Magic lantern
The magic lantern known by its Latin name lanterna magica, is an early type of image projector employing pictures painted, printed or produced photographically on transparent plates, one or more lenses, a light source. It was developed in the 17th century and used for entertainment purposes, it was applied to educational purposes during the 19th century. Since the late 19th century smaller versions were mass-produced as a toy for children; the magic lantern was in wide use from the 18th century until the mid-20th century, when it was superseded by a compact version that could hold many 35 mm photographic slides: the slide projector. The magic lantern used a concave mirror in back of a light source to direct as much of the light as possible through a small rectangular sheet of glass—a "lantern slide"—on, the image to be projected, onward into a lens at the front of the apparatus; the lens was adjusted to optimally focus the plane of the slide at the distance of the projection screen, which could be a white wall, it therefore formed an enlarged image of the slide on the screen.
Some lanterns, including those of Christiaan Huygens and Jan van Musschenbroek, used 3 lenses. The pictures were hand painted on glass slides. Figures were rendered with black paint but soon transparent colors were used. Sometimes the painting was done on oiled paper. Black paint was used as a background to block superfluous light, so the figures could be projected without distracting borders or frames. Many slides were finished with a layer of transparent lacquer, but in a period cover glasses were used to protect the painted layer. Most hand-made slides were mounted in wood frames with a square opening for the picture. After 1820 the manufacturing of hand colored printed slides started making use of decalcomania transfers. Many manufactured slides were produced on strips of glass with several pictures on them and rimmed with a strip of glued paper; the first photographic lantern slides, called "Hyalotypes", were invented by the German-born brothers Ernst Wilhelm and Friedrich Langenheim in 1848 in Philadelphia and patented in 1850.
Apart from sunlight, the only light sources available at the time of invention in the 17th century were candles and oil lamps, which were inefficient and produced dim projected images. The invention of the Argand lamp in the 1790s helped to make the images brighter; the invention of limelight in the 1820s made them much brighter. The invention of the intensely bright electric arc lamp in the 1860s eliminated the need for combustible gases or hazardous chemicals, the incandescent electric lamp further improved safety and convenience, although not brightness. Several types of projection systems existed before the invention of the magic lantern. Giovanni Fontana, Leonardo Da Vinci and Cornelis Drebbel did describe and/or draw image projectors that may have been quite similar to the magic lantern. In the 17th century there was an immense interest in optics; the telescope and microscope were invented and apart from being useful to some scientists, such instruments were popular as entertaining curiosities with people who could afford them.
The magic lantern would prove to be a perfect successor. The magic lantern can be seen as a further development of camera obscura; this is a natural phenomenon that occurs when an image of a scene at the other side of a screen is projected through a small hole in that screen as an inverted image on a surface opposite to the opening. It was known at least since the 5th century BCE and experimented with in darkened rooms at least since circa 1000 CE; the use of a lens in the hole has been traced back to circa 1550. The portable camera obscura box with a lens was developed in the 17th century. Dutch inventor Cornelis Drebbel is thought to have sold one to Dutch poet and diplomat Constantijn Huygens in 1622, while the oldest known clear description of a box-type camera is in German Jesuit scientist Gaspar Schott's 1657 book Magia universalis naturæ et artis; the 1645 first edition of German Jesuit scholar Athanasius Kircher's book Ars Magna Lucis et Umbrae included a description of his invention, the "Steganographic Mirror": a primitive projection system with a focusing lens and text or pictures painted on a concave mirror reflecting sunlight intended for long distance communication.
He saw limitations in the increase of size and diminished clarity over a long distance and expressed his hope that someone would find a method to improve on this. In 1654 Belgian Jesuit mathematician André Tacquet used Kircher's technique to show the journey from China to Belgium of Italian Jesuit missionary Martino Martini, it is sometimes reported that Martini lectured throughout Europe with a magic lantern which he might have imported from China, but there's no evidence that anything other than Kircher's technique was used. However, Tacquet was a correspondent and friend of Christiaan Huygens and may thus have been a early adapter of the magic lantern technique that Huygens developed around this period. Prominent Dutch scientist Christiaan Huygens, is nowadays accepted as the true inventor of the magic lantern, he knew Athanasius Kircher's 1645 edition of Ars Magna Lucis et Umbrae which described a primitive projection system with a focusing lens and text or pictures painted on a concave mirror reflecting sunlight.
Christiaan's father Constantijn had been acquainted with Cornelis Drebbel who used some unidentified optical techniques to transform himself and summon wonderful appearances in magical performances. Constantijn Huygens wrote very
David Brewster
Sir David Brewster KH PRSE FRS FSA FSSA MICE was a Scottish scientist, inventor and academic administrator. In science he is principally remembered for his experimental work in physical optics concerned with the study of the polarization of light and including the discovery of Brewster's angle, he studied the birefringence of crystals under compression and discovered photoelasticity, thereby creating the field of optical mineralogy. For this work, William Whewell dubbed him the "father of modern experimental optics" and "the Johannes Kepler of optics."A pioneer in photography, Brewster invented an improved stereoscope, which he called "lenticular stereoscope" and which became the first portable 3D-viewing device. He invented the binocular camera, two types of polarimeters, the polyzonal lens, the lighthouse illuminator, the kaleidoscope. Brewster was a Presbyterian and walked arm in arm with his brother on the Disruption procession which formed the Free Church of Scotland; as a historian of science, Brewster focused on the work of his hero, Isaac Newton.
Brewster published a detailed biography of Newton in 1831 and became the first scientific historian to examine many of the papers in Newton's Nachlass. Brewster wrote numerous works of popular science, was one of the founders of the British Science Association, of which he was elected President in 1849, he became the public face of higher education in Scotland, serving as Principal of the University of St Andrews and of the University of Edinburgh. Brewster edited the 18-volume Edinburgh Encyclopædia. David Brewster was born at the Canongate in Jedburgh, Roxburghshire, to Margaret Key and James Brewster, the rector of Jedburgh Grammar School and a teacher of high reputation. David was the third of six children, two daughters and four sons: James, minister at Craig, Ferryden. At the age of 12, David was sent to the University of Edinburgh, being intended for the clergy, he was licensed a minister of the Church of Scotland, preached around Edinburgh on several occasions. He had shown a strong inclination for natural science, this had been fostered by his intimacy with a "self-taught philosopher and mathematician", as Sir Walter Scott called him, of great local fame, James Veitch of Inchbonny, a man, skilful in making telescopes.
Though Brewster duly finished his theological studies and was licensed to preach, his other interests distracted him from the duties of his profession. In 1799 fellow-student Henry Brougham persuaded him to study the diffraction of light; the results of his investigations were communicated from time to time in papers to the Philosophical Transactions of London and other scientific journals. The fact that other scientists – notably Étienne-Louis Malus and Augustin Fresnel – were pursuing the same investigations contemporaneously in France does not invalidate Brewster's claim to independent discovery though in one or two cases the priority must be assigned to others. A lesser-known classmate of his, Thomas Dick went on to become a popular astronomical writer; the most important subjects of his inquiries can be enumerated under the following five headings: The laws of light polarization by reflection and refraction, other quantitative laws of phenomena. In this line of investigation, the prime importance belongs to the discovery of the connection between the refractive index and the polarizing angle.
These discoveries were promptly recognised. As early as 1807 the degree of LL. D. was conferred upon Brewster by Aberdeen. In 1821, he was made a foreign member of the Royal Swedish Academy of Sciences, in 1822 a Foreign Honorary Member of the American Academy of Arts and Sciences. Among the non-scientific public, his fame spread more effectually by his invention in about 1815 of the kaleidoscope, for which there was a great demand in both the United Kingdom and the United States; as a reflection of this fame, Brewster portrait was printed in some cigar boxes. Brewster chose renowned achromatic lens developer Philip Carpenter as the sole manufacturer of the kaleidoscope in 1817. Although Brewster patented the kaleidoscope in 1817, a copy of the prototype was shown to London opticians and copied before the patent was granted; as a consequence, the kaleidoscope became produced in large numbers, but yielded no direct financial benefits to Brewster. It proved to be a massive success with two hundred thousand kaleidoscopes sold in London and Paris in just three months.
An instrument of more significance, the stereoscope, which – though of much date – along with the kaleidoscope did more than anything else to popularise his name, was not as has been asserted the invention of Brewster. Sir Charles Wheatstone discovered its principle and applied it as early as 1838 to
Camera obscura
Camera obscura referred to as pinhole image, is the natural optical phenomenon that occurs when an image of a scene at the other side of a screen is projected through a small hole in that screen as a reversed and inverted image on a surface opposite to the opening. The surroundings of the projected image have to be dark for the image to be clear, so many historical camera obscura experiments were performed in dark rooms; the term "camera obscura" refers to constructions or devices that make use of the principle within a box, tent or room. Camera obscuras with a lens in the opening have been used since the second half of the 16th century and became popular as an aid for drawing and painting; the camera obscura box was developed further into the photographic camera in the first half of the 19th century when camera obscura boxes were used to expose light-sensitive materials to the projected image. The camera obscura was used as a means to study eclipses, without the risk of damaging the eyes by looking into the sun directly.
As a drawing aid, the camera obscura allowed tracing the projected image to produce a accurate representation appreciated as an easy way to achieve a proper graphical perspective. Before the term "camera obscura" was first used in 1604, many other expressions were used including "cubiculum obscurum", "cubiculum tenebricosum", "conclave obscurum" and "locus obscurus". A camera obscura device without a lens but with a small hole is sometimes referred to as a "pinhole camera", although this more refers to simple lens-less cameras in which photographic film or photographic paper is used. Rays of light travel in straight lines and change when they are reflected and absorbed by an object, retaining information about the color and brightness of the surface of that object. Lit objects reflect rays of light in all directions. A small enough opening in a screen only lets through rays that travel directly from different points in the scene on the other side and these rays form an image of that scene when they are collected on a surface opposite the opening.
In simple terms, the way your retina sees a specific image through your eye is vertically switched to the object you see and how pieces in your brain are shown to switch that object right-side up to the way you see The human eye works much like a camera obscura with an opening, a biconvex lens and a surface where the image is formed. A camera obscura device consists of a tent or room with a small hole in one side. Light from an external scene passes through the hole and strikes a surface inside, where the scene is reproduced and reversed, but with color and perspective preserved. In order to produce a reasonably clear projected image, the aperture has to be about 1/100th the distance to the screen, or less; as the pinhole is made smaller, the image gets sharper. With too small a pinhole, the sharpness worsens, due to diffraction. Many camera obscuras use a lens rather than a pinhole because it allows a larger aperture, giving a usable brightness while maintaining focus. If the image is caught on a semi-transparent screen, it can be viewed from the back so that it is no longer reversed.
Using mirrors it is possible to project a right-side-up image. The projection can be diverted onto a horizontal surface; the 18th-century overhead version in tents used mirrors inside a kind of periscope on the top of the tent. The box-type camera obscura has an angled mirror projecting an upright image onto tracing paper placed on the glass top. Although the image is viewed from the back, it is now reversed by the mirror. There are theories. Distortions in the shapes of animals in many paleolithic cave artworks might be inspired by distortions seen when the surface on which an image was projected was not straight or not in the right angle, it is suggested that camera obscura projections could have played a role in Neolithic structures. Perforated gnomons projecting a pinhole image of the sun were described in the Chinese Zhoubi Suanjing writings; the location of the bright circle can be measured to tell the time of year. In Arab and European cultures its invention was much attributed to Egyptian astronomer and mathematician Ibn Yunus around 1000 CE.
Some ancient sightings of gods and spirits in temple worship, are thought to have been conjured up by means of camera obscura projections. The earliest known written record of the camera obscura is to be found in Chinese writings called Mozi and dated to the 4th century BCE, traditionally ascribed to and named for Mozi, a Han Chinese philosopher and the founder of Mohist School of Logic. In these writings it is explained how the inverted image in a "collecting-point" or "treasure house" is inverted by an intersecting point that collected the light. Light coming from the foot of an illuminated person would be hidden below and form the top part of the image. Rays from the head would be hidden above and form the lower part of the image; this is a remarkably early correct description of the camera obscura.
Fractal
In mathematics, a fractal is a subset of a Euclidean space for which the Hausdorff dimension exceeds the topological dimension. Fractals tend to appear nearly the same at different levels, as is illustrated here in the successively small magnifications of the Mandelbrot set. Fractals exhibit similar patterns at small scales called self similarity known as expanding symmetry or unfolding symmetry. One way that fractals are different from finite geometric figures is the way. Doubling the edge lengths of a polygon multiplies its area by four, two raised to the power of two. If the radius of a sphere is doubled, its volume scales by eight, two to the power of three. However, if a fractal's one-dimensional lengths are all doubled, the spatial content of the fractal scales by a power, not an integer; this power is called the fractal dimension of the fractal, it exceeds the fractal's topological dimension. Analytically, fractals are nowhere differentiable. An infinite fractal curve can be conceived of as winding through space differently from an ordinary line – although it is still 1-dimensional, its fractal dimension indicates that it resembles a surface.
Starting in the 17th century with notions of recursion, fractals have moved through rigorous mathematical treatment of the concept to the study of continuous but not differentiable functions in the 19th century by the seminal work of Bernard Bolzano, Bernhard Riemann, Karl Weierstrass, on to the coining of the word fractal in the 20th century with a subsequent burgeoning of interest in fractals and computer-based modelling in the 20th century. The term "fractal" was first used by mathematician Benoit Mandelbrot in 1975. Mandelbrot based it on the Latin frāctus, meaning "broken" or "fractured", used it to extend the concept of theoretical fractional dimensions to geometric patterns in nature. There is some disagreement among mathematicians about how the concept of a fractal should be formally defined. Mandelbrot himself summarized it as "beautiful, damn hard useful. That's fractals." More formally, in 1982 Mandelbrot stated that "A fractal is by definition a set for which the Hausdorff–Besicovitch dimension exceeds the topological dimension."
Seeing this as too restrictive, he simplified and expanded the definition to: "A fractal is a shape made of parts similar to the whole in some way." Still Mandelbrot settled on this use of the language: "...to use fractal without a pedantic definition, to use fractal dimension as a generic term applicable to all the variants". The consensus is that theoretical fractals are infinitely self-similar and detailed mathematical constructs having fractal dimensions, of which many examples have been formulated and studied in great depth. Fractals are not limited to geometric patterns, but can describe processes in time. Fractal patterns with various degrees of self-similarity have been rendered or studied in images and sounds and found in nature, art and law. Fractals are of particular relevance in the field of chaos theory, since the graphs of most chaotic processes are fractals; the word "fractal" has different connotations for laymen as opposed to mathematicians, where the layman is more to be familiar with fractal art than the mathematical concept.
The mathematical concept is difficult to define formally for mathematicians, but key features can be understood with little mathematical background. The feature of "self-similarity", for instance, is understood by analogy to zooming in with a lens or other device that zooms in on digital images to uncover finer invisible, new structure. If this is done on fractals, however, no new detail appears. Self-similarity itself is not counter-intuitive; the difference for fractals is. This idea of being detailed relates to another feature that can be understood without mathematical background: Having a fractal dimension greater than its topological dimension, for instance, refers to how a fractal scales compared to how geometric shapes are perceived. A regular line, for instance, is conventionally understood to be one-dimensional. A solid square is understood to be two-dimensional. We see that for ordinary self-similar objects, being n-dimensional means that when it is rep-tiled into pieces each scaled down by a scale-factor of 1/r, there are a total of rn pieces.
Now, consider the Koch curve. It can be rep-tiled into four sub-copies, each scaled down by a scale-factor of 1/3. So by analogy, we can consider the "dimension" of the Koch curve as being the unique real number D that satisfies 3D = 4, which by no means is an integer! This number is; the fact th
Telescope
A telescope is an optical instrument that makes distant objects appear magnified by using an arrangement of lenses or curved mirrors and lenses, or various devices used to observe distant objects by their emission, absorption, or reflection of electromagnetic radiation. The first known practical telescopes were refracting telescopes invented in the Netherlands at the beginning of the 17th century, by using glass lenses, they were used for both terrestrial applications and astronomy. The reflecting telescope, which uses mirrors to collect and focus light, was invented within a few decades of the first refracting telescope. In the 20th century, many new types of telescopes were invented, including radio telescopes in the 1930s and infrared telescopes in the 1960s; the word telescope now refers to a wide range of instruments capable of detecting different regions of the electromagnetic spectrum, in some cases other types of detectors. The word telescope was coined in 1611 by the Greek mathematician Giovanni Demisiani for one of Galileo Galilei's instruments presented at a banquet at the Accademia dei Lincei.
In the Starry Messenger, Galileo had used the term perspicillum. The earliest existing record of a telescope was a 1608 patent submitted to the government in the Netherlands by Middelburg spectacle maker Hans Lippershey for a refracting telescope; the actual inventor is unknown but word of it spread through Europe. Galileo heard about it and, in 1609, built his own version, made his telescopic observations of celestial objects; the idea that the objective, or light-gathering element, could be a mirror instead of a lens was being investigated soon after the invention of the refracting telescope. The potential advantages of using parabolic mirrors—reduction of spherical aberration and no chromatic aberration—led to many proposed designs and several attempts to build reflecting telescopes. In 1668, Isaac Newton built the first practical reflecting telescope, of a design which now bears his name, the Newtonian reflector; the invention of the achromatic lens in 1733 corrected color aberrations present in the simple lens and enabled the construction of shorter, more functional refracting telescopes.
Reflecting telescopes, though not limited by the color problems seen in refractors, were hampered by the use of fast tarnishing speculum metal mirrors employed during the 18th and early 19th century—a problem alleviated by the introduction of silver coated glass mirrors in 1857, aluminized mirrors in 1932. The maximum physical size limit for refracting telescopes is about 1 meter, dictating that the vast majority of large optical researching telescopes built since the turn of the 20th century have been reflectors; the largest reflecting telescopes have objectives larger than 10 m, work is underway on several 30-40m designs. The 20th century saw the development of telescopes that worked in a wide range of wavelengths from radio to gamma-rays; the first purpose built radio telescope went into operation in 1937. Since a large variety of complex astronomical instruments have been developed; the name "telescope" covers a wide range of instruments. Most detect electromagnetic radiation, but there are major differences in how astronomers must go about collecting light in different frequency bands.
Telescopes may be classified by the wavelengths of light they detect: X-ray telescopes, using shorter wavelengths than ultraviolet light Ultraviolet telescopes, using shorter wavelengths than visible light Optical telescopes, using visible light Infrared telescopes, using longer wavelengths than visible light Submillimetre telescopes, using longer wavelengths than infrared light Fresnel Imager, an optical lens technology X-ray optics, optics for certain X-ray wavelengthsAs wavelengths become longer, it becomes easier to use antenna technology to interact with electromagnetic radiation. The near-infrared can be collected much like visible light, however in the far-infrared and submillimetre range, telescopes can operate more like a radio telescope. For example, the James Clerk Maxwell Telescope observes from wavelengths from 3 μm to 2000 μm, but uses a parabolic aluminum antenna. On the other hand, the Spitzer Space Telescope, observing from about 3 μm to 180 μm uses a mirror. Using reflecting optics, the Hubble Space Telescope with Wide Field Camera 3 can observe in the frequency range from about 0.2 μm to 1.7 μm.
With photons of the shorter wavelengths, with the higher frequencies, glancing-incident optics, rather than reflecting optics are used. Telescopes such as TRACE and SOHO use special mirrors to reflect Extreme ultraviolet, producing higher resolution and brighter images than are otherwise possible. A larger aperture does not just mean that more light is collected, it enables a finer angular resolution. Telescopes may be classified by location: ground telescope, space telescope, or flying telescope, they may be classified by whether they are operated by professional astronomers or amateur astronomers. A vehicle or permanent campus containing one or more telescopes or other instruments is called an observatory. An optical telescope gathers and focuses light from the visible part of the electromagnetic spectrum. Optical telescopes increase the apparent angular size of distant objects as well as their apparent brightness. In order for the image to be observed, photographed and sent to a computer, telescopes work by employing one or
Mirror
A mirror is an object that reflects light in such a way that, for incident light in some range of wavelengths, the reflected light preserves many or most of the detailed physical characteristics of the original light, called specular reflection. This is different from other light-reflecting objects that do not preserve much of the original wave signal other than color and diffuse reflected light, such as flat-white paint; the most familiar type of mirror is the plane mirror. Curved mirrors are used, to produce magnified or diminished images or focus light or distort the reflected image. Mirrors are used for personal grooming or admiring oneself, for viewing the area behind and on the sides on motor vehicles while driving, for decoration, architecture. Mirrors are used in scientific apparatus such as telescopes and lasers and industrial machinery. Most mirrors are designed for visible light. There are many types of glass mirrors, each representing a different manufacturing process and reflection type.
An aluminium glass mirror is made of a float glass manufactured using vacuum coating, i.e. aluminium powder is evaporated onto the exposed surface of the glass in a vacuum chamber and coated with two or more layers of waterproof protective paint. A low aluminium glass mirror is manufactured by coating silver and two layers of protective paint on the back surface of glass. A low aluminium glass mirror is clear, light transmissive and reflects accurate natural colors; this type of glass is used for framing presentations and exhibitions in which a precise color representation of the artwork is essential or when the background color of the frame is predominantly white. A safety glass mirror is made by adhering a special protective film to the back surface of a silver glass mirror, which prevents injuries in case the mirror is broken; this kind of mirror is used for furniture, glass walls, commercial shelves, or public areas. A silkscreen printed glass mirror is produced using inorganic color ink that prints patterns through a special screen onto glass.
Various colors and glass shapes are available. Such a glass mirror is durable and more moisture resistant than ordinary printed glass and can serve for over 20 years; this type of glass is used for decorative purposes. A silver glass mirror is an ordinary mirror, coated on its back surface with silver, which produces images by reflection; this kind of glass mirror is produced by coating a silver, copper film and two or more layers of waterproof paint on the back surface of float glass, which resists acid and moisture. A silver glass mirror provides clear and actual images, is quite durable, is used for furniture and other decorative purposes. Decorative glass mirrors are handcrafted. A variety of shades and glass thickness are available. A beam of light reflects off a mirror at an angle of reflection equal to its angle of incidence; that is, if the beam of light is shining on a mirror's surface, at a θ ° angle vertically it reflects from the point of incidence at a θ ° angle, vertically in the opposite direction.
This law mathematically follows from the interference of a plane wave on a flat boundary. In a plane mirror, a parallel beam of light changes its direction as a whole, while still remaining parallel. In a concave mirror, parallel beams of light become a convergent beam, whose rays intersect in the focus of the mirror. Known as converging mirror In a convex mirror, parallel beams become divergent, with the rays appearing to diverge from a common point of intersection "behind" the mirror. Spherical concave and convex mirrors do not focus parallel rays to a single point due to spherical aberration. However, the ideal of focusing to a point is a used approximation. Parabolic reflectors resolve this. Parabolic reflectors are not suitable for imaging nearby objects because the light rays are not parallel. Objects viewed in a mirror will appear not vertically inverted. However, a mirror does not "swap" left and right any more than it swaps top and bottom. A mirror reverses the forward/backward axis. To be precise, it reverses the object in the direction perpendicular to the mirror surface.
Because left and right are defined relative to front-back and top-bottom, the "flipping" of front and back results in the perception of a left-right reversal in the image. Looking at an image of oneself with the front-back axis flipped results in the perception of an image with its left-right axis flipped; when reflected in the mirror, your right hand remains directly opposite your real right hand, but it is perceived as the left hand of your image. When a person looks into a mirror, the image is front-back reversed, an effect similar to the holl
Reflection (physics)
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
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