See, individual light rays can't talk to each other—if you're riding on a light ray, causality prevents you from talking to somebody riding on an adjacent light ray.
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Andrew Strominger of Harvard discovered that, when viewed from the right mathematical perspective — that of a light ray headed toward the infinite future — black holes are more complicated than we thought.
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But, as engineerguy explains, if a light ray hits a surface at an angle greater than the critical angle, it will be reflected and not refracted, which is exactly what happened in the University of Utah's experiment.
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Because we also know that light propagates at a constant speed, this means that a light ray that started out at a very early time has traveled a particular distance by today (called the "horizon distance" or the "Hubble distance").
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The laser source is characterized to have a transverse field characteristic having a central null intensity region. A mirror transmits a ray of light to a detector. The detector is positioned to be centered to the light ray and responds to the transmitted light ray intensity to provide an intensity signal. The intensity signal is characterized to have a magnitude related to the intensity of the transmitted light ray.
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At this point, any combination of three things might happen with this light ray: absorption, reflection, and refraction. The surface may reflect all or part of the light ray, in one or more directions. It might also absorb part of the light ray, resulting in a loss of intensity of the reflected and/or refracted light. If the surface has any transparent or translucent properties, it refracts a portion of the light beam into itself in a different direction while absorbing some (or all) of the spectrum (and possibly altering the color).
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The light-ray- direction mappings can be very general. METATOYs can even create pixellated light-ray fields that could not exist in non-pixellated form due to a condition imposed by wave optics. Much of the work on METATOYs is currently theoretical, backed up by computer simulations. A small number of experiments have been performed to date; more experimental work is ongoing.
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The proof mass blanking surface is centrally positioned within and normal to the light ray null intensity region to provide increased blanking of the light ray in response to transverse movement of the mass on the input axis. The proof mass deflects the flexible beam and moves the blanking surface in a direction transverse to the light ray to partially blank the light beam in response to acceleration in the direction of the input axis. A control responds to the intensity signal to apply a restoring force to restore the proof mass to a central position and provides an output signal proportional to the restoring force.
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In volumetric path tracing, scattering events can occur alongside with ray tracing. When a light ray hits a surface, a certain amount gets scattered into the media.
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Input parameters: D - Thread direction ( In original papers this appears as T ) s - Shininess exponent. Values are between 0 and infinity N - Real surface normal L - Vector from point to light V - Vector from point to viewer T - Thread direction based on real surface normal. P - Projection of vector L onto plane with normal T ( in original paper this appears as N ). R - Reflected incoming light ray against T. Incoming light ray is equal to negative L. All vectors are unit.
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Modern physics discredits Michell's notion of a light ray shooting directly from the surface of a supermassive star, being slowed down by the star's gravity, stopping, and then free-falling back to the star's surface.
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Arguably amongst the most startling properties of metamaterials are some that are fundamentally wave-optical, and therefore not reproduced in METATOYs. These include amplification of evanescent waves, which can, in principle, lead to perfect lenses ("superlenses") and magnifying superlenses ("hyperlenses"); reversal of the phase velocity; reversal of the Doppler shift. However, because they are not bound by wave-optical constraints on light-ray fields, it can be argued that METATOYs can perform light-ray-direction changes that metamaterials could not, unless a METATOY was effectively built out of metamaterials.
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A surface may absorb part of the light ray, resulting in a loss of intensity of the reflected and/or refracted light. It might also reflect all or part of the light ray, in one or more directions. If the surface has any transparent or translucent properties, it refracts a portion of the light beam into itself in a different direction while absorbing some (or all) of the spectrum (and possibly altering the color). Less commonly, a surface may absorb some portion of the light and fluorescently re-emit the light at a longer wavelength color in a random direction, though this is rare enough that it can be discounted from most rendering applications.
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A laser accelerometer comprises a frame having three orthogonal input axes and multiple proof masses, each proof mass having a predetermined blanking surface. A flexible beam supports each proof mass. The flexible beam permits movement of the proof mass on the input axis. A laser light source provides a light ray.
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205 Anthemius had a sophisticated understanding of the involved optics, as demonstrated by a light-ray diagram he constructed in 555 CE. In the 10th century Yu Chao-Lung supposedly projected images of pagoda models through a small hole onto a screen to study directions and divergence of rays of light.
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Colias nebulosa is much darker than Colias sifanica; the forewing without middle spot, but with light spot at the distal margin; the hindwing almost uniformly black, with large, conspicuous, light yellow middle spot, and light ray-like spots on the veins. We regard nebulosa as a distinct species.Röber, Julius (1906). Pieridae, pp.
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The rim of Autolycus is somewhat irregular, although generally circular overall. It has a small outer rampart and an irregular interior with no central peak. It possesses a light ray system that extends for a distance of over 400 kilometers. Due to its rays, Autolycus is mapped as part of the Copernican System.
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Wavelength-based computing can be used to solve the 3-SAT problem with n variables, m clauses and with no more than 3 variables per clause. Each wavelength, contained in a light ray, is considered as possible value-assignments to n variables. The optical device contains prisms and mirrors are used to discriminate proper wavelengths which satisfy the formula.
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METATOY is an acronym for "metamaterial for rays", representing a number of analogies with metamaterials; METATOYs even satisfy a few definitions of metamaterials, but are certainly not metamaterials in the usual sense. When seen from a distance, the view through each individual telescopic optical component acts as one pixel of the view through the METATOY as a whole. In the simplest case, the individual optical components are all identical; the METATOY then behaves like a homogeneous, but pixellated, window that can have very unusual optical properties (see the picture of the view through a METATOY). METATOYs are usually treated within the framework of geometrical optics; the light-ray-direction change performed by a METATOY is described by a mapping of the direction of any incoming light ray onto the corresponding direction of the outgoing ray.
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The sum of these deflections is the deviation angle. When the entrance and exit angles are equal, the deviation angle of a ray passing through a prism will be minimal. In Minimum Deviation, the refracted ray in the prism is parallel to its base. In other words, the light ray is symmetrical about the axis of symmetry of the prism.
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Erasmus Bartholin School of Mathematics and Statistics. University of St Andrews, Scotland He wrote, in Latin, the first grammar of the Danish language, the 1657 De studio lingvæ danicæ. Rasmus Bartholin is remembered especially for his discovery (1669) of the double refraction of a light ray by Iceland spar (calcite).Erasmus Bartholin, Experimenta crystalli islandici disdiaclastici quibus mira & insolita refractio detegitur (Copenhagen ("Hafniæ"), Denmark: Daniel Paulli, 1669).
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The path that a light ray follows as it passes through an optical medium or system is often called the optical path. The physical length of an optical device can be reduced to less than the length of the optical path by using folded optics. The optical path length as defined in optics is the length of the path multiplied by the refractive index of the medium.
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During their duel, Karna's chariot wheel got stuck in the mud and Karna asked for a pause. Krishna reminded Arjuna about Karna's ruthlessness onto Abhimanyu while he was similarly left without chariot and weapons. Hearing his son's fate, Arjuna shot his arrow which cut the head off of Karna. Karna's head fell on ground and a light ray from Karna's body got absorbed into Sun.
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His mentor at the University was Rasmus Bartholin, who published his discovery of the double refraction of a light ray by Iceland spar (calcite) in 1668, while Rømer was living in his home. Rømer was given every opportunity to learn mathematics and astronomy using Tycho Brahe's astronomical observations, as Bartholin had been given the task of preparing them for publication.Friedrichsen; Tortzen (2001), pp. 19–20.
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In nature, a light source emits a ray of light which travels, eventually, to a surface that interrupts its progress. One can think of this "ray" as a stream of photons traveling along the same path. In a perfect vacuum this ray will be a straight line (ignoring relativistic effects). Any combination of four things might happen with this light ray: absorption, reflection, refraction and fluorescence.
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The light ray from the heaven represents Mary's impregnation by the Holy Spirit. The closed passage into the depth at the left and the flask of pure water in Mary's bedroom conventionally refer to Mary's virginity. The winged angel Gabriel is depicted with Saint Emidius, the patron saint of Ascoli Piceno carrying a model of that town. The apple in the foreground represents the forbidden fruit and associated fall of man.
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He was studying the temperature of different colors by moving a thermometer through light split by a prism. He noticed that the highest temperature was beyond red. He theorized that this temperature change was due to "calorific rays", a type of light ray that could not be seen. The next year, Johann Ritter, working at the other end of the spectrum, noticed what he called "chemical rays" (invisible light rays that induced certain chemical reactions).
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The fundamental misunderstanding of this paradox is the assumption that the projected image caused by the light ray is a physical object, and therefore must follow physical law. In reality no physical laws are being broken as there is no physical object travelling faster than light. This paradox uses kinematic processes to explain the motion of this apparent object. However, the projected image on the moon, or the image created by the lighthouse, is not a real object.
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A slightly more rigorous definition of a light ray follows from Fermat's principle, which states that the path taken between two points by a ray of light is the path that can be traversed in the least time.Arthur Schuster, An Introduction to the Theory of Optics, London: Edward Arnold, 1904 online. Geometrical optics is often simplified by making the paraxial approximation, or "small angle approximation." The mathematical behavior then becomes linear, allowing optical components and systems to be described by simple matrices.
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In astronomy, air mass or airmass is the "amount of air that one is looking through" (Green 1992) when seeing a star or other celestial source from below Earth's atmosphere. It is formulated as the integral of air density along the light ray. As it penetrates the atmosphere, light is attenuated by scattering and absorption; the thicker atmosphere through which it passes, the greater the attenuation. Consequently, celestial bodies when nearer the horizon appear less bright than when nearer the zenith.
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The paradoxical aspect of each of the described thought experiments arises from Einstein’s theory of special relativity, which proclaims the speed of light (approx. 300,000 km/s) is the upper limit of speed in our universe."", Simonetti, J. Virginia Tech Physics: Frequently Asked Questions About Relativity. The uniformity of the speed of light is so absolute that regardless of the speed of the observer as well as the speed of the source of light the speed of the light ray should remain constant.
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"Ray casting" implies that the light ray is following a straight path (which may include travelling through semi- transparent objects). The ray cast is a vector that can originate from the camera or from the scene endpoint ("back to front", or "front to back"). Sometimes the final light value is derived from a "transfer function" and sometimes it's used directly. Rough simulations of optical properties may be additionally employed: a simple calculation of the ray from the object to the point of view is made.
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The lunar terminator (or tilt) illusion is an optical illusion arising from the erroneous expectation of an observer on Earth that the direction of sunlight illuminating the Moon (i.e. a line perpendicular to the terminator) should correspond with the position of the Sun, but does not appear to do so. The cause of the illusion is simply the observer not taking into account that the observed slope of a light ray will change across the sky because of the lack of visual clues to establish 3D perspective.
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Furthermore, the equivalence principle postulates that phenomena that are caused by inertial effects will also be present due to gravitational effects. Consider a beam of light that is shined horizontally across a rocket ship, which is accelerating. According to a non- accelerating observer outside the rocket ship, the floor of the rocket ship accelerates towards the light beam. Therefore, the light beam does not seem to travel on a horizontal path according to the inside observer, rather the light ray appears to bend toward the floor.
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Objects trapped in the optical stretcher usually have diameters on the scale of 10 micrometer, which is very large compared to the laser wavelengths used (often 1064 nm). It is thus sufficient to consider the interaction with the laser light in terms of ray optics. When a ray enters the object, it is refracted due to the different refractive index according to Snell's law. Because photons carry momentum, a change in the direction of propagation of a light ray implies a momentum change, i.e.
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The book had been written earlier in Ingolstadt. Oculus is subdivided into three parts: the first part treats the anatomy of the eye, the second part the refraction of the light ray inside the eye, and the third part deals with the retina and the visual angle. Scheiner once again chooses the way of observation and experiment. Like Kepler before him, he found that the retina is the seat of vision and that the optic nerve transmits the images from the retina to the brain.
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The properties of lines are then determined by the axioms which refer to them. One advantage to this approach is the flexibility it gives to users of the geometry. Thus in differential geometry, a line may be interpreted as a geodesic (shortest path between points), while in some projective geometries, a line is a 2-dimensional vector space (all linear combinations of two independent vectors). This flexibility also extends beyond mathematics and, for example, permits physicists to think of the path of a light ray as being a line.
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Color pattern of a plastic box with "frozen in" mechanical stress placed between two crossed polarizers Isotropic solids do not exhibit birefringence. However, when they are under mechanical stress, birefringence results. The stress can be applied externally or is "frozen in" after a birefringent plastic ware is cooled after it is manufactured using injection molding. When such a sample is placed between two crossed polarizers, colour patterns can be observed, because polarization of a light ray is rotated after passing through a birefringent material and the amount of rotation is dependent on wavelength.
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Furthermore, the amount by which light is refracted depends upon its wavelength, and hence its colour. This effect is called dispersion. Blue light (shorter wavelength) is refracted at a greater angle than red light, but due to the reflection of light rays from the back of the droplet, the blue light emerges from the droplet at a smaller angle to the original incident white light ray than the red light. Due to this angle, blue is seen on the inside of the arc of the primary rainbow, and red on the outside.
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As observed by Lord Rayleigh, a thin film (such as tarnish) on the surface of glass can reduce the reflectivity. This effect can be explained by envisioning a thin layer of material with refractive index n1 between the air (index n0) and the glass (index nS). The light ray now reflects twice: once from the surface between air and the thin layer, and once from the layer-to-glass interface. From the equation above and the known refractive indices, reflectivities for both interfaces can be calculated, denoted R01 and R1S respectively.
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Snell's Law can be used to predict the deflection of light rays as they pass through linear media as long as the indexes of refraction and the geometry of the media are known. For example, the propagation of light through a prism results in the light ray being deflected depending on the shape and orientation of the prism. In most materials, the index of refraction varies with the frequency of the light. Taking this into account, Snell's Law can be used to predict how a prism will disperse light into a spectrum.
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The range with a negative dispersion is relatively short since prism P2 can only be moved upwards over a short distance before the light ray misses it altogether. In principle, the α angle can be varied to tune the dispersion properties of a prism compressor. In practice, however, the geometry is chosen such that the incident and refracted beam have the same angle at the central wavelength of the spectrum to be compressed. This configuration is known as the "angle of minimum deviation", and is easier to align than arbitrary angles.
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Photothermal deflection spectroscopy is a kind of spectroscopy that measures the change in refractive index due to heating of a medium by light. It works via a sort of "mirage effect"In the true mirage, however, a light ray is bent gradually until it is totally reflected by the very hot air near soil. Here, instead, there is no reflection, and the ray is bent in a smooth way by the refraction index gradient, which acts like a prism. where a refractive index gradient exists adjacent to the test sample surface.
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The angle of incidence required for such a scenario is known as Brewster's angle. Snell's Law can be used to predict the deflection of light rays as they pass through "linear media" as long as the indexes of refraction and the geometry of the media are known. For example, the propagation of light through a prism results in the light ray being deflected depending on the shape and orientation of the prism. Additionally, since different frequencies of light have slightly different indexes of refraction in most materials, refraction can be used to produce dispersion spectra that appear as rainbows.
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In the most general case, a certain fraction of the light is reflected from the interface, and 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, and 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.
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The waves act as lenses to focus and defocus sunlight: focused sunlight produces the lighter rays, while defocused sunlight produces the darker rays. Suspended particles in the water help make the aureole effect more pronounced. The effect extends a greater angular distance from the viewer's shadow when the viewer is higher above the water, and can sometimes be seen from a plane. Although the focused (light) ray cones are actually more or less parallel to each other, the rays from the aureole effect appear to be radiating from the shadow of the viewer’s head due to perspective effects.
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He also demonstrated some properties of curves. The first is that, for a light ray parallel to the axis of a parabola and reflected so as to pass through the focus, the sum of the incident angle and its reflection is equal to that of any other similar ray. He then demonstrated similar results for hyperbolas and ellipses. The second result, useful in the design of reflecting telescopes, is that if a line is extended from a point outside of a parabola to the focus, then the reflection of this line on the outside surface of the parabola is parallel to the axis.
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It may be helpful to visualize this situation using spacetime diagrams. For a given observer, the t-axis is defined to be a point traced out in time by the origin of the spatial coordinate x, and is drawn vertically. The x-axis is defined as the set of all points in space at the time t = 0, and is drawn horizontally. The statement that the speed of light is the same for all observers is represented by drawing a light ray as a 45° line, regardless of the speed of the source relative to the speed of the observer.
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Between absorption, reflection, and refraction, all of the incoming light must be accounted for, and no more. A surface cannot, for instance, reflect 66% of an incoming light ray, and refract 50%, since the two would add up to be 116%. From here, the reflected and/or refracted rays may strike other surfaces, where their absorptive, refractive, and reflective properties are again calculated based on the incoming rays. Some of these rays travel in such a way that they hit our eye, causing us to see the scene and so contribute to the final rendered image.
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Geometrical optics provides further matrix applications. In this approximative theory, the wave nature of light is neglected. The result is a model in which light rays are indeed geometrical rays. If the deflection of light rays by optical elements is small, the action of a lens or reflective element on a given light ray can be expressed as multiplication of a two-component vector with a two- by-two matrix called ray transfer matrix analysis: the vector's components are the light ray's slope and its distance from the optical axis, while the matrix encodes the properties of the optical element.
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Light may pass through anisotropic inhomogeneous media at different rates depending on the direction and starting position of a light ray. The boundary of the set of points to which light can travel from a given point q after a time t is known as the wave front after time t, denoted here by Φq(t). It consists of precisely the points that can be reached from q in time t by travelling at the speed of light. Huygens's principle asserts that the wave front set is the envelope of the family of wave fronts for q ∈ Φq0(t).
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Controlling caustic pattern is rather a challenging problem as very minor changes of the surface will significantly affect the quality of the pattern since light ray directions might be interfered by other light rays as they intersect with and refract through the material. This will lead to a scattered, discontinuous pattern. To tackle this problem, optimal- transport-based is one of the existing proposed methods to control caustic pattern by redirecting light's directions as it propagates through the surface of a certain transparent material. This is done by solving an inverse optimization problem based on optimal transport.
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Between absorption, reflection, refraction and fluorescence, all of the incoming light must be accounted for, and no more. A surface cannot, for instance, reflect 66% of an incoming light ray, and refract 50%, since the two would add up to be 116%. From here, the reflected and/or refracted rays may strike other surfaces, where their absorptive, refractive, reflective and fluorescent properties again affect the progress of the incoming rays. Some of these rays travel in such a way that they hit our eye, causing us to see the scene and so contribute to the final rendered image.
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Ray transfer matrix analysis (also known as ABCD matrix analysis) is a mathematical form for performing ray tracing calculations in sufficiently simple problems which can be solved considering only paraxial rays. Each optical element (surface, interface, mirror, or beam travel) is described by a 2×2 ray transfer matrix which operates on a vector describing an incoming light ray to calculate the outgoing ray. Multiplication of the successive matrices thus yields a concise ray transfer matrix describing the entire optical system. The same mathematics is also used in accelerator physics to track particles through the magnet installations of a particle accelerator, see electron optics.
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Using dissections and the knowledge of previous scholars, he was able to begin to explain how light enters the eye. He asserted that the light ray is focused, but the actual explanation of how light projected to the back of the eye had to wait until 1604. His Treatise on Light explained the camera obscura, hundreds of years before the modern development of photography. alt=Ibn Al-Haytham (Alhazen) drawing The seven-volume Book of Optics (Kitab al-Manathir) hugely influenced thinking across disciplines from the theory of visual perception to the nature of perspective in medieval art, in both the East and the West, for more than 600 years.
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Her formative story was changed so that she overtook her father's would-be assassins with her fists instead of a newspaper. Lastly, she was given a more active role in the acquisition of her black light ray, which she no longer received from a mere family friend but instead from a scientist named Dr. Abraham Davis, who had escaped from Nazi-controlled Europe. In the retelling, Sandra Knight gave asylum to Davis, setting him up in a laboratory and helping him to complete his invention. Ted Knight, now established as her cousin, also aided Davis, as a result acquiring the technology that allowed him to become the first Starman.
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Reflection also occurs at the surface of transparent media, such as water or glass. Diagram of specular reflection In the diagram, a light ray PO strikes a vertical mirror at point O, and 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.
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During the 78 era, when the maximum capacity of a single ordinary record side or cylinder was less than five minutes, Spalding recorded extensively for Edison Records, with some issues on cylinders and many more on diamond discs. Most featured short works or encore pieces that could fit on a single record side. These recordings were all by the acoustical process, as well as vertically-cut, through 1925, but he made his first electrical recordings in 1926 for Brunswick Records using that company's problematic "Light-Ray" system. After his unsatisfactory experience with Brunswick, Spalding went back to Edison and made some electrical Edison hill-and-dale Diamond Discs as well as a very few Edison "Needle Cut" lateral recordings in late 1928.
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Last centers of resistance in space can do nothing but continue their hopeless struggle. Ivan goes to hell but is taken from there by a light ray. He sees Archangel Michael and then God (in image of grey-eyed fair-haired men, which is prototypic appearance of Petukhov's Ruses). God tells him that a "chain of worlds" has been before – each world was created good with some beings having soul (in Ivan's world, they were Ruses) and some not, but afterwards by freedom of will evil appeared and by cunning way took the upper hand so that the world turned into hell-like place; after that world was destroyed by "Big Bang", but some evil forces can stay alive and get into future and another worlds.
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The phase is proportional to the optical path length the light ray has traversed, and thus gives a measure of the integral of the refractive index along the ray path. The phase cannot be measured directly at optical or higher frequencies, and therefore needs to be converted into intensity by interference with a reference beam. In the visual spectrum this is done using Zernike phase-contrast microscopy, differential interference contrast microscopy (DIC) or interferometry. Zernike phase-contrast microscopy introduces a phase shift to the low spatial frequency components of the image with a phase-shifting annulus in the Fourier plane of the sample, so that high-spatial-frequency parts of the image can interfere with the low-frequency reference beam.
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On Earth-X, Nazi Germany had won World War II. The team was later featured in its own series for 15 issues (1976–1978), in which they temporarily left Earth-X for "Earth-1" (where most DC titles are set) and Phantom Lady was given real phantom-like powers. During the final issue of the original Freedom Fighters series, the writers gave the character an origin story. One night, Sandra happened across two would-be assassins targeting her father, and stealthily thwarted them with nothing more than a rolled-up newspaper. Knight consequently developed a taste for adventure and crime- fighting, and after finding a "black light ray projector" that a family friend named Professor Davis sent to her father, she adopted the device as a weapon.
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Replica of Newton's second reflecting telescope, which he presented to the Royal Society in 1672 In 1666, Newton observed that the spectrum of colours exiting a prism in the position of minimum deviation is oblong, even when the light ray entering the prism is circular, which is to say, the prism refracts different colours by different angles. This led him to conclude that colour is a property intrinsic to light – a point which had, until then, been a matter of debate. From 1670 to 1672, Newton lectured on optics. During this period he investigated the refraction of light, demonstrating that the multicoloured spectrum produced by a prism could be recomposed into white light by a lens and a second prism.
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Illustration of Snell's Law Refraction occurs when light travels through an area of space that has a changing index of refraction. The simplest case of refraction occurs when there is an interface between a uniform medium with index of refraction n_1 and another medium with index of refraction n_2. In such situations, Snell's Law describes the resulting deflection of the light ray: :n_1\sin\theta_1 = n_2\sin\theta_2\ where \theta_1 and \theta_2 are the angles between the normal (to the interface) and the incident and refracted waves, respectively. This phenomenon is also associated with a changing speed of light as seen from the definition of index of refraction provided above which implies: :v_1\sin\theta_2\ = v_2\sin\theta_1 where v_1 and v_2 are the wave velocities through the respective media.
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This guaranteed that the opposite beams would pass through equivalent paths, so that fringes readily formed even when using the sun as a light source. Figure 4. Setup of the Fizeau Experiment (1851) A light ray emanating from the source S′ is reflected by a beam splitter G and is collimated into a parallel beam by lens L. After passing the slits O1 and O2, two rays of light travel through the tubes A1 and A2, through which water is streaming back and forth as shown by the arrows. The rays reflect off a mirror m at the focus of lens L′, so that one ray always propagates in the same direction as the water stream, and the other ray opposite to the direction of the water stream.
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In the 1960s, Ehlers collaborated with Felix Pirani and Alfred Schild on a constructive-axiomatic approach to general relativity: a way of deriving the theory from a minimal set of elementary objects and a set of axioms specifying these objects' properties. The basic ingredients of their approach are primitive concepts such as event, light ray, particle and freely falling particle. At the outset, spacetime is a mere set of events, without any further structure. They postulated the basic properties of light and freely falling particles as axioms, and with their help constructed the differential topology, conformal structure and, finally, the metric structure of spacetime, that is: the notion of when two events are close to each other, the role of light rays in linking up events, and a notion of distance between events.
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For cavities much larger than the wavelength of the light they contain, cavities with very high Q factors have already been realized (~125,000,000). However, high Q cavities on the order of the same size as the optical wavelength have been difficult to produce due to the inverse relationship between radiation losses and cavity size. When dealing with a cavity much larger than the optical wavelength, it is simple to design interfaces such that light ray paths fulfill total internal reflection conditions or Bragg reflection conditions. For light confined within much smaller cavities near the size of the optical wavelength, deviations from ray optics approximations become severe and it becomes infeasible, if not impossible to design a cavity which fulfills optimum reflection conditions for all three spatial components of the propagating light wave vectors.
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According to the "strong" form of Fermat's principle, the problem of finding the path of a light ray from point A in a medium of faster propagation, to point B in a medium of slower propagation (Fig.1), is analogous to the problem faced by a lifeguard in deciding where to enter the water in order to reach a drowning swimmer as soon as possible, given that the lifeguard can run faster than (s)he can swim. But that analogy falls short of explaining the behavior of the light, because the lifeguard can think about the problem (even if only for an instant) whereas the light presumably cannot. The discovery that ants are capable of similar calculations does not bridge the gap between the animate and the inanimate.
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It consists of a rhombohedral crystal of Iceland spar (a variety of calcite) that has been cut at an angle of 68° with respect to the crystal axis, cut again diagonally, and then rejoined as shown, using a layer of transparent Canada balsam as a glue. Unpolarized light ray enters through the left face of the crystal, as shown in the diagram, and is split into two orthogonally polarized, differently directed rays by the birefringence property of the calcite. The ordinary ray, or o-ray, experiences a refractive index of no = 1.658 in the calcite and undergoes total internal reflection at the calcite–glue interface because its angle of incidence at the glue layer (refractive index n = 1.55) exceeds the critical angle for the interface. It passes out the top side of the upper half of the prism with some refraction, as shown.
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Although he himself possessed unimpeded insight and had the power to authoritatively recognize and enthrone tulkus, which he occasionally did as he foresaw would be helpful, Lama Gönpo did not consider his own enthronement as a reincarnate master to be necessary and so dispensed with that formality. As were Choje Longchen Rabjam, Kunkhyen Jigme Lingpa, and Jamyang Khyentse Wangpo, Gonpo Tseten Rinpoche was considered to be a secret emanation of Panchen Vimalamitra, who brought the Dzogchen teachings to Tibet. This fact is alluded to in his long life prayer, written by H.E. Dungse Thinley Norbu Rinpoche of Pemakö: > Of the millions of knowledge-holders The chief is the Supreme Vimalamitra, > Whose light-ray sunlike activity you invite as guests Into the lotus-like > Wisdom Mansion of your heart. Glorious teacher Rigdzin Trinley Ozer, may you > live long.
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Thee Sheffield Phonographic Corporation, or Thee SPC, is an independent record label based in Sheffield, UK. It is one of the most influential labels in the Yorkshire area, having given early breaks and support to many bands in the so- called New Yorkshire scene. The label was formed by Markie Mofo, Rob Chuck, Darren Chuck and Missy Tassles; all one-time members of bands including Velodrome 2000, The Motherfuckers and Chuck, Mark went on to be in The Parallellograms and The Mini Skips whilst Missy has continued in bands Flying Wing, Light Ray, The Sleazoids performed briefly with The Wedding Present and solo as The Girl Next Door. The SPC label has an extensive catalogue; their trademarks are thick, coloured vinyl and sleevenotes written in a comical Victorian style. They used to broadcast a weekly radio show on the internet station Sheffield Live.
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Illustration of Snell's Law for the case n1 < n2, such as air/water interface Refraction occurs when light travels through an area of space that has a changing index of refraction; this principle allows for lenses and the focusing of light. The simplest case of refraction occurs when there is an interface between a uniform medium with index of refraction n_1 and another medium with index of refraction n_2. In such situations, Snell's Law describes the resulting deflection of the light ray: :n_1\sin\theta_1 = n_2\sin\theta_2\ where \theta_1 and \theta_2 are the angles between the normal (to the interface) and the incident and refracted waves, respectively. The index of refraction of a medium is related to the speed, , of light in that medium by :n=c/v, where is the speed of light in vacuum.
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The first class contains terms which refer to theoretical entities, that is to entities not directly observable such as electrons, atoms and molecules; the second class contains terms which denote quantities or observable entities, and the third class consists of precisely the coordinative definitions which contain both types of terms because they connect the theoretical terms with empirical procedures of measurement or with observable entities. For example, the interpretation of "the geodesic between two points" as correspondent to "the path of a light ray in a vacuum" provides a coordinative definition. This is very similar to, but distinct from an operational definition. The difference is that coordinative definitions do not necessarily define theoretical terms in terms of laboratory procedures or experimentation, as operationalism does, but may also define them in terms of observable or empirical entities.
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The word "radio" is derived from the Latin word "radius", meaning "spoke of a wheel, beam of light, ray". It was first applied to communications in 1881 when, at the suggestion of French scientist Ernest Mercadier, Alexander Graham Bell adopted "radiophone" (meaning "radiated sound") as an alternate name for his photophone optical transmission system."Production of Sound by Radiant Energy" by Alexander Graham Bell, Popular Science Monthly, July, 1881, pages 329–330: "[W]e have named the apparatus for the production and reproduction of sound in this way the "photophone", because an ordinary beam of light contains the rays which are operative. To avoid in future any misunderstandings upon this point, we have decided to adopt the term "radiophone", proposed by M. Mercadier, as a general term signifying the production of sound by any form of radiant energy..." However, this invention would not be widely adopted.
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In the year 1926 the astrophysicist Robert Emden published the article Aberration und Relativitätstheorie in the journal Naturwissenschaften. (14. Jahrgang, Heft 16) In this article he states that the direction of a light ray isn't influenced by the motion of the star or by the motion of Earth.R. Emden's (rhetorical) question "How will the direction of the light rays of stars incident upon Earth be influenced by the motion of Earth and the motion (not the location) of the star at the time of emission?" is answered by him with "Not at all." At that time, the opponents of the special theory of relativity reasoned that the theory must be flawed, because it would state that the stellar aberration would depend on the relative velocity of the star — which would be in contradiction to observation — and R. Emden's article explains that the special theory of relativity does not predict this.
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Mengelberg and Toscanini both led the Philharmonic in recording sessions for the Victor Talking Machine Company and Brunswick Records, initially in a recording studio (for the acoustically-recorded Victors, all under Mengelberg) and eventually in Carnegie Hall as electrical recording was developed. All of the early electrical recordings for Victor were made with a single microphone, usually placed near or above the conductor, a process Victor called "Orthophonic"; the Brunswick electricals used the company's proprietary non- microphone "Light-Ray" selenium-cell system, which was much more prone to sonic distortion than Victor's. Mengelberg's first records for Victor were acousticals made in 1922; Toscanini's recordings with the Philharmonic actually began with a single disc for Brunswick in 1926, recorded in a rehearsal hall at Carnegie Hall. Mengelberg's most successful recording with the Philharmonic was a 1927 performance in Carnegie Hall of Richard Strauss' Ein Heldenleben.
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Since a point cannot support rotation or angular momentum in classical physics (general relativity being a classical theory), the minimal shape of the singularity that can support these properties is instead a ring with zero thickness but non-zero radius, and this is referred to as a ringularity or Kerr singularity. A rotating hole's rotational frame- dragging effects, described by the Kerr metric, causes spacetime in the vicinity of the ring to undergo curvature in the direction of the ring's motion. Effectively this means that different observers placed around a Kerr black hole who are asked to point to the hole's apparent center of gravity may point to different points on the ring. Falling objects will begin to acquire angular momentum from the ring before they actually strike it, and the path taken by a perpendicular light ray (initially traveling toward the ring's center) will curve in the direction of ring motion before intersecting with the ring.
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The gravitational weakening of light from high- gravity stars was predicted by John Michell in 1783 and Pierre-Simon Laplace in 1796, using Isaac Newton's concept of light corpuscles (see: emission theory) and who predicted that some stars would have a gravity so strong that light would not be able to escape. The effect of gravity on light was then explored by Johann Georg von Soldner (1801), who calculated the amount of deflection of a light ray by the sun, arriving at the Newtonian answer which is half the value predicted by general relativity. All of this early work assumed that light could slow down and fall, which is inconsistent with the modern understanding of light waves. Once it became accepted that light was an electromagnetic wave, it was clear that the frequency of light should not change from place to place, since waves from a source with a fixed frequency keep the same frequency everywhere.
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