Speed of light
The speed of light in vacuum denoted c, is a universal physical constant important in many areas of physics. Its exact value is 299,792,458 metres per second, it is exact because by international agreement a metre is defined as the length of the path travelled by light in vacuum during a time interval of 1/299792458 second. According to special relativity, c is the maximum speed at which all conventional matter and hence all known forms of information in the universe can travel. Though this speed is most associated with light, it is in fact the speed at which all massless particles and changes of the associated fields travel in vacuum; such particles and waves travel at c regardless of the motion of the source or the inertial reference frame of the observer. In the special and general theories of relativity, c interrelates space and time, appears in the famous equation of mass–energy equivalence E = mc2; the speed at which light propagates through transparent materials, such as glass or air, is less than c.
The ratio between c and the speed v at which light travels in a material is called the refractive index n of the material. For example, for visible light the refractive index of glass is around 1.5, meaning that light in glass travels at c / 1.5 ≈ 200,000 km/s. For many practical purposes and other electromagnetic waves will appear to propagate instantaneously, but for long distances and sensitive measurements, their finite speed has noticeable effects. In communicating with distant space probes, it can take minutes to hours for a message to get from Earth to the spacecraft, or vice versa; the light seen from stars left them many years ago, allowing the study of the history of the universe by looking at distant objects. The finite speed of light limits the theoretical maximum speed of computers, since information must be sent within the computer from chip to chip; the speed of light can be used with time of flight measurements to measure large distances to high precision. Ole Rømer first demonstrated in 1676 that light travels at a finite speed by studying the apparent motion of Jupiter's moon Io.
In 1865, James Clerk Maxwell proposed that light was an electromagnetic wave, therefore travelled at the speed c appearing in his theory of electromagnetism. In 1905, Albert Einstein postulated that the speed of light c with respect to any inertial frame is a constant and is independent of the motion of the light source, he explored the consequences of that postulate by deriving the theory of relativity and in doing so showed that the parameter c had relevance outside of the context of light and electromagnetism. After centuries of precise measurements, in 1975 the speed of light was known to be 299792458 m/s with a measurement uncertainty of 4 parts per billion. In 1983, the metre was redefined in the International System of Units as the distance travelled by light in vacuum in 1/299792458 of a second; the speed of light in vacuum is denoted by a lowercase c, for "constant" or the Latin celeritas. In 1856, Wilhelm Eduard Weber and Rudolf Kohlrausch had used c for a different constant shown to equal √2 times the speed of light in vacuum.
The symbol V was used as an alternative symbol for the speed of light, introduced by James Clerk Maxwell in 1865. In 1894, Paul Drude redefined c with its modern meaning. Einstein used V in his original German-language papers on special relativity in 1905, but in 1907 he switched to c, which by had become the standard symbol for the speed of light. Sometimes c is used for the speed of waves in any material medium, c0 for the speed of light in vacuum; this subscripted notation, endorsed in official SI literature, has the same form as other related constants: namely, μ0 for the vacuum permeability or magnetic constant, ε0 for the vacuum permittivity or electric constant, Z0 for the impedance of free space. This article uses c for the speed of light in vacuum. Since 1983, the metre has been defined in the International System of Units as the distance light travels in vacuum in 1⁄299792458 of a second; this definition fixes the speed of light in vacuum at 299,792,458 m/s. As a dimensional physical constant, the numerical value of c is different for different unit systems.
In branches of physics in which c appears such as in relativity, it is common to use systems of natural units of measurement or the geometrized unit system where c = 1. Using these units, c does not appear explicitly because multiplication or division by 1 does not affect the result; the speed at which light waves propagate in vacuum is independent both of the motion of the wave source and of the inertial frame of reference of the observer. This invariance of the speed of light was postulated by Einstein in 1905, after being motivated by Maxwell's theory of electromagnetism and the lack of evidence for the luminiferous aether, it is only possible to verify experimentally that the two-way speed of light is frame-independent, because it is impossible to measure the one-way speed of light without some convention as to how clocks at the source and at the detector should be synchronized. However
The Planck constant is a physical constant, the quantum of electromagnetic action, which relates the energy carried by a photon to its frequency. A photon's energy is equal to its frequency multiplied by the Planck constant; the Planck constant is of fundamental importance in quantum mechanics, in metrology it is the basis for the definition of the kilogram. At the end of the 19th century, physicists were unable to explain why the observed spectrum of black body radiation, which by had been measured, diverged at higher frequencies from that predicted by existing theories. In 1900, Max Planck empirically derived a formula for the observed spectrum, he assumed that a hypothetical electrically charged oscillator in a cavity that contained black body radiation could only change its energy in a minimal increment, E, proportional to the frequency of its associated electromagnetic wave. He was able to calculate the proportionality constant, h, from the experimental measurements, that constant is named in his honor.
In 1905, the value E was associated by Albert Einstein with a "quantum" or minimal element of the energy of the electromagnetic wave itself. The light quantum behaved in some respects as an electrically neutral particle, as opposed to an electromagnetic wave, it was called a photon. Max Planck received the 1918 Nobel Prize in Physics "in recognition of the services he rendered to the advancement of Physics by his discovery of energy quanta". Since energy and mass are equivalent, the Planck constant relates mass to frequency. By 2017, the Planck constant had been measured with sufficient accuracy in terms of the SI base units, that it was central to replacing the metal cylinder, called the International Prototype of the Kilogram, that had defined the kilogram since 1889; the new definition was unanimously approved at the General Conference on Weights and Measures on 16 November 2018 as part of the 2019 redefinition of SI base units. For this new definition of the kilogram, the Planck constant, as defined by the ISO standard, was set to 6.62607015×10−34 J⋅s exactly.
The kilogram was the last SI base unit to be re-defined by a fundamental physical property to replace a physical artefact. In the last years of the 19th century, Max Planck was investigating the problem of black-body radiation first posed by Kirchhoff some 40 years earlier; every physical body continuously emits electromagnetic radiation. At low frequencies, Planck's law tends to the Rayleigh–Jeans law, while in the limit of high frequencies it tends to the Wien approximation but there was no overall expression or explanation for the shape of the observed emission spectrum. Approaching this problem, Planck hypothesized that the equations of motion for light describe a set of harmonic oscillators, one for each possible frequency, he examined how the entropy of the oscillators varied with the temperature of the body, trying to match Wien's law, was able to derive an approximate mathematical function for black-body spectrum. To create Planck's law, which predicts blackbody emissions by fitting the observed curves, he multiplied the classical expression by a complex factor that involves a constant, h, in both the numerator and the denominator, which subsequently became known as the Planck Constant.
The spectral radiance of a body, Bν, describes the amount of energy it emits at different radiation frequencies. It is the power emitted per unit area of the body, per unit solid angle of emission, per unit frequency. Planck showed that the spectral radiance of a body for frequency ν at absolute temperature T is given by B ν = 2 h ν 3 c 2 1 e h ν k B T − 1 where kB is the Boltzmann constant, h is the Planck constant, c is the speed of light in the medium, whether material or vacuum; the spectral radiance can be expressed per unit wavelength λ instead of per unit frequency. In this case, it is given by B λ = 2 h c 2 λ 5 1 e h c λ k B T − 1. Showing how radiated energy emitted at shorter wavelengths increases more with temperature than energy emitted at longer wavelengths; the law may be expressed in other terms, such as the number of photons emitted at a certain wavelength, or the energy density in a volume of radiation. The SI units of Bν are W·sr−1·m−2·Hz−1, while those of Bλ are W·sr−1·m−3.
Planck soon realized. There were several different solutions, each of which gave a different value for the entropy of the oscillators. To save his theory, Planck resorted to using the then-controversial theory of statistical mechanics, which he described as "an act of despair … I was ready to sacrifice any of my previous convictions about physics." One of his new boundary conditions was to interpret UN [the vibrational energy
Luminance is a photometric measure of the luminous intensity per unit area of light travelling in a given direction. It describes the amount of light that passes through, is emitted or reflected from a particular area, falls within a given solid angle; the SI unit for luminance is candela per square metre. A non-SI term for the same unit is the nit; the CGS unit of luminance is the stilb, equal to one candela per square centimetre or 10 kcd/m2. Luminance is used to characterize emission or reflection from flat, diffuse surfaces; the luminance indicates how much luminous power will be detected by an eye looking at the surface from a particular angle of view. Luminance is thus an indicator of. In this case, the solid angle of interest is the solid angle subtended by the eye's pupil. Luminance is used in the video industry to characterize the brightness of displays. A typical computer display emits between 50 and 300 cd/m2; the sun has a luminance of about 1.6×109 cd/m2 at noon. Luminance is invariant in geometric optics.
This means that for an ideal optical system, the luminance at the output is the same as the input luminance. For real, optical systems, the output luminance is at most equal to the input; as an example, if one uses a lens to form an image, smaller than the source object, the luminous power is concentrated into a smaller area, meaning that the illuminance is higher at the image. The light at the image plane, fills a larger solid angle so the luminance comes out to be the same assuming there is no loss at the lens; the image can never be "brighter" than the source. The luminance of a specified point of a light source, in a specified direction, is defined by the derivative L v = d 2 Φ v d Σ d Ω Σ cos θ Σ where Lv is the luminance, d2Φv is the luminous flux leaving the area dΣ in any direction contained inside the solid angle dΩΣ, dΣ is an infinitesimal area of the source containing the specified point, dΩΣ is an infinitesimal solid angle containing the specified direction, θΣ is the angle between the normal nΣ to the surface dΣ and the specified direction.
If light travels through a lossless medium, the luminance does not change along a given light ray. As the ray crosses an arbitrary surface S, the luminance is given by L v = d 2 Φ v d S d Ω S cos θ S where dS is the infinitesimal area of S seen from the source inside the solid angle dΩΣ, dΩS is the infinitesimal solid angle subtended by dΣ as seen from dS, θS is the angle between the normal nS to dS and the direction of the light. More the luminance along a light ray can be defined as L v = n 2 d Φ v d G where dG is the etendue of an infinitesimally narrow beam containing the specified ray, dΦv is the luminous flux carried by this beam, n is the index of refraction of the medium; the luminance of a reflecting surface is related to the illuminance it receives: ∫ Ω Σ L v d Ω Σ cos θ Σ = M v = E v R where the integral covers all the directions of emission ΩΣ, Mv is the surface's luminous exitance Ev is the received illuminance, R is the reflectance. In the case of a diffuse reflector, the luminance is isotropic, per Lambert's cosine law.
The relationship is L v = E v R / π A variety of units have been used for luminance, besides the candela per square metre. One candela per square metre is equal to: 10−4 stilbs π apostilbs π×10−4 lamberts 0.292 foot-lamberts Retinal damage can occur when the eye is exposed to high luminance. Damage can occur due to local heating of the retina. Photochemical effects can cause damage at short wavelengths. A luminance meter is a device used in photometry that can measure the luminance in a particular direction and with a particular solid angle; the simplest devices measure the luminance in a single direction while imaging luminance meters measure luminance in a way similar to the way a digital camera records color images. Relative luminance Orders of magnitude Diffuse reflection Etendue Exposure value Lambertian reflectance Lightness, property of a color Luma, the repres
International Commission on Illumination
The International Commission on Illumination is the international authority on light, illumination and colour spaces. It was established in 1913 as a successor to the Commission Internationale de Photométrie and is today based in Vienna, Austria; the President from 2015 is Yoshihiro Ohno from the US. The CIE has eight divisions, each of which establishes technical committees to carry out its program under the supervision of the division's director: Vision and Colour Measurement of Light and Radiation Interior Environment and Lighting Design Lighting and Signalling for Transport Exterior Lighting and Other Applications Photobiology and Photochemistry General Aspects of Lighting Image Technology In 1924 it established the standard photopic observer defined by the spectral luminous efficiency function V, followed in 1951 by the standard scotopic observer defined by the function V’. Building on the Optical Society of America's report on colorimetry in 1922, the CIE convened its eighth session in 1931, with the intention of establishing an international agreement on colorimetric specifications and updating the OSA's 1922 recommendations based on the developments during the past decade.
The meeting, held in Cambridge, United Kingdom, concluded with the formalization of the CIE 1931 XYZ colour space and definitions of the 1931 CIE 2° standard observer with the corresponding colour matching functions, standard illuminants A, B, C. In 1964 the 10° CIE standard observer and its corresponding colour matching functions as well as the new standard daylight illuminant D6500 were added, as well as a method for calculating daylight illuminants at correlated colour temperatures other than 6500 kelvins. In 1976, the commission developed the CIELAB and CIELUV colour spaces, which are used today. Based on CIELAB, colour difference formulas CIEDE94 and CIEDE2000 were recommended in the corresponding years. International Color Consortium International Colour Association International Electrotechnical Commission International Organization for Standardization CIE Web site List of CIE publications and standards Inter-Society Color Council
Green is the color between blue and yellow on the visible spectrum. It is evoked by light which has a dominant wavelength of 495–570 nm. In subtractive color systems, used in painting and color printing, it is created by a combination of yellow and blue, or yellow and cyan. By far the largest contributor to green in nature is chlorophyll, the chemical by which plants photosynthesize and convert sunlight into chemical energy. Many creatures have adapted to their green environments by taking on a green hue themselves as camouflage. Several minerals have a green color, including the emerald, colored green by its chromium content. During post-classical and early modern Europe, green was the color associated with wealth, merchants and the gentry, while red was reserved for the nobility. For this reason, the costume of the Mona Lisa by Leonardo da Vinci and the benches in the British House of Commons are green while those in the House of Lords are red, it has a long historical tradition as the color of Ireland and of Gaelic culture.
It is the historic color of Islam, representing the lush vegetation of Paradise. It was the color of the banner of Muhammad, is found in the flags of nearly all Islamic countries. In surveys made in American and Islamic countries, green is the color most associated with nature, health, spring and envy. In the European Union and the United States, green is sometimes associated with toxicity and poor health, but in China and most of Asia, its associations are positive, as the symbol of fertility and happiness; because of its association with nature, it is the color of the environmental movement. Political groups advocating environmental protection and social justice describe themselves as part of the Green movement, some naming themselves Green parties; this has led to similar campaigns in advertising, as companies have sold green, or environmentally friendly, products. Green is the traditional color of safety and permission; the word green comes from the Middle English and Old English word grene, like the German word grün, has the same root as the words grass and grow.
It is from a Common Germanic *gronja-, reflected in Old Norse grænn, Old High German gruoni from a PIE root *ghre- "to grow", root-cognate with grass and to grow. The first recorded use of the word as a color term in Old English dates to ca. AD 700. Latin with viridis has a genuine and used term for "green". Related to virere "to grow" and ver "spring", it gave rise to words in several Romance languages, French vert, Italian verde; the Slavic languages with zelenъ. Ancient Greek had a term for yellowish, pale green – χλωρός, cognate with χλοερός "verdant" and χλόη "chloe, the green of new growth". Thus, the languages mentioned above have old terms for "green" which are derived from words for fresh, sprouting vegetation. However, comparative linguistics makes clear that these terms were coined independently, over the past few millennia, there is no identifiable single Proto-Indo-European or word for "green". For example, the Slavic zelenъ is cognate with Sanskrit hari "yellow, golden"; the Turkic languages have jašɨl "green" or "yellowish green", compared to a Mongolian word for "meadow".
In some languages, including old Chinese, old Japanese, Vietnamese, the same word can mean either blue or green. The Chinese character 青 has a meaning that covers both green. In more contemporary terms, they are 綠 respectively. Japanese has two terms that refer to the color green, 緑 and グリーン. However, in Japan, although the traffic lights have the same colors as other countries have, the green light is described using the same word as for blue, because green is considered a shade of aoi. Vietnamese uses a single word for both blue and green, with variants such as xanh da trời, lục. "Green" in modern European languages corresponds to about 520–570 nm, but many historical and non-European languages make other choices, e.g. using a term for the range of ca. 450–530 nm and another for ca. 530–590 nm. In the comparative study of color terms in the world's languages, green is only found as a separate category in languages with the developed range of six colors, or more in systems with five colors; these languages have introduced supplementary vocabulary to denote "green", but these terms are recognizable as recent adoptions that are not in origin color terms.
Thus, the Thai word เขียว kheīyw, besides mean
The human eye is an organ which reacts to light and pressure. As a sense organ, the mammalian eye allows vision. Human eyes help to provide a three dimensional, moving image coloured in daylight. Rod and cone cells in the retina allow conscious light perception and vision including color differentiation and the perception of depth; the human eye can differentiate between about 10 million colors and is capable of detecting a single photon. Similar to the eyes of other mammals, the human eye's non-image-forming photosensitive ganglion cells in the retina receive light signals which affect adjustment of the size of the pupil and suppression of the hormone melatonin and entrainment of the body clock; the eye is not shaped like a perfect sphere, rather it is a fused two-piece unit, composed of the anterior segment and the posterior segment. The anterior segment is made up of the cornea and lens; the cornea is transparent and more curved, is linked to the larger posterior segment, composed of the vitreous, retina and the outer white shell called the sclera.
The cornea is about 11.5 mm in diameter, 1/2 mm in thickness near its center. The posterior chamber constitutes the remaining five-sixths; the cornea and sclera are connected by an area termed the limbus. The iris is the pigmented circular structure concentrically surrounding the center of the eye, the pupil, which appears to be black; the size of the pupil, which controls the amount of light entering the eye, is adjusted by the iris' dilator and sphincter muscles. Light energy enters the eye through the cornea, through the pupil and through the lens; the lens shape is controlled by the ciliary muscle. Photons of light falling on the light-sensitive cells of the retina are converted into electrical signals that are transmitted to the brain by the optic nerve and interpreted as sight and vision. Dimensions differ among adults by only one or two millimetres, remarkably consistent across different ethnicities; the vertical measure less than the horizontal, is about 24 mm. The transverse size of a human adult eye is 24.2 mm and the sagittal size is 23.7 mm with no significant difference between sexes and age groups.
Strong correlation has been found between the width of the orbit. The typical adult eye has an anterior to posterior diameter of 24 millimetres, a volume of six cubic centimetres, a mass of 7.5 grams.. The eyeball grows increasing from about 16–17 millimetres at birth to 22.5–23 mm by three years of age. By age 12, the eye attains its full size; the eye is made up of layers, enclosing various anatomical structures. The outermost layer, known as the fibrous tunic, is composed of the sclera; the middle layer, known as the vascular tunic or uvea, consists of the choroid, ciliary body, pigmented epithelium and iris. The innermost is the retina, which gets its oxygenation from the blood vessels of the choroid as well as the retinal vessels; the spaces of the eye are filled with the aqueous humour anteriorly, between the cornea and lens, the vitreous body, a jelly-like substance, behind the lens, filling the entire posterior cavity. The aqueous humour is a clear watery fluid, contained in two areas: the anterior chamber between the cornea and the iris, the posterior chamber between the iris and the lens.
The lens is suspended to the ciliary body by the suspensory ligament, made up of hundreds of fine transparent fibers which transmit muscular forces to change the shape of the lens for accommodation. The vitreous body is a clear substance composed of water and proteins, which give it a jelly-like and sticky composition; the approximate field of view of an individual human eye varies by facial anatomy, but is 30° superior, 45° nasal, 70° inferior, 100° temporal. For both eyes combined visual field is 200 ° horizontal, it is 13700 square degrees for binocular vision. When viewed at large angles from the side, the iris and pupil may still be visible by the viewer, indicating the person has peripheral vision possible at that angle. About 15° temporal and 1.5° below the horizontal is the blind spot created by the optic nerve nasally, 7.5° high and 5.5° wide. The retina has a static contrast ratio of around 100:1; as soon as the eye moves to acquire a target, it re-adjusts its exposure by adjusting the iris, which adjusts the size of the pupil.
Initial dark adaptation takes place in four seconds of profound, uninterrupted darkness. The process is nonlinear and multifaceted, so an interruption by light exposure requires restarting the dark adaptation process over again. Full adaptation is dependent on good blood flow; the human eye can detect a luminance range of 1014, or one hundred trillion, from 10−6 cd/m2, or one millionth of a candela per square meter to 108 cd/m2 or one hundred million candelas per square meter. This range does not include looking at the midday lightning discharge. At the low end o
In engineering and science, dimensional analysis is the analysis of the relationships between different physical quantities by identifying their base quantities and units of measure and tracking these dimensions as calculations or comparisons are performed. The conversion of units from one dimensional unit to another is somewhat complex. Dimensional analysis, or more the factor-label method known as the unit-factor method, is a used technique for such conversions using the rules of algebra; the concept of physical dimension was introduced by Joseph Fourier in 1822. Physical quantities that are of the same kind have the same dimension and can be directly compared to each other if they are expressed in differing units of measure. If physical quantities have different dimensions, they cannot be expressed in terms of similar units and cannot be compared in quantity. For example, asking whether a kilogram is larger than an hour is meaningless. Any physically meaningful equation will have the same dimensions on its left and right sides, a property known as dimensional homogeneity.
Checking for dimensional homogeneity is a common application of dimensional analysis, serving as a plausibility check on derived equations and computations. It serves as a guide and constraint in deriving equations that may describe a physical system in the absence of a more rigorous derivation. Many parameters and measurements in the physical sciences and engineering are expressed as a concrete number – a numerical quantity and a corresponding dimensional unit. A quantity is expressed in terms of several other quantities. Compound relations with "per" are expressed with division, e.g. 60 mi/1 h. Other relations can involve powers, or combinations thereof. A set of base units for a system of measurement is a conventionally chosen set of units, none of which can be expressed as a combination of the others, in terms of which all the remaining units of the system can be expressed. For example, units for length and time are chosen as base units. Units for volume, can be factored into the base units of length, thus they are considered derived or compound units.
Sometimes the names of units obscure the fact. For example, a newton is a unit of force; the newton is defined as 1 N = 1 kg⋅m⋅s−2. Percentages are dimensionless quantities, since they are ratios of two quantities with the same dimensions. In other words, the % sign can be read as "hundredths", since 1% = 1/100. Taking a derivative with respect to a quantity adds the dimension of the variable one is differentiating with respect to, in the denominator. Thus: position has the dimension L. In economics, one distinguishes between stocks and flows: a stock has units of "units", while a flow is a derivative of a stock, has units of "units/time". In some contexts, dimensional quantities are expressed as dimensionless quantities or percentages by omitting some dimensions. For example, debt-to-GDP ratios are expressed as percentages: total debt outstanding divided by annual GDP – but one may argue that in comparing a stock to a flow, annual GDP should have dimensions of currency/time, thus Debt-to-GDP should have units of years, which indicates that Debt-to-GDP is the number of years needed for a constant GDP to pay the debt, if all GDP is spent on the debt and the debt is otherwise unchanged.
In dimensional analysis, a ratio which converts one unit of measure into another without changing the quantity is called a conversion factor. For example, kPa and bar are both units of pressure, 100 kPa = 1 bar; the rules of algebra allow both sides of an equation to be divided by the same expression, so this is equivalent to 100 kPa / 1 bar = 1. Since any quantity can be multiplied by 1 without changing it, the expression "100 kPa / 1 bar" can be used to convert from bars to kPa by multiplying it with the quantity to be converted, including units. For example, 5 bar × 100 kPa / 1 bar = 500 kPa because 5 × 100 / 1 = 500, bar/bar cancels out, so 5 bar = 500 kPa; the most basic rule of dimensional analysis is that of dimensional homogeneity. 1. Only commensurable quantities may be compared, added, or subtracted. However, the dimensions form an abelian group under multiplication, so: 2. One may take ratios of incommensurable quantities, multiply or divide them. For example, it makes no sense to ask whether 1 hour is more, the same, or less than 1 kilometer, as these have different dimensions, nor to add 1 hour to 1 kilometer.
However, it makes perfect sense to ask whether 1 mile is more, the same, or less than 1 kilometer being the same dimension of physical quantity though the units are different. On the other hand, if an object travels 100 km in 2 hours, one may divide these and conclude that the object's average speed was 50 km/h; the rule implies that in a physically mea