submillimetre wavelengths of the electromagnetic spectrum. Astronomers place the submillimetre waveband between the far-infrared and microwave wavebands taken to be between a few hundred micrometres and a millimetre, it is still common in submillimetre astronomy to quote wavelengths in'microns', the old name for micrometre. Using submillimetre observations, astronomers examine molecular clouds and dark cloud cores with a goal of clarifying the process of star formation from earliest collapse to stellar birth. Submillimetre observations of these dark clouds can be used to determine chemical abundances and cooling mechanisms for the molecules which comprise them. In addition, submillimetre observations give information on the mechanisms for the formation and evolution of galaxies; the most significant limitation to the detection of astronomical emission at submillimetre wavelengths with ground-based observatories is atmospheric emission and attenuation.
Like the infrared, the submillimetre atmosphere is dominated by numerous water vapour absorption bands and it is only through "windows" between these bands that observations are possible. The ideal submillimetre observing site is dry, has stable weather conditions and is away from urban population centres. There are only a handful of such sites identified, they include Mauna Kea, the Llano de Chajnantor Observatory on the Atacama Plateau, the South Pole, Hanle in India. Comparisons show that all four sites are excellent for submillimetre astronomy, of these sites Mauna Kea is the most established and arguably the most accessible. There has been some recent interest in high-altitude Arctic sites Summit Station in Greenland where the PWV measure is always better than at Mauna Kea; the Llano de Chajnantor Observatory site hosts the Atacama Pathfinder Experiment, the largest submillimetre telescope operating in the southern hemisphere, the world's largest ground based astronomy project, the Atacama Large Millimeter Array, an interferometer for submillimetre wavelength observations made of 54 12-metre and 12 7-metre radio telescopes.
The Submillimeter Array is another interferometer, located at Mauna Kea, consisting of eight 6-metre diameter radio telescopes. The largest existing submillimetre telescope, the James Clerk Maxwell Telescope, is located on Mauna Kea. With high-altitude balloons and aircraft, one can get above more of the atmosphere; the BLAST experiment and SOFIA are two examples although SOFIA can handle near infrared observations. Space-based observations at the submillimetre wavelengths remove the ground-based limitations of atmospheric absorption; the Submillimeter Wave Astronomy Satellite was launched into low Earth orbit on December 5, 1998 as one of NASA's Small Explorer Program missions. The mission of the spacecraft is to make targeted observations of giant molecular clouds and dark cloud cores; the focus of SWAS is five spectral lines: water, isotopic water, isotopic carbon monoxide, molecular oxygen, neutral carbon. The SWAS satellite was repurposed in 2005 to provide support for the NASA Deep Impact mission.
SWAS provided water production data on the comet until the end of August 2005. The European Space Agency launched a space-based mission known as the Herschel Space Observatory in 2009. Herschel deployed the largest mirror launched into space and studied radiation in the far infrared and submillimetre wavebands. Rather than an Earth orbit, Herschel entered into a Lissajous orbit around L2, the second Lagrangian point of the Earth-Sun system. L2 is located 1.5 million km from Earth and the placement of Herschel there lessened the interference by infrared and visible radiation from the Earth and Sun. Herschel's mission focused on the origins of galaxies and galactic formation. Event Horizon Telescope Terahertz radiation Far infrared astronomy SCUBA-2 All Sky Survey Radio window Infrared window Optical window Category:Submillimetre telescopes Arizona Radio Observatory page on Submillimeter Astronomy Atacama Pathfinder Experiment Home Page Atacama Large Millimeter Array Home Page SWAS Home Page Herschel Space Observatory
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
A physicist is a scientist who specializes in the field of physics, which encompasses the interactions of matter and energy at all length and time scales in the physical universe. Physicists are interested in the root or ultimate causes of phenomena, frame their understanding in mathematical terms. Physicists work across a wide range of research fields, spanning all length scales: from sub-atomic and particle physics, through biological physics, to cosmological length scales encompassing the universe as a whole; the field includes two types of physicists: experimental physicists who specialize in the observation of physical phenomena and the analysis of experiments, theoretical physicists who specialize in mathematical modeling of physical systems to rationalize and predict natural phenomena. Physicists can apply their knowledge towards solving practical problems or to developing new technologies; the study and practice of physics is based on an intellectual ladder of discoveries and insights from ancient times to the present.
Many mathematical and physical ideas used today found their earliest expression in ancient Greek culture, for example in the work of Euclid, Thales of Miletus and Aristarchus. Roots emerged in ancient Asian culture and in the Islamic medieval period, for example the work of Alhazen in the 11th century; the modern scientific worldview and the bulk of physics education can be said to flow from the scientific revolution in Europe, starting with the work of Galileo Galilei and Johannes Kepler in the early 1600s. Newton's laws of motion and Newton's law of universal gravitation were formulated in the 17th century; the experimental discoveries of Faraday and the theory of Maxwell's equations of electromagnetism were developmental high points during the 19th century. Many physicists contributed to the development of quantum mechanics in the early-to-mid 20th century. New knowledge in the early 21st century includes a large increase in understanding physical cosmology; the broad and general study of nature, natural philosophy, was divided into several fields in the 19th century, when the concept of "science" received its modern shape.
Specific categories emerged, such as "biology" and "biologist", "physics" and "physicist", "chemistry" and "chemist", among other technical fields and titles. The term physicist was coined by William Whewell in his 1840 book The Philosophy of the Inductive Sciences. A standard undergraduate physics curriculum consists of classical mechanics and magnetism, non-relativistic quantum mechanics, statistical mechanics and thermodynamics, laboratory experience. Physics students need training in mathematics, in computer science. Any physics-oriented career position requires at least an undergraduate degree in physics or applied physics, while career options widen with a Master's degree like MSc, MPhil, MPhys or MSci. For research-oriented careers, students work toward a doctoral degree specializing in a particular field. Fields of specialization include experimental and theoretical astrophysics, atomic physics, biological physics, chemical physics, condensed matter physics, geophysics, gravitational physics, material science, medical physics, molecular physics, nuclear physics, radiophysics, electromagnetic field and microwave physics, particle physics, plasma physics.
The highest honor awarded to physicists is the Nobel Prize in Physics, awarded since 1901 by the Royal Swedish Academy of Sciences. National physics professional societies have many awards for professional recognition. In the case of the American Physical Society, as of 2017, there are 33 separate prizes and 38 separate awards in the field; the three major employers of career physicists are academic institutions and private industries, with the largest employer being the last. Physicists in academia or government labs tend to have titles such as Assistants, Professors, Sr./Jr. Scientist, or postdocs; as per the American Institute of Physics, some 20% of new physics Ph. D.s holds jobs in engineering development programs, while 14% turn to computer software and about 11% are in business/education. A majority of physicists employed apply their skills and training to interdisciplinary sectors. Job titles for graduate physicists include Agricultural Scientist, Air Traffic Controller, Computer Programmer, Electrical Engineer, Environmental Analyst, Medical Physicist, Oceanographer, Physics Teacher/Professor/Researcher, Research Scientist, Reactor Physicist, Engineering Physicist, Satellite Missions Analyst, Science Writer, Software Engineer, Systems Engineer, Microelectronics Engineer, Radar Developer, Technical Consultant, etc.
A majority of Physics terminal bachelor's degree holders are employed in the private sector. Other fields are academia and military service, nonprofit entities and teaching. Typical duties of physicists with master's and doctoral degrees working in their domain involve research and analysis, data preparation, instrumentation and development of industrial or medical equipment and software development, etc. Chartered Physicist is a chartered status and a professional qualification awarded by the Institute of Physics, it is denoted by the postnominals "CPhys". Achieving chartered status in any profession denotes to the wider community a high level of specialised subject knowledge and professional competence. According to the Institute of Physics, holders of the award of the Chartered Physicist demonst
Frederick William Herschel, was a German-born British astronomer and brother of fellow astronomer Caroline Herschel, with whom he worked. Born in the Electorate of Hanover, Herschel followed his father into the Military Band of Hanover, before migrating to Great Britain in 1757 at the age of nineteen. Herschel constructed his first large telescope in 1774, after which he spent nine years carrying out sky surveys to investigate double stars. Herschel published catalogues of nebulae in 1802 and in 1820; the resolving power of the Herschel telescopes revealed that many objects called nebulae in the Messier catalogue were clusters of stars. On 13 March 1781 while making observations he made note of a new object in the constellation of Gemini; this would, after several weeks of verification and consultation with other astronomers, be confirmed to be a new planet given the name of Uranus. This was the first planet to be discovered since antiquity and Herschel became famous overnight; as a result of this discovery, George III appointed him Court Astronomer.
He was elected as a Fellow of the Royal Society and grants were provided for the construction of new telescopes. Herschel pioneered the use of astronomical spectrophotometry, using prisms and temperature measuring equipment to measure the wavelength distribution of stellar spectra. In addition, Herschel discovered infrared radiation. Other work included an improved determination of the rotation period of Mars, the discovery that the Martian polar caps vary seasonally, the discovery of Titania and Oberon and Enceladus and Mimas. Herschel was made a Knight of the Royal Guelphic Order in 1816, he was the first President of the Royal Astronomical Society when it was founded in 1820. He died in August 1822, his work was continued by his only son, John Herschel. Herschel was born in the Electorate of Hanover in Germany part of the Holy Roman Empire, one of ten children of Isaac Herschel by his marriage to Anna Ilse Moritzen, of German Lutheran ancestry, it has been proposed by Hershel's biographer Holden that his father's family traced its roots back to Jews from Moravia who converted to Christianity in the seventeenth century, they themselves were Lutheran Christians.
Herschel's father was an oboist in the Hanover Military Band. In 1755 the Hanoverian Guards regiment, in whose band Wilhelm and his brother Jakob were engaged as oboists, was ordered to England. At the time the crowns of Great Britain and Hanover were united under King George II; as the threat of war with France loomed, the Hanoverian Guards were recalled from England to defend Hanover. After they were defeated at the Battle of Hastenbeck, Herschel's father Isaak sent his two sons to seek refuge in England in late 1757. Although his older brother Jakob had received his dismissal from the Hanoverian Guards, Wilhelm was accused of desertion. Wilhelm, nineteen years old at this time, was a quick student of the English language. In England he went by the English rendition of Frederick William Herschel. In addition to the oboe, he played the violin and harpsichord and the organ, he composed numerous musical works, including 24 symphonies and many concertos, as well as some church music. Six of his symphonies were recorded in April 2002 by the London Mozart Players, conducted by Matthias Bamert.
Herschel moved to Sunderland in 1761 when Charles Avison engaged him as first violin and soloist for his Newcastle orchestra, where he played for one season. In "Sunderland in the County of Durh: apprill 20th 1761" he wrote his Symphony No. 8 in C Minor. He was head of the Durham Militia band from 1760 to 1761, he visited the home of Sir Ralph Milbanke at Halnaby Hall near Darlington in 1760, where he wrote two symphonies, as well as giving performances himself. After Newcastle, he moved to Leeds and Halifax where he was the first organist at St John the Baptist church. In 1766, Herschel became organist of the Octagon Chapel, Bath, a fashionable chapel in a well-known spa, in which city he was Director of Public Concerts, he was appointed as the organist in 1766 and gave his introductory concert on 1 January 1767. As the organ was still incomplete, he showed off his versatility by performing his own compositions including a violin concerto, an oboe concerto and a harpsichord sonata. On 4 October 1767, he performed on the organ for the official opening of the Octagon Chapel.
His sister Caroline arrived in England on 24 August 1772 to live with William in New King Street, Bath. The house they shared is now the location of the Herschel Museum of Astronomy. Herschel's brothers Dietrich and Jakob appeared as musicians of Bath. In 1780, Herschel was appointed director of the Bath orchestra, with his sister appearing as soprano soloist. Herschel's reading in natural philosophy during the 1770s indicates his personal interests but suggests an intention to be upwardly mobile and professionally, he was well-positioned to engage with eighteenth-century "philosophical Gentleman" or philomaths, of wide-ranging logical and practical tastes. Herschel's intellectual curiosity and interest in music led him to astronomy. After reading Robert Smith's Harmonics, or the Philosophy of Musical Sounds, he took up Smith's A Compleat System of Opticks, which described techniques of telescope construction, he read James Ferguson's Astronomy explained upon Sir Isaac Newton's principles and made easy to those who have not studied mathematics and William Emerson's The elements of trigonometry, The elements of optics a
In optics, a prism is a transparent optical element with flat, polished surfaces that refract light. At least two of the flat surfaces must have an angle between them; the exact angles between the surfaces depend on the application. The traditional geometrical shape is that of a triangular prism with a triangular base and rectangular sides, in colloquial use "prism" refers to this type; some types of optical prism are not in fact in the shape of geometric prisms. Prisms can be made from any material, transparent to the wavelengths for which they are designed. Typical materials include glass and fluorite. A dispersive prism can be used to break light up into its constituent spectral colors. Furthermore, prisms can be used to reflect light, or to split light into components with different polarizations. Light changes speed; this speed change causes the light to enter the new medium at a different angle. The degree of bending of the light's path depends on the angle that the incident beam of light makes with the surface, on the ratio between the refractive indices of the two media.
The refractive index of many materials varies with the wavelength or color of the light used, a phenomenon known as dispersion. This causes light of different colors to be refracted differently and to leave the prism at different angles, creating an effect similar to a rainbow; this can be used to separate a beam of white light into its constituent spectrum of colors. A similar separation happens with iridescent materials, such as a soap bubble. Prisms will disperse light over a much larger frequency bandwidth than diffraction gratings, making them useful for broad-spectrum spectroscopy. Furthermore, prisms do not suffer from complications arising from overlapping spectral orders, which all gratings have. Prisms are sometimes used for the internal reflection at the surfaces rather than for dispersion. If light inside the prism hits one of the surfaces at a sufficiently steep angle, total internal reflection occurs and all of the light is reflected; this makes a prism a useful substitute for a mirror in some situations.
Ray angle deviation and dispersion through a prism can be determined by tracing a sample ray through the element and using Snell's law at each interface. For the prism shown at right, the indicated angles are given by θ 0 ′ = arcsin θ 1 = α − θ 0 ′ θ 1 ′ = arcsin θ 2 = θ 1 ′ − α. All angles are positive in the direction shown in the image. For a prism in air n 0 = n 2 ≃ 1. Defining n = n 1, the deviation angle δ is given by δ = θ 0 + θ 2 = θ 0 + arcsin − α If the angle of incidence θ 0 and prism apex angle α are both small, sin θ ≈ θ and arcsin x ≈ x if the angles are expressed in radians; this allows the nonlinear equation in the deviation angle δ to be approximated by δ ≈ θ 0 − α + = θ 0 − α + n α − θ 0 = α