Sunlight is a portion of the electromagnetic radiation given off by the Sun, in particular infrared and ultraviolet light. On Earth, sunlight is filtered through Earth's atmosphere, is obvious as daylight when the Sun is above the horizon; when the direct solar radiation is not blocked by clouds, it is experienced as sunshine, a combination of bright light and radiant heat. When it is blocked by clouds or reflects off other objects, it is experienced as diffused light; the World Meteorological Organization uses the term "sunshine duration" to mean the cumulative time during which an area receives direct irradiance from the Sun of at least 120 watts per square meter. Other sources indicate an "Average over the entire earth" of "164 Watts per square meter over a 24 hour day"; the ultraviolet radiation in sunlight has both positive and negative health effects, as it is both a requisite for vitamin D3 synthesis and a mutagen. Sunlight takes about 8.3 minutes to reach Earth from the surface of the Sun.
A photon starting at the center of the Sun and changing direction every time it encounters a charged particle would take between 10,000 and 170,000 years to get to the surface. Sunlight is a key factor in photosynthesis, the process used by plants and other autotrophic organisms to convert light energy from the Sun, into chemical energy that can be used to synthesize carbohydrates and to fuel the organisms' activities. Researchers can measure the intensity of sunlight using a sunshine recorder, pyranometer, or pyrheliometer. To calculate the amount of sunlight reaching the ground, both the eccentricity of Earth's elliptic orbit and the attenuation by Earth's atmosphere have to be taken into account; the extraterrestrial solar illuminance, corrected for the elliptic orbit by using the day number of the year, is given to a good approximation by E e x t = E s c ⋅, where dn=1 on January 1st. In this formula dn–3 is used, because in modern times Earth's perihelion, the closest approach to the Sun and, the maximum Eext occurs around January 3 each year.
The value of 0.033412 is determined knowing that the ratio between the perihelion squared and the aphelion squared should be 0.935338. The solar illuminance constant, is equal to 128×103 lux; the direct normal illuminance, corrected for the attenuating effects of the atmosphere is given by: E d n = E e x t e − c m, where c is the atmospheric extinction and m is the relative optical airmass. The atmospheric extinction brings the number of lux down to around 100 000 lux; the total amount of energy received at ground level from the Sun at the zenith depends on the distance to the Sun and thus on the time of year. It is 3.3 % lower in July. If the extraterrestrial solar radiation is 1367 watts per square meter the direct sunlight at Earth's surface when the Sun is at the zenith is about 1050 W/m2, but the total amount hitting the ground is around 1120 W/m2. In terms of energy, sunlight at Earth's surface is around 52 to 55 percent infrared, 42 to 43 percent visible, 3 to 5 percent ultraviolet. At the top of the atmosphere, sunlight is about 30% more intense, having about 8% ultraviolet, with most of the extra UV consisting of biologically damaging short-wave ultraviolet.
Direct sunlight has a luminous efficacy of about 93 lumens per watt of radiant flux. Multiplying the figure of 1050 watts per square metre by 93 lumens per watt indicates that bright sunlight provides an illuminance of 98 000 lux on a perpendicular surface at sea level; the illumination of a horizontal surface will be less than this if the Sun is not high in the sky. Averaged over a day, the highest amount of sunlight on a horizontal surface occurs in January at the South Pole. Dividing the irradiance of 1050 W/m2 by the size of the Sun's disk in steradians gives an average radiance of 15.4 MW per square metre per steradian. Multiplying this by π gives an upper limit to the irradiance which can be focused on a surface using mirrors: 48.5 MW/m2. The spectrum of the Sun's solar radiation is close to that of a black body with a temperature of about 5,800 K; the Sun emits EM radiation across most of the electromagnetic spectrum. Although the Sun produces gamma rays as a result of the nuclear-fusion process, internal absorption and thermalization convert these super-high-energy photons to lower-energy photons before they reach the Sun's surface and are emitted out into space.
As a result, the Sun does not emit gamma rays from this process, but it does emit gamma rays from solar flares. The Sun emits X-rays, vis
Ray tracing (graphics)
In computer graphics, ray tracing is a rendering technique for generating an image by tracing the path of light as pixels in an image plane and simulating the effects of its encounters with virtual objects. The technique is capable of producing a high degree of visual realism higher than that of typical scanline rendering methods, but at a greater computational cost; this makes ray tracing best suited for applications where taking a long time to render a frame can be tolerated, such as in still images and film and television visual effects, more poorly suited for real-time applications such as video games where speed is critical. Ray tracing is capable of simulating a wide variety of optical effects, such as reflection and refraction and dispersion phenomena. Optical ray tracing describes a method for producing visual images constructed in 3D computer graphics environments, with more photorealism than either ray casting or scanline rendering techniques, it works by tracing a path from an imaginary eye through each pixel in a virtual screen, calculating the color of the object visible through it.
Scenes in ray tracing are described mathematically by a visual artist. Scenes may incorporate data from images and models captured by means such as digital photography; each ray must be tested for intersection with some subset of all the objects in the scene. Once the nearest object has been identified, the algorithm will estimate the incoming light at the point of intersection, examine the material properties of the object, combine this information to calculate the final color of the pixel. Certain illumination algorithms and reflective or translucent materials may require more rays to be re-cast into the scene, it may at first seem counterintuitive or "backward" to send rays away from the camera, rather than into it, but doing so is many orders of magnitude more efficient. Since the overwhelming majority of light rays from a given light source do not make it directly into the viewer's eye, a "forward" simulation could waste a tremendous amount of computation on light paths that are never recorded.
Therefore, the shortcut taken in raytracing is to presuppose that a given ray intersects the view frame. After either a maximum number of reflections or a ray traveling a certain distance without intersection, the ray ceases to travel and the pixel's value is updated. On input we have: E ∈ R 3 eye position T ∈ R 3 target position θ ∈ [ 0, π ) field of view - for human we can assume ≈ π / 2 rad = 90 ∘ m, k ∈ N numbers of square pixels on viewport vertical and horizontal direction i, j ∈ N, 1 ≤ i ≤ k ∧ 1 ≤ j ≤ m numbers of actual pixel w → ∈ R 3 vertical vector which indicates where is up and down w → = - roll component which determine viewport rotation around point C The idea is to find the position of each viewport pixel center P i j which allows us to find the line going from eye E through that pixel and get the ray described by point E and vector R → i j = P i j − E. First we need to find the coordinates of the bottom left viewport pixel P 1 m and find the next pixel by making a shift along directions parallel to viewport multiplied by the size of the pixel.
Below we introduce formulas which include distance d between the eye and the viewport. However, this value will be reduced during ray normalization r → i j. Pre-calculations: let's find and normalise vector t → and vectors b →, v → which are parallel to the viewport t → = T
In computer graphics, photon mapping is a two-pass global illumination algorithm developed by Henrik Wann Jensen that solves the rendering equation. Rays from the light source and rays from the camera are traced independently until some termination criterion is met they are connected in a second step to produce a radiance value, it is used to realistically simulate the interaction of light with different objects. It is capable of simulating the refraction of light through a transparent substance such as glass or water, diffuse interreflection between illuminated objects, the subsurface scattering of light in translucent materials, some of the effects caused by particulate matter such as smoke or water vapor, it can be extended to more accurate simulations of light such as spectral rendering. Unlike path tracing, bidirectional path tracing, volumetric path tracing and Metropolis light transport, photon mapping is a "biased" rendering algorithm, which means that averaging many renders using this method does not converge to a correct solution to the rendering equation.
However, since it is a consistent method, any desired accuracy can be achieved by increasing the number of photons. Light refracted or reflected causes patterns called caustics visible as concentrated patches of light on nearby surfaces. For example, as light rays pass through a wine glass sitting on a table, they are refracted and patterns of light are visible on the table. Photon mapping can trace the paths of individual photons to model where these concentrated patches of light will appear. Diffuse interreflection is apparent. Photon mapping is adept at handling this effect because the algorithm reflects photons from one surface to another based on that surface's bidirectional reflectance distribution function, thus light from one object striking another is a natural result of the method. Diffuse interreflection was first modeled using radiosity solutions. Photon mapping differs though in that it separates the light transport from the nature of the geometry in the scene. Color bleed is an example of diffuse interreflection.
Subsurface scattering is the effect evident when light enters a material and is scattered before being absorbed or reflected in a different direction. Subsurface scattering can be modeled using photon mapping; this was the original way. With photon mapping, light packets called photons are sent out into the scene from the light sources. Whenever a photon intersects with a surface, the intersection point and incoming direction are stored in a cache called the photon map. Two photon maps are created for a scene: one for caustics and a global one for other light. After intersecting the surface, a probability for either reflecting, absorbing, or transmitting/refracting is given by the material. A Monte Carlo method called. If the photon is absorbed, no new direction is given, tracing for that photon ends. If the photon reflects, the surface's bidirectional reflectance distribution function is used to determine the ratio of reflected radiance. If the photon is transmitting, a function for its direction is given depending upon the nature of the transmission.
Once the photon map is constructed, it is arranged in a manner, optimal for the k-nearest neighbor algorithm, as photon look-up time depends on the spatial distribution of the photons. Jensen advocates the usage of kd-trees; the photon map is stored on disk or in memory for usage. In this step of the algorithm, the photon map created in the first pass is used to estimate the radiance of every pixel of the output image. For each pixel, the scene is ray traced. At this point, the rendering equation is used to calculate the surface radiance leaving the point of intersection in the direction of the ray that struck it. To facilitate efficiency, the equation is decomposed into four separate factors: direct illumination, specular reflection and soft indirect illumination. For an accurate estimate of direct illumination, a ray is traced from the point of intersection to each light source; as long as a ray does not intersect another object, the light source is used to calculate the direct illumination.
For an approximate estimate of indirect illumination, the photon map is used to calculate the radiance contribution. Specular reflection can be, in most cases tracing procedures; the contribution to the surface radiance from caustics is calculated using the caustics photon map directly. The number of photons in this map must be sufficiently large, as the map is the only source for caustics information in the scene. For soft indirect illumination, radiance is calculated using the photon map directly; this contribution, does not need to be as accurate as the caustics contribution and thus uses the global photon map. In order to calculate surface radiance at an intersection point, one of the cached photon maps is used; the steps are: Gather the N nearest photons using the nearest neighbor search function on the photon map. Let S be the sphere that contains these N photons. For each photon, divide the amount of flux that the photon represents by the area of S and multiply by the BRDF applied to that photon.
The sum of those results for each photon represents total surface radiance returned by the surface intersecti
Circle of confusion
In optics, a circle of confusion is an optical spot caused by a cone of light rays from a lens not coming to a perfect focus when imaging a point source. It is known as disk of confusion, circle of indistinctness, blur circle, or blur spot. In photography, the circle of confusion is used to determine the depth of field, the part of an image, acceptably sharp. A standard value of CoC is associated with each image format, but the most appropriate value depends on visual acuity, viewing conditions, the amount of enlargement. Usages in context include maximum permissible circle of confusion, circle of confusion diameter limit, the circle of confusion criterion. Real lenses do not focus all rays so that at best focus, a point is imaged as a spot rather than a point; the smallest such spot that a lens can produce is referred to as the circle of least confusion. Two important uses of this term and concept need to be distinguished: 1. For describing the largest blur spot, indistinguishable from a point.
A lens can focus objects at only one distance. Defocused object points are imaged as blur spots rather than points; such a blur spot has the same shape as the lens aperture, but for simplicity, is treated as if it were circular. In practice, objects at different distances from the camera can still appear sharp; the common criterion for “acceptable sharpness” in the final image is that the blur spot be indistinguishable from a point. 2. For describing the blur spot achieved at its best focus or more generally. Recognizing that real lenses do not focus all rays under the best conditions, the term circle of least confusion is used for the smallest blur spot a lens can make, for example by picking a best focus position that makes a good compromise between the varying effective focal lengths of different lens zones due to spherical or other aberrations; the term circle of confusion is applied more to the size of the out-of-focus spot to which a lens images an object point. Diffraction effects from wave optics and the finite aperture of a lens determine the circle of least confusion.
In idealized ray optics, where rays are assumed to converge to a point when focused, the shape of a defocus blur spot from a lens with a circular aperture is a hard-edged circle of light. A more general blur spot has soft edges due to diffraction and aberrations, may be non-circular due to the aperture shape. Therefore, the diameter concept needs to be defined in order to be meaningful. Suitable definitions use the concept of encircled energy, the fraction of the total optical energy of the spot, within the specified diameter. Values of the fraction vary with application. In photography, the circle of confusion diameter limit is defined as the largest blur spot that will still be perceived by the human eye as a point, when viewed on a final image from a standard viewing distance; the CoC limit can be specified on the original image. With this definition, the CoC limit in the original image can be set based on several factors: The common values for CoC limit may not be applicable if reproduction or viewing conditions differ from those assumed in determining those values.
If the original image will be given greater enlargement, or viewed at a closer distance a smaller CoC will be required. All three factors above are accommodated with this formula: CoC in mm = / / enlargementFor example, to support a final-image resolution equivalent to 5 lp/mm for a 25 cm viewing distance when the anticipated viewing distance is 50 cm and the anticipated enlargement is 8: CoC = / 5 / 8 = 0.05 mmSince the final-image size is not known at the time of taking a photograph, it is common to assume a standard size such as 25 cm width, along with a conventional final-image CoC of 0.2 mm, 1/1250 of the image width. Conventions in terms of the diagonal measure are commonly used; the DoF computed using these conventions will need to be adjusted if the original image is cropped before enlarging to the final image size, or if the size and viewing assumptions are altered. For full-frame 35 mm format, a used CoC limit is d/1500, or 0.029 mm for full-frame 35 mm format, which corresponds to resolving 5 lines per millimeter on a print of 30 cm diagonal.
Values of 0.030 mm and 0.033 mm are common for full-frame 35 mm format. Criteria relating CoC to the lens focal length have been used. Kodak, 5) recommended 2 minutes of arc for critical viewing, giving CoC ≈ f /1720, where f is the lens focal length. For a 50 mm lens on full-frame 35 mm format, this gave CoC ≈ 0.0291 mm. This criterion evidently assumed that a final image would be viewed at “perspective-correct” distance: Viewing distance = focal length of taking lens × enlargementHowever, images are viewed at the “correct” distance.
Max Born was a German-Jewish physicist and mathematician, instrumental in the development of quantum mechanics. He made contributions to solid-state physics and optics and supervised the work of a number of notable physicists in the 1920s and 1930s. Born won the 1954 Nobel Prize in Physics for his "fundamental research in quantum mechanics in the statistical interpretation of the wave function". Born entered the University of Göttingen in 1904, where he found the three renowned mathematicians Felix Klein, David Hilbert, Hermann Minkowski, he wrote his Ph. D. thesis on the subject of "Stability of Elastica in a Plane and Space", winning the University's Philosophy Faculty Prize. In 1905, he began researching special relativity with Minkowski, subsequently wrote his habilitation thesis on the Thomson model of the atom. A chance meeting with Fritz Haber in Berlin in 1918 led to discussion of the manner in which an ionic compound is formed when a metal reacts with a halogen, today known as the Born–Haber cycle.
In the First World War, after being placed as a radio operator, he was moved to research duties regarding sound ranging due to his specialist knowledge. In 1921, Born returned to Göttingen, arranging another chair for his long-time friend and colleague James Franck. Under Born, Göttingen became one of the world's foremost centres for physics. In 1925, Born and Werner Heisenberg formulated the matrix mechanics representation of quantum mechanics; the following year, he formulated the now-standard interpretation of the probability density function for ψ*ψ in the Schrödinger equation, for which he was awarded the Nobel Prize in 1954. His influence extended far beyond his own research. Max Delbrück, Siegfried Flügge, Friedrich Hund, Pascual Jordan, Maria Goeppert-Mayer, Lothar Wolfgang Nordheim, Robert Oppenheimer, Victor Weisskopf all received their Ph. D. degrees under Born at Göttingen, his assistants included Enrico Fermi, Werner Heisenberg, Gerhard Herzberg, Friedrich Hund, Pascual Jordan, Wolfgang Pauli, Léon Rosenfeld, Edward Teller, Eugene Wigner.
In January 1933, the Nazi Party came to power in Germany, Born, Jewish, was suspended from his professorship at the University of Göttingen. He emigrated to the United Kingdom, where he took a job at St John's College and wrote a popular science book, The Restless Universe, as well as Atomic Physics, which soon became a standard textbook. In October 1936, he became the Tait Professor of Natural Philosophy at the University of Edinburgh, working with German-born assistants E. Walter Kellermann and Klaus Fuchs, he continued his research into physics. Born became a naturalised British subject on 31 August 1939, one day before World War II broke out in Europe, he remained at Edinburgh until 1952. He retired to Bad Pyrmont, in West Germany, died in hospital in Göttingen on 5 January 1970. Max Born was born on 11 December 1882 in Breslau, which at the time of Born's birth was part of the Prussian Province of Silesia in the German Empire, to a family of Jewish descent, he was one of two children born to Gustav Born, an anatomist and embryologist, a professor of embryology at the University of Breslau, his wife Margarethe née Kauffmann, from a Silesian family of industrialists.
She died when Max was four years old, on 29 August 1886. Max had a sister, Käthe, born in 1884, a half-brother, from his father's second marriage, to Bertha Lipstein. Wolfgang became Professor of Art History at the City College of New York. Educated at the König-Wilhelm-Gymnasium in Breslau, Born entered the University of Breslau in 1901; the German university system allowed students to move from one university to another, so he spent summer semesters at Heidelberg University in 1902 and the University of Zurich in 1903. Fellow students at Breslau, Otto Toeplitz and Ernst Hellinger, told Born about the University of Göttingen, Born went there in April 1904. At Göttingen he found three renowned mathematicians: Felix Klein, David Hilbert and Hermann Minkowski. Soon after his arrival, Born formed close ties to the latter two men. From the first class he took with Hilbert, Hilbert identified Born as having exceptional abilities and selected him as the lecture scribe, whose function was to write up the class notes for the students' mathematics reading room at the University of Göttingen.
Being class scribe put Born into regular, invaluable contact with Hilbert. Hilbert became Born's mentor after selecting him to be the first to hold the unpaid, semi-official position of assistant. Born's introduction to Minkowski came through Born's stepmother, Bertha, as she knew Minkowski from dancing classes in Königsberg; the introduction netted Born invitations to the Minkowski household for Sunday dinners. In addition, while performing his duties as scribe and assistant, Born saw Minkowski at Hilbert's house. Born's relationship with Klein was more problematic. Born attended a seminar conducted by Klein and professors of applied mathematics, Carl Runge and Ludwig Prandtl, on the subject of elasticity. Although not interested in the subject, Born was obliged to present a paper. Using Hilbert's calculus of variations, he presented one in which, using a curved configuration of a wire with both ends fixed, he demonstrated would be the most stable. Klein was impressed, invited Born to submit a thesis on the subject of "Stability of Elastica in a Plane and Space" – a subject near and dear to Klein – which Klein had arranged to be the subject for the prestigious annual Philosophy Faculty Prize offered by the University.
Entries could qualify as doctoral dissertations. Born responded by turning down the offer, as applied mathematics was
Reflection is the change in direction of a wavefront at an interface between two different media so that the wavefront returns into the medium from which it originated. Common examples include the reflection of light and water waves; the law of reflection says that for specular reflection the angle at which the wave is incident on the surface equals the angle at which it is reflected. Mirrors exhibit specular reflection. In acoustics, reflection is used in sonar. In geology, it is important in the study of seismic waves. Reflection is observed with surface waves in bodies of water. Reflection is observed with many types besides visible light. Reflection of VHF and higher frequencies is important for radar. Hard X-rays and gamma rays can be reflected at shallow angles with special "grazing" mirrors. Reflection of light is either diffuse depending on the nature of the interface. In specular reflection the phase of the reflected waves depends on the choice of the origin of coordinates, but the relative phase between s and p polarizations is fixed by the properties of the media and of the interface between them.
A mirror provides the most common model for specular light reflection, consists of a glass sheet with a metallic coating where the significant reflection occurs. Reflection is enhanced in metals by suppression of wave propagation beyond their skin depths. Reflection occurs at the surface of transparent media, such as water or glass. In the diagram, a light ray PO strikes a vertical mirror at point O, the reflected ray is OQ. By projecting an imaginary line through point O perpendicular to the mirror, known as the normal, we can measure the angle of incidence, θi and the angle of reflection, θr; the law of reflection states that θi = θr, or in other words, the angle of incidence equals the angle of reflection. In fact, reflection of light may occur whenever light travels from a medium of a given refractive index into a medium with a different refractive index. In the most general case, a certain fraction of the light is reflected from the interface, the remainder is refracted. Solving Maxwell's equations for a light ray striking a boundary allows the derivation of the Fresnel equations, which can be used to predict how much of the light is reflected, how much is refracted in a given situation.
This is analogous to the way impedance mismatch in an electric circuit causes reflection of signals. Total internal reflection of light from a denser medium occurs if the angle of incidence is greater than the critical angle. Total internal reflection is used as a means of focusing waves that cannot be reflected by common means. X-ray telescopes are constructed by creating a converging "tunnel" for the waves; as the waves interact at low angle with the surface of this tunnel they are reflected toward the focus point. A conventional reflector would be useless as the X-rays would pass through the intended reflector; when light reflects off a material denser than the external medium, it undergoes a phase inversion. In contrast, a less dense, lower refractive index material will reflect light in phase; this is an important principle in the field of thin-film optics. Specular reflection forms images. Reflection from a flat surface forms a mirror image, which appears to be reversed from left to right because we compare the image we see to what we would see if we were rotated into the position of the image.
Specular reflection at a curved surface forms an image which may be demagnified. Such mirrors may have surfaces that are parabolic. If the reflecting surface is smooth, the reflection of light that occurs is called specular or regular reflection; the laws of reflection are as follows: The incident ray, the reflected ray and the normal to the reflection surface at the point of the incidence lie in the same plane. The angle which the incident ray makes with the normal is equal to the angle which the reflected ray makes to the same normal; the reflected ray and the incident ray are on the opposite sides of the normal. These three laws can all be derived from the Fresnel equations. In classical electrodynamics, light is considered as an electromagnetic wave, described by Maxwell's equations. Light waves incident on a material induce small oscillations of polarisation in the individual atoms, causing each particle to radiate a small secondary wave in all directions, like a dipole antenna. All these waves add up to give specular reflection and refraction, according to the Huygens–Fresnel principle.
In the case of dielectrics such as glass, the electric field of the light acts on the electrons in the material, the moving electrons generate fields and become new radiators. The refracted light in the glass is the combination of the forward radiation of the electrons and the incident light; the reflected light is the combination of the backward radiation of all of the electrons. In metals, electrons with no binding energy are called free electrons; when these electrons oscillate with the incident light, the phase difference between their radiation field and the incident field is π, so the forward radiation cancels the incident light, backward radiation is just the reflected light. Light–matter interaction in terms of photons is a topic of quantum electrodynamics, is described in detail by Richard Feynman in his popular book QED: The Strange Theory of Light and Matter; when light strikes the surface of a mate
Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics describes the behaviour of visible and infrared light; because light is an electromagnetic wave, other forms of electromagnetic radiation such as X-rays and radio waves exhibit similar properties. Most optical phenomena can be accounted for using the classical electromagnetic description of light. Complete electromagnetic descriptions of light are, however difficult to apply in practice. Practical optics is done using simplified models; the most common of these, geometric optics, treats light as a collection of rays that travel in straight lines and bend when they pass through or reflect from surfaces. 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; the ray-based 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 light waves were in fact electromagnetic radiation. Some phenomena depend on the fact that light has both particle-like properties. Explanation of these effects requires quantum mechanics; when considering light's 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 and medicine. Practical applications of optics are found in a variety of technologies and everyday objects, including mirrors, telescopes, microscopes and fibre optics. Optics began with the development of lenses by Mesopotamians; the earliest known lenses, made from polished crystal 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.
These practical developments were followed by the development of theories of light and vision by ancient Greek and Indian philosophers, the development of geometrical optics in the Greco-Roman world. 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 "intromission 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. With many propagators including Democritus, Epicurus and their followers, this theory seems to have some contact with modern theories of what vision is, but it remained only speculation lacking any experimental foundation. Plato first articulated the emission theory, the idea that visual perception is accomplished by rays emitted by the eyes, he commented on the parity reversal of mirrors in Timaeus. Some hundred years Euclid wrote a treatise entitled Optics where he linked vision to geometry, creating geometrical optics.
He based his work on Plato's emission theory wherein he described the mathematical rules of perspective and described the effects of refraction qualitatively, although he questioned that a beam of light from the eye could instantaneously light up the stars every time someone blinked. Ptolemy, in his treatise Optics, held an extramission-intromission theory of vision: the rays from the eye formed a cone, the vertex being within the eye, the base defining the visual field; the rays were sensitive, conveyed information back to the observer's intellect about the distance and orientation of surfaces. He summarised much of Euclid and went on to describe a way to measure the angle of refraction, though he failed to notice the empirical relationship between it and the angle of incidence. During the Middle Ages, Greek ideas about optics were resurrected and extended by writers in the Muslim world. One of the earliest of these was Al-Kindi who wrote on the merits of Aristotelian and Euclidean ideas of optics, favouring the emission theory since it could better quantify optical phenomena.
In 984, the Persian mathematician Ibn Sahl wrote the treatise "On burning mirrors and lenses" describing a law of refraction equivalent to Snell's law. He used this law to compute optimum shapes for curved mirrors. In the early 11th century, Alhazen wrote the Book of Optics in which he explored reflection and refraction and proposed a new system for explaining vision and light based on observation and experiment, he rejected the "emission theory" of Ptolemaic optics with its rays being emitted by the eye, instead put forward the idea that light reflected in all directions in straight lines from all points of the objects being viewed and entered the eye, although he was unable to explain how the eye captured the rays. Alhazen's work was ignored in the Arabic world but it was anonymously translated into Latin around 1200 A. D. and further summarised and expanded on by the Polish monk Witelo making it a standard text on optics in Europe for the next 400 years. In the 13th century in medieval Europe, English bishop Robert Grosseteste wrote on a wide range of scientific topics, discussed light from four different perspectives: an epistemology of light, a metaphysics or cosmogony of light, an etiology or physics of light, a theology of light, basing it on the works Aristotle and Platonism.
Grosseteste's most famous disciple, Roger Bacon, wrote w