1.
Prism
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In optics, a prism is a transparent optical element with flat, polished surfaces that refract light. At least two of the 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, and in colloquial use prism usually 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 that is transparent to the wavelengths for which they are designed. Typical materials include glass, plastic and fluorite, a dispersive prism can be used to break light up into its constituent spectral colors. Furthermore, prisms can be used to light, or to split light into components with different polarizations. Light changes speed as it moves from one medium to another and this speed change causes the light to be refracted and to enter the new medium at a different angle. The degree of bending of the lights path depends on the angle that the incident beam of light makes with the surface, 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 and this can be used to separate a beam of white light into its constituent spectrum of colors. Prisms will generally disperse light over a larger frequency bandwidth than diffraction gratings. Furthermore, prisms do not suffer from complications arising from overlapping spectral orders, 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 steep angle, total internal reflection occurs. 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 Snells law at each interface. For the prism shown at right, the angles are given by θ0 ′ = arcsin θ1 = α − θ0 ′ θ1 ′ = arcsin θ2 = θ1 ′ − α. All angles are positive in the shown in the image. For a prism in air n 0 = n 2 ≃1 and this allows the nonlinear equation in the deviation angle δ to be approximated by δ ≈ θ0 − α + = θ0 − α + n α − θ0 = α. The deviation angle depends on wavelength through n, so for a thin prism the deviation angle varies with wavelength according to δ ≈ α, before Isaac Newton, it was believed that white light was colorless, and that the prism itself produced the color. It was only later that Young and Fresnel combined Newtons particle theory with Huygens wave theory to show that color is the manifestation of lights wavelength
2.
Optics
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Optics is the branch of physics which involves the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behaviour of visible, ultraviolet, and infrared light, because light is an electromagnetic wave, other forms of electromagnetic radiation such as X-rays, microwaves, and radio waves exhibit similar properties. Most optical phenomena can be accounted for using the classical description of light. Complete electromagnetic descriptions of light are, however, often difficult to apply in practice, practical optics is usually done using simplified models. The most common of these, geometric optics, treats light as a collection of rays that travel in straight lines, physical optics is a more comprehensive model of light, which includes wave effects such as diffraction and interference that cannot be accounted for in geometric optics. Historically, the model of light was developed first, followed by the wave model of light. Progress in electromagnetic theory in the 19th century led to the discovery that waves were in fact electromagnetic radiation. Some phenomena depend on the fact that light has both wave-like and particle-like properties, explanation of these effects requires quantum mechanics. When considering lights particle-like properties, the light is modelled as a collection of particles called photons, quantum optics deals with the application of quantum mechanics to optical systems. Optical science is relevant to and studied in many related disciplines including astronomy, various engineering fields, photography, practical applications of optics are found in a variety of technologies and everyday objects, including mirrors, lenses, telescopes, microscopes, lasers, and fibre optics. Optics began with the development of lenses by the ancient Egyptians and Mesopotamians, the earliest known lenses, made from polished crystal, often quartz, date from as early as 700 BC for Assyrian lenses such as the Layard/Nimrud lens. The ancient Romans and Greeks filled glass spheres with water to make lenses, the word optics comes from the ancient Greek word ὀπτική, meaning appearance, look. Greek philosophy on optics broke down into two opposing theories on how vision worked, the theory and the emission theory. The intro-mission approach saw vision as coming from objects casting off copies of themselves that were captured by the eye, plato first articulated the emission theory, the idea that visual perception is accomplished by rays emitted by the eyes. He also commented on the parity reversal of mirrors in Timaeus, some hundred years later, Euclid wrote a treatise entitled Optics where he linked vision to geometry, creating geometrical optics. Ptolemy, in his treatise Optics, held a theory of vision, the rays from the eye formed a cone, the vertex being within the eye. The rays were sensitive, and conveyed back to the observer’s intellect about the distance. He summarised much of Euclid and went on to describe a way to measure the angle of refraction, during the Middle Ages, Greek ideas about optics were resurrected and extended by writers in the Muslim world
3.
Triangular prism
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In geometry, a triangular prism is a three-sided prism, it is a polyhedron made of a triangular base, a translated copy, and 3 faces joining corresponding sides. A right triangular prism has rectangular sides, otherwise it is oblique, a uniform triangular prism is a right triangular prism with equilateral bases, and square sides. Equivalently, it is a polyhedron of which two faces are parallel, while the normals of the other three are in the same plane. All cross-sections parallel to the faces are the same triangle. A right triangular prism is semiregular or, more generally, a uniform if the base faces are equilateral triangles. It can be seen as a truncated trigonal hosohedron, represented by Schläfli symbol t, alternately it can be seen as the Cartesian product of a triangle and a line segment, and represented by the product x. The dual of a prism is a triangular bipyramid. The symmetry group of a right 3-sided prism with triangular base is D3h of order 12, the rotation group is D3 of order 6. The symmetry group does not contain inversion, the volume of any prism is the product of the area of the base and the distance between the two bases. A truncated right triangular prism has one triangular face truncated at an oblique angle, there are two full D2h symmetry facetings of a triangular prism, both with 6 isosceles triangle faces, one keeping the original top and bottom triangles, and one the original squares. Two lower C3v symmetry faceting have one triangle,3 lateral crossed square faces. This polyhedron is topologically related as a part of sequence of uniform truncated polyhedra with vertex configurations and this polyhedron is topologically related as a part of sequence of cantellated polyhedra with vertex figure, and continues as tilings of the hyperbolic plane. These vertex-transitive figures have reflectional symmetry and this polyhedron is topologically related as a part of sequence of cantellated polyhedra with vertex figure, and continues as tilings of the hyperbolic plane. These vertex-transitive figures have reflectional symmetry, there are 4 uniform compounds of triangular prisms, Compound of four triangular prisms, compound of eight triangular prisms, compound of ten triangular prisms, compound of twenty triangular prisms. Each progressive uniform polytope is constructed vertex figure of the previous polytope, thorold Gosset identified this series in 1900 as containing all regular polytope facets, containing all simplexes and orthoplexes. In Coxeters notation the triangular prism is given the symbol −121, the triangular prism exists as cells of a number of four-dimensional uniform 4-polytopes, including, Wedge Weisstein, Eric W. Triangular prism. Interactive Polyhedron, Triangular Prism surface area and volume of a triangular prism
4.
Spectroscopy
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Spectroscopy /spɛkˈtrɒskəpi/ is the study of the interaction between matter and electromagnetic radiation. Historically, spectroscopy originated through the study of visible light dispersed according to its wavelength, later the concept was expanded greatly to include any interaction with radiative energy as a function of its wavelength or frequency. Spectroscopic data is represented by an emission spectrum, a plot of the response of interest as a function of wavelength or frequency. Spectroscopy and spectrography are terms used to refer to the measurement of radiation intensity as a function of wavelength and are used to describe experimental spectroscopic methods. Spectral measurement devices are referred to as spectrometers, spectrophotometers, spectrographs or spectral analyzers, daily observations of color can be related to spectroscopy. Neon lighting is an application of atomic spectroscopy. Neon and other noble gases have characteristic emission frequencies, neon lamps use collision of electrons with the gas to excite these emissions. Inks, dyes and paints include chemical compounds selected for their characteristics in order to generate specific colors. A commonly encountered molecular spectrum is that of nitrogen dioxide, gaseous nitrogen dioxide has a characteristic red absorption feature, and this gives air polluted with nitrogen dioxide a reddish-brown color. Rayleigh scattering is a spectroscopic scattering phenomenon that accounts for the color of the sky, Spectroscopy is used in physical and analytical chemistry because atoms and molecules have unique spectra. As a result, these spectra can be used to detect, identify and quantify information about the atoms, Spectroscopy is also used in astronomy and remote sensing on earth. The measured spectra are used to determine the composition and physical properties of astronomical objects. One of the concepts in spectroscopy is a resonance and its corresponding resonant frequency. Resonances were first characterized in mechanical systems such as pendulums, mechanical systems that vibrate or oscillate will experience large amplitude oscillations when they are driven at their resonant frequency. A plot of amplitude vs. excitation frequency will have a peak centered at the resonance frequency and this plot is one type of spectrum, with the peak often referred to as a spectral line, and most spectral lines have a similar appearance. In quantum mechanical systems, the resonance is a coupling of two quantum mechanical stationary states of one system, such as an atom, via an oscillatory source of energy such as a photon. The coupling of the two states is strongest when the energy of the matches the energy difference between the two states. The energy of a photon is related to its frequency by E = h ν where h is Plancks constant, spectra of atoms and molecules often consist of a series of spectral lines, each one representing a resonance between two different quantum states
5.
Dispersion (optics)
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In optics, dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency. Media having this property may be termed dispersive media. Sometimes the term chromatic dispersion is used for specificity, the most familiar example of dispersion is probably a rainbow, in which dispersion causes the spatial separation of a white light into components of different wavelengths. Most often, chromatic dispersion refers to material dispersion, that is. However, in a waveguide there is also the phenomenon of waveguide dispersion, more generally, 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 generally be present, although they are not strictly additive, for example, in fiber optics the material and waveguide dispersion can effectively 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 effect that may degrade images in microscopes, telescopes. The phase velocity, v, of a wave in a uniform medium is given by v = c n where c is the speed of light in a vacuum. In general, the index is some function of the frequency f of the light, thus n = n, or alternatively. The wavelength dependence of a refractive index is usually quantified by its Abbe number or its coefficients in an empirical formula such as the Cauchy or Sellmeier equations. In particular, for materials, the susceptibility χ that appears in the Kramers–Kronig relations is the electric susceptibility χe = n2 −1. The most commonly seen consequence of dispersion in optics is the separation of light into a color spectrum by a prism. From Snells law it can be seen that the angle of refraction of light in a prism depends on the index of the prism material. For visible light, refraction indices n of most transparent materials decrease with increasing wavelength λ,1 < n < n < n, or alternatively, 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, Snells law predicts that light incident at an angle θ to the normal will be refracted at an angle arcsin. Thus, blue light, with a refractive index, will be bent more strongly than red light
6.
Spectrum
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A spectrum is a condition that is not limited to a specific set of values but can vary, without steps, across a continuum. The word was first used scientifically in optics to describe the rainbow of colors in visible light after passing through a prism, as scientific understanding of light advanced, it came to apply to the entire electromagnetic spectrum. Spectrum has since been applied by analogy to topics outside of optics, thus, one might talk about the spectrum of political opinion, or the spectrum of activity of a drug, or the autism spectrum. In these uses, values within a spectrum may not be associated with precisely quantifiable numbers or definitions, such uses imply a broad range of conditions or behaviors grouped together and studied under a single title for ease of discussion. Nonscientific uses of the spectrum are sometimes misleading. For instance, a single left–right spectrum of opinion does not capture the full range of peoples political beliefs. Political scientists use a variety of biaxial and multiaxial systems to accurately characterize political opinion. In most modern usages of spectrum there is a theme between the extremes at either end. This was not always true in older usage, in Latin spectrum means image or apparition, including the meaning spectre. Spectral evidence is testimony about what was done by spectres of persons not present physically and it was used to convict a number of persons of witchcraft at Salem, Massachusetts in the late 17th century. The word spectrum was used to designate a ghostly optical afterimage by Goethe in his Theory of Colors and Schopenhauer in On Vision. The prefix spectro- is used to form words relating to spectra, for example, a spectrometer is a device used to record spectra and spectroscopy is the use of a spectrometer for chemical analysis. In the 17th century the word spectrum was introduced into optics by Isaac Newton, soon the term referred to a plot of light intensity or power as a function of frequency or wavelength, also known as a spectral density plot. The term spectrum was expanded to apply to other waves, such as sound waves that could also be measured as a function of frequency, frequency spectrum and power spectrum of a signal. The term now applies to any signal that can be measured or decomposed along a variable such as energy in electron spectroscopy or mass to charge ratio in mass spectrometry. Spectrum is also used to refer to a representation of the signal as a function of the dependent variable. Devices used to measure an electromagnetic spectrum are called spectrograph or spectrometer, the visible spectrum is the part of the electromagnetic spectrum that can be seen by the human eye. The wavelength of light ranges from 390 to 700 nm
7.
Color
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Color or colour is the characteristic of human visual perception described through color categories, with names such as red, yellow, purple, or blue. This perception of color derives from the stimulation of cells in the human eye by electromagnetic radiation in the spectrum of light. Color categories and physical specifications of color are associated with objects through the wavelength of the light that is reflected from them and this reflection is governed by the objects physical properties such as light absorption, emission spectra, etc. By defining a color space, colors can be identified numerically by coordinates, there may also be more than three color dimensions in other color spaces, such as in the CMYK color model, wherein one of the dimensions relates to a colours colorfulness). The photo-receptivity of the eyes of species also varies considerably from our own. Honeybees and bumblebees for instance have trichromatic color vision sensitive to ultraviolet but is insensitive to red, papilio butterflies possess six types of photoreceptors and may have pentachromatic vision. The most complex color vision system in the kingdom has been found in stomatopods with up to 12 spectral receptor types thought to work as multiple dichromatic units. The science of color is sometimes called chromatics, colorimetry, or simply color science and it includes the perception of color by the human eye and brain, the origin of color in materials, color theory in art, and the physics of electromagnetic radiation in the visible range. Electromagnetic radiation is characterized by its wavelength and its intensity, when the wavelength is within the visible spectrum, it is known as visible light. Most light sources emit light at different wavelengths, a sources spectrum is a distribution giving its intensity at each wavelength. Although the spectrum of light arriving at the eye from a given direction determines the color sensation in that direction, in each such class the members are called metamers of the color in question. The table at right shows approximate frequencies and wavelengths for various pure spectral colors, the wavelengths listed are as measured in air or vacuum. A common list identifies six main bands, red, orange, yellow, green, blue, Newtons conception included a seventh color, indigo, between blue and violet. It is possible that what Newton referred to as blue is nearer to what today is known as cyan, the color of an object depends on both the physics of the object in its environment and the characteristics of the perceiving eye and brain. Some objects not only light, but also transmit light or emit light themselves. This effect is known as color constancy, opaque objects that do not reflect specularly have their color determined by which wavelengths of light they scatter strongly. If objects scatter all wavelengths with roughly equal strength, they appear white, if they absorb all wavelengths, they appear black. Opaque objects that reflect light of different wavelengths with different efficiencies look like mirrors tinted with colors determined by those differences
8.
Rainbow
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A rainbow is a meteorological phenomenon that is caused by reflection, refraction and dispersion of light in water droplets resulting in a spectrum of light appearing in the sky. It takes the form of a multicoloured arc, Rainbows caused by sunlight always appear in the section of sky directly opposite the sun. However, the observer sees only an arc formed by illuminated droplets above the ground. In a primary rainbow, the arc shows red on the outer part and this rainbow is caused by light being refracted when entering a droplet of water, then reflected inside on the back of the droplet and refracted again when leaving it. In a double rainbow, an arc is seen outside the primary arc. A rainbow is not located at a distance from the observer. Thus, a rainbow is not an object and cannot be physically approached, indeed, it is impossible for an observer to see a rainbow from water droplets at any angle other than the customary one of 42 degrees from the direction opposite the light source. Even if an observer sees another observer who seems under or at the end of a rainbow, Rainbows span a continuous spectrum of colours. Rainbows can be caused by many forms of airborne water and these include not only rain, but also mist, spray, and airborne dew. Rainbows can be observed there are water drops in the air. Because of this, rainbows are seen in the western sky during the morning. The most spectacular rainbow displays happen when half the sky is dark with raining clouds. The result is a rainbow that contrasts with the darkened background. During such good visibility conditions, the larger but fainter secondary rainbow is often visible and it appears about 10° outside of the primary rainbow, with inverse order of colours. The rainbow effect is commonly seen near waterfalls or fountains. In addition, the effect can be created by dispersing water droplets into the air during a sunny day. Rarely, a moonbow, lunar rainbow or nighttime rainbow, can be seen on strongly moonlit nights, as human visual perception for colour is poor in low light, moonbows are often perceived to be white. It is difficult to photograph the complete semicircle of a rainbow in one frame, for a 35 mm camera, a wide-angle lens with a focal length of 19 mm or less would be required
9.
Index of refraction
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In optics, the refractive index or index of refraction n of a material is a dimensionless number that describes how light propagates through that medium. It is defined as n = c v, where c is the speed of light in vacuum, for example, the refractive index of water is 1.333, meaning that light travels 1.333 times faster in a vacuum than it does in water. The refractive index determines how light is bent, or refracted. The refractive indices also determine the amount of light that is reflected when reaching the interface, as well as the angle for total internal reflection. This implies that vacuum has a index of 1. The refractive index varies with the wavelength of light and this is called dispersion and causes the splitting of white light into its constituent colors in prisms and rainbows, and chromatic aberration in lenses. Light propagation in absorbing materials can be described using a refractive index. The imaginary part then handles the attenuation, while the real part accounts for refraction, the concept of refractive index is widely used within the full electromagnetic spectrum, from X-rays to radio waves. It can also be used with wave phenomena such as sound, in this case the speed of sound is used instead of that of light and a reference medium other than vacuum must be chosen. Thomas Young was presumably the person who first used, and invented, 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, 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 the next years, others started using different symbols, n, m, and µ. 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, gases at atmospheric pressure have refractive indices close to 1 because of their low density. Almost all solids and liquids have refractive indices above 1.3, aerogel is a very low density solid that can be produced with refractive index in the range from 1.002 to 1.265. Moissanite lies at the 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, for infrared light refractive indices can be considerably higher
10.
Snell's law
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In optics, the law is used in ray tracing to compute the angles of incidence or refraction, and in experimental optics to find the refractive index of a material. The law is also satisfied in metamaterials, which light to be bent backward at a negative angle of refraction with a negative refractive index. Although named after Dutch astronomer Willebrord Snellius, the law was first accurately described by the scientist Ibn Sahl at the Baghdad court in 984, in the manuscript On Burning Mirrors and Lenses, Sahl used the law to derive lens shapes that focus light with no geometric aberrations. The law follows from Fermats principle of least time, which in turn follows from the propagation of light as waves, ptolemy, a Greek living in Alexandria, Egypt, had found a relationship regarding refraction angles, but it was inaccurate for angles that were not small. Ptolemy was confident he had found an empirical law, partially as a result of fudging his data to fit theory. Alhazen, in his Book of Optics, came closer to discovering the law of refraction, although named after Dutch astronomer Willebrord Snellius, the law was first accurately described by the Persian scientist Ibn Sahl at the Baghdad court in 984. In the manuscript On Burning Mirrors and Lenses, Sahl used the law to derive lens shapes that focus light with no geometric aberrations. The law was rediscovered by Thomas Harriot in 1602, who however did not publish his results although he had corresponded with Kepler on this very subject, in 1621, Willebrord Snellius derived a mathematically equivalent form, that remained unpublished during his lifetime. René Descartes independently derived the law using heuristic momentum conservation arguments in terms of sines in his 1637 essay Dioptrics, rejecting Descartes solution, Pierre de Fermat arrived at the same solution based solely on his principle of least time. Interestingly, Descartes assumed the speed of light was infinite, yet in his derivation of Snells law he also assumed the denser the medium, the greater the speed of light. Fermat supported the assumptions, i. e. the speed of light is finite. Fermats derivation also utilized his invention of adequality, a mathematical equivalent to differential calculus, for finding maxima, minima. In his influential mathematics book Geometry, Descartes solves a problem that was worked on by Apollonius of Perga, given n lines L and a point P on each line, find the locus of points Q such that the lengths of the line segments QP satisfy certain conditions. For example, when n =4, given the lines a, b, c, and d and a point A on a, B on b, and so on, find the locus of points Q such that the product QA*QB equals the product QC*QD. When the lines are not all parallel, Pappus showed that the loci are conics, to show that the cubic curves were interesting, he showed that they arose naturally in optics from Snells law. According to Dijksterhuis, In De natura lucis et proprietate Isaac Vossius said that Descartes had seen Snells paper and we now know this charge to be undeserved but it has been adopted many times since. Both Fermat and Huygens repeated this accusation that Descartes had copied Snell, in French, Snells Law is called la loi de Descartes or loi de Snell-Descartes. As the development of optical and electromagnetic theory, the ancient Snells law was brought into a new stage
