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The Plane Mirror
Convex and Concave Mirrors
Convex and concave mirrors are known collectively as spherical mirrors, since their curved reflecting surfaces are usually part of the surface of a sphere. The concave type is one in which the midpoint or vertex of the reflecting surface is farther away from the object than are the edges. The center of the imaginary sphere of which it is a part is called the center of curvature and each point of the mirror surface is, therefore, equidistant from this point. A line extending through the center of curvature and the vertex of the mirror is the principal axis, and rays parallel to it are all reflected in such a way that they meet at a point on it lying halfway between the center of curvature and the vertex. This point is called the principal focus.
The size, nature, and position of an image formed by a concave spherical mirror depend on the position of the object in relation to the principal focus and the center of curvature. If the object is at a point farther from the mirror than the center of curvature, the image is real (i.e., it is formed directly by the reflected rays), inverted, and smaller than the object. If the object is at the center of curvature, the image is the same size as the object and is real and inverted. If the object is between the center of curvature and the principal focus, the image is larger, real, and inverted. If the object is inside the principal focus, the image is virtual, erect (right side up), and larger than the object. The position of the object can be found from the equation relating the focal length f of the mirror (the distance from the mirror to the principal focus), the distance do of the object from the mirror, and the distance di of the image from the mirror: 1/f=1/do+1/di. In the case of the virtual image, this equation yields a negative image distance, indicating that the image is behind the mirror. In the case of both the real and the virtual image, the size of the image is to the size of the object as the distance of the image from the mirror is to the distance of the object from the mirror.
In a convex spherical mirror the vertex of the mirror is nearer to the object than the edges—the mirror bulges toward the object. The image formed by it is always smaller than the object and always erect. It is never real because the reflected rays diverge outward from the face of the mirror and are not brought to a focus, and the image, therefore, is determined by their prolongation behind the mirror as in the case of the plane mirror.
History and Development
mirrorAn optical element designed to reflect light or other radiation, normally consisting of a glass or glasslike substrate on which is deposited a thin but uniform coating of highly reflective material. Aluminum is now usually used in telescope mirrors (see aluminizing). A very high quality reflecting surface can also be made from a multilayered stack of very thin films. The films have alternately high and low refractive indices and are of such a thickness and spacing that almost all the incident light is reflected.
Mirrors may be planar, i.e. flat. Alternatively the shapes may be concave (converging) or convex (diverging) and are generally spherical or paraboloid in form. The mirror base must be accurately ground and the surface polished to within one quarter of the wavelength used, i.e. to about 0.1 micrometer for optical wavelengths, if good quality images are to be produced. Paraboloid mirrors do not suffer from spherical aberration but for wide fields have severe coma. Spherical mirrors are free of coma and astigmatism if a suitable stop is used; they do, however, suffer from spherical aberration. See also grazing incidence; primary mirror.
Mirror(religion, spiritualism, and occult)
Mirrors have been associated with magic in many stories, myths, and legends. It was once believed that one's reflection in a mirror, or any reflective surface, was a vital part of one's soul. Mirrors were therefore regarded as "soul catchers," and were therefore draped with black cloth in the sick room of a dying person. Today's superstition that breaking a mirror causes bad luck stems from these old beliefs. Walker points out that the ancient Egyptian word for "mirror" is also the word for "life." Buddhists claim that all existence is like a reflection in a mirror.
In Witchcraft, mirrors are mainly used for divination, the user gazing into the reflective surface as into a crystal ball. Some such mirrors are blackened to cancel out any extraneous sights, while some are made with concave glass to help draw the eyes into the image.
The murals on the walls of the Initiation Room in the Villa of Mysteries at Pompeii include a scene of the initiate gazing into a polished copper mirror held aloft by a priest. In it, the initiate sees and relives the death of Dionysus. Leonardo da Vinci drew a picture (now in the library of Christ Church, Oxford) of two witches using a magic mirror to see the future. A similar illustration is found in the miniature from the eighteenth-century manuscript attributed to the Comte de Saint-Germain, La Très Sainte Trinosophie.
De Givry suggests that Catherine de Medici possessed a magic mirror in which she studied the future of France. Queen Elizabeth I's astrologer, Dr. John Dee, owned a magic mirror made of polished obsidian, a black volcanic glass. This mirror, or speculum, is preserved in the British Museum. Dee and his assistant, Edward Kelley, toured sixteenth-century Europe using the mirror in the service of various rulers and aristocrats.
Old grimoires for Ceremonial Magic give recipes for the paint used to turn a piece of clear glass into a black gazing mirror. Ingredients include turpentine and multiple coats of asphaltum. Some suggested inscribing the edge of the glass with the words "S. Solam S. Tattler S. Echogordner Gematur." Others say the mirror should be standing within a triangle whose three sides are marked with the words "Alpha— Omega—Tetragrammaton" (others say "Adonay—Eloy—Tetragrammaton").
The Roman god Vulcan had a magic mirror that showed past, present, and future. Al-Asnam, in the Arabian Nights, had a similar mirror. Other magic mirrors appear in fairy stories and folk tales around the world.
Mirror(religion, spiritualism, and occult)
The mirror can be a useful tool for developing clairvoyance. It also features in much ancient folklore. In American lore, if an unmarried woman looks into a mirror by the light of a candle at midnight on Hallowe’en night, she will see the reflection of her future husband looking at her over her left shoulder. An older legend from Europe has it that by gazing into a reflection of the moon in a hand mirror, a young woman can tell how many years will pass before she marries, based on the length of time before either a cloud passes before the moon or a bird flies across it.
In earliest times, Chinese sages, together with wise men and women of ancient Greece and Rome, believed that to dream of seeing your own reflection—be it in water, polished brass or copper, or wherever—was an omen of death. The death was not necessarily yours but was of a person close to you. Seeing your reflection at various times of the day also had meaning. This was all brought together in what was known as catoptromancy, or enoptromancy, divination by mirror. Hydromancy, divination by water, was but a small part of it.
Catoptromancy, as an aspect of mirror-gazing, is referred to by Sir Thomas Urquhart in The Third Book of the Works of Mr. Francis Rabelais (London, 1693), which reads, “Catoptromancy is held in such account by the emperor Didius Julianus,” implying that it was practiced in ancient Rome. The (London) Annual Register of 1758 says, “He understands all the mysteries of catoptromancy, he having a magical glass to be consulted upon some extraordinary occasions.” Pausanius, the fifth century BCE Spartan regent of the Greek forces and admiral of the Greek fleet, described how this form of divination was performed, “Before the Temple of Ceres, at Patras, there was a fountain, separated from the temple by a wall, and there was an oracle, very truthful, but not for all events—for the sick only. The sick person let down a mirror (of bronze or silver), suspended by a thread, till its base touched the surface of the water, having first prayed to the goddess and offered incense. Then looking in the mirror, he saw the presage of death or recovery, according as the face appeared fresh and healthy or of a ghastly aspect.” The Romans and the Egyptians also used this form of divination.
Mirror gazing is one of the many forms of scrying, of divining by looking into a reflective surface. The mirror is used much like a crystal ball in crystal gazing, being gazed into with the diviner or medium seeing scenes from the past, present, or future. The Roman god Vulcan had a magic mirror in which he was able to see all things. England’s Merlin had one that warned him of treason. In Chaucer’s Canterbury Tales, the mirror of Cambuscan told of misfortunes to come. In Goldsmith’s Citizen of the World, Lao’s mirror reflected pure thought. In the Arabian Nights, there is the all-seeing mirror of Al-Asnam, and in Snow White and the Seven Dwarfs there is the magic mirror of the wicked Queen, in which she can see Snow White. A drawing by Leonardo da Vinci now in the Library of Christ Church, Oxford, England, shows a woman holding up a mirror to a seeress as part of a ritual. In the mirror can be seen the face of an old man.
In Étienne Pasquier’s Recherches de la France (1560), he speaks of a magic mirror owned and used by Catherine de Médicis (1519–1589). She supposedly could clairvoyantly see the future of France, especially as it pertained to the de Médicis family. According to Grillot de Givry, Père Cotton used that same mirror to show Henri IV all the plots that were being hatched against him.
All types of mirrors have been used over the ages, with polished metal faces, glass, crystal, and obsidian. The mirror may or may not be enclosed in a frame. If it is, the frame is usually engraved or marked in some way with sigils to help generate and amplify the images seen. In Francis Barrett’s book The Magus (1801), there is shown a mirror set in a frame of “pure gold” with the sacred names MICHAEL, GABRIEL, URIEL, and RAPHAEL inscribed around it, inside a double circle. These are the angels ruling over the Sun, Moon, Venus, and Mercury. Above the name Michael is drawn a six-pointed star. On the other side of the frame there is also a circle engraved, inside which (next to the glass) is a six-pointed star together with a five-pointed star and a Maltese-style cross. These are followed by the word TETRAGRAMMATON. The glass, Barrett says, should be “of a lapidary good clear pellucid crystal … about one inch and a half in diameter.” There are also instructions for the preparation and inscribing of the table on which the glass should stand. Other authorities give other instructions and suggestions as to what would be appropriate to mark around the frame, though some leave the frame unmarked.
Many diviners say that a black mirror is far superior to any other. Similarly, a concave mirror is an advantage. One way to make a mirror that follows both these suggestions is to obtain one of the old framed pictures, from around the turn of the previous century, which has an oval, convex glass. Reversing the glass and painting what then becomes the back of it with black paint produces a convex black mirror that is perfect for mirror gazing. Old books of magic state that the glass should be painted three times with asphaltum. To make the asphaltum stick to the glass, it first needs to be cleaned with turpentine. The asphalt should be laid on with a camel-hair brush. However, using modern black enamel from a spray can seems to work just as well. As with all magical practices, while making the object you should be concentrating on its purpose, on it being good for projecting scenes from past, present, and future.
The Revue Archéologique of 1846 contains an illustration and description of a magic mirror that belonged to a Spanish family at Saragossa in the seventeenth century. It was a metal, convex mirror decorated with figures and with the words MUERTE, ETAM, TETECEME, and ZAPS. It was said that images appeared on the surface of any liquid reflected in the mirror’s surface.
Some people training to become Spiritualist mediums will begin their exercises with scrying, using either a crystal ball or a mirror. It can be an effective way to get started so long as the medium does not come to rely solely on the object but merely uses it as a tool for further development.
(or speculum, Russian zerkal’tse), in biology.
(1) The shiny pigmented membrane of the eye in some animals that reflects light on the retina and thereby intensifies the light stimulation of the visual cells. It causes the apparent luminosity of the eye in almost complete darkness. In vertebrates (some fish, reptiles, and birds and almost all predatory and aquatic mammals) it is located on the internal surface of the vascular tunic of the eye; in many fish and some reptiles it is in the cells of the pigmented epithelium of the retina (in the form of crystals of a shiny pigment). In invertebrates with lens eyes (some mollusks, annelid worms, and arthropods) it is formed of pigmented cells of the reflecting layer.
(2) [Usually “speculum.”] Areas of brightly colored plumage, sometimes with a mirror-like gleam, on the wings in the area of the secondaries in male birds, especially in many species of ducks. They serve as signals, for example, in mating games.
(3) [In English, “wax plate.”] Organs of wax secretion in worker bees (two wax mirrors for each four to seven sternites of the abdomen). They consist of a layer of hypodermal cells and a transparent cuticle that covers them, through which the wax secreted by the gland cells of the hypodermis is exuded.
(4) Part of the sound (stridulating) organs in the males of some crickets. It is a thin, smooth, transparent plate with edges inflated in the form of a ridge and is located on the surface of the right wing, which is covered with the left one. It serves as a resonator that intensifies sounds arising during stridulation from rubbing the left wing on the ridge of the right one.
a body that has a polished surface and is capable of forming optical images of objects (including light sources) by reflecting light rays.
The first mention of the use of metal mirrors (made of bronze or silver) in daily life dates to the third millennium B.C. In the Bronze Age mirrors were known chiefly in the countries of the ancient East; in the Iron Age they were used more extensively. The face of metal mirrors was smoothly polished, and the reverse side was covered with engraved or raised designs or images. The mirrors were usually round, with a handle (among the ancient Greeks the handle was often in the form of a sculptured figure). Glass mirrors with a tin or lead backing began to be used by the Romans in the first century A.D.; they disappeared in the early Middle Ages and reappeared only in the 13th century. In the 16th century the backing of glass mirrors with tin amalgam was discovered.
The diversity of the shapes and types of mirrors, from pocket mirrors to very large cheval glasses, began to increase in the 17th century. Mirror frames became more ornate. Mirrors often served as a finishing touch on walls and mantles in court interiors during the baroque era and the period of classicism. In the 20th century, with the development of functionalist tendencies in architecture, mirrors have almost lost their decorative role and are now usually manufactured according to their domestic function (in a simple metal frame or unframed).
Optical properties. The closer the shape of a mirror’s surface to a mathematically regular shape, the higher the quality of the mirror. The maximum permissible size of microscopic surface irregularities is determined by the intended purpose of the mirror: for astronomical mirrors and some laser mirrors it must not exceed 0.1 of the shortest wavelength λmin of the radiation incident on the mirror, but for searchlight or converging mirrors it may be as high as 10λmin.
The position of the optical image produced by a mirror can be determined according to the laws of geometric optics. It depends on the shape of the mirror surface and the position of the represented object.
A flat mirror is a natural optical system that produces a wholly aberration-free image (always a virtual image) for any light beams incident on it. This property of flat mirrors is responsible for their extensive use for various design purposes (rotation of a light beam, autocollimation, image reversal, and so on). Such mirrors are also used in high-precision measuring instruments, such as interferometers.
Concave and convex mirrors are also used in optical systems. Their reflecting surfaces are spherical, paraboloidal, ellipsoidal, or toroidal; mirrors with surfaces of more complex shapes are also used. Concave mirrors usually (but not always) concentrate the energy of a light beam by collecting it; convex mirrors scatter it. Nonflat mirrors have all the aberrations inherent in optical systems, except chromatic aberrations. The position of the image of the object created by a mirror whose surface has an axis of symmetry is related to the radius of curvature r of the mirror at its apex O (Figure 1) by the ratio
l/s + l/s’ = 2/r
where s is the distance from the apex O to the object A and s’ is the distance to the imaged’. This formula is strictly valid
only in the extreme case of the infinitesimal angles formed by the light rays with the axis of the mirror; however, it is a good approximation even at finite but sufficiently small angles. If the object is located at a distance that may be considered infinitely large, s’ is equal to the focal distance of the mirror: s’ = f’ = r/2.
Properties of reflecting surfaces. A mirror must have a high reflection coefficient. Smooth metal surfaces, such as aluminum in the ultraviolet, visible, and infrared bands, silver in the visible and infrared bands, and gold in the infrared band, have high reflection coefficients. The reflection from any metal depends strongly on the wavelength of the light A: as A increases, the reflection coefficient Rλ rises to 99 percent or more for some metals (Figure 2).
The reflection coefficients of dielectrics are much smaller than those of metals (only 4 percent for glass with an index of refraction n = 1.5). However, by using light interference in multilayer combinations of transparent dielectrics it is possible to obtain (in a relatively narrow region of the spectrum) reflecting surfaces with reflection coefficients of over 99 per-cent not only in the visible band but also in the ultraviolet, which is impossible with metallic surfaces. Dielectric mirrors consist of a large number (13–17) of alternating layers of dielectrics with high and low n. The thickness of each layer is such that the optical length of the light’s path in it is one-fourth of the wavelength. Odd layers are made of a material that has a high n (such as sulfides of zinc and antimony and oxides of titanium, zirconium, hafnium, and thorium), and even layers are made of a material that has a low n (fluorides of magnesium and strontium; silica). The reflection coefficients of dielectric mirrors depend not only on the wavelength but also on the angle of incidence of the radiation.
Production of mirrors. In antiquity, polished metal plates were used as mirrors. As glassmaking developed, metal mirrors gave way to glass mirrors, whose reflecting surfaces were thin layers of metals applied to the glass. Originally small mirrors of irregular shape were produced by pouring into a spherical glass vessel a molten metal which, upon hardening, formed a reflective layer (after cooling, the vessel was cut up). The first glass mirrors of significant size were manufactured by coating the glass with a mercury-tin amalgam. This method, which is harmful to the health of workers, was later replaced by chemical silvering, which is based on the ability of some compounds that contain the aldehyde group to recover silver from saline solutions in the form of a metallic film. The most widely used industrial process for producing mirrors by silver-plating consists in the removal of impurities and corrosion products from the surface of the glass, the application of silver deposition centers, silvering, and the application of protective coatings to the reflecting layer. The thickness of the silver film usually varies from 0.15 to 0.30 microns (μm). To provide electrochemical protection of the reflecting layer, it is coated with a copper film of thickness comparable to that of the silver film. Paint and varnish materials such as polyvinyl-butyral, nitroepoxy, and epoxy enamels, which prevent physical damage to the protective coating, are applied to the copper film. Mirrors intended for technical use are manufactured with reflecting films consisting of gold, palladium, platinum, lead, chromium, or nickel.
Mirrors are also manufactured by plating glass by cathode sputtering and vacuum vaporization. Thermal vaporization of aluminum in a vacuum at a pressure of 6.7 x 102to l.3 x 10-3 newtons per sq m (N/m2), or 5 x 10-4 to 10-5 mm of mercury (mm Hg), is becoming particularly widespread. The aluminum is vaporized from braids made of tungsten wire or from a fireproof crucible. The preparation of the glass surface for aluminum coating is performed even more carefully than before chemical silvering; it includes dehydration and treatment by electrical discharge in a vacuum of 13.3 N/m2 (10”1 mm Hg). To produce a mirror with maximum reflectance, the thickness of the aluminum coating should be at least 0.12 μm. Because of their increased chemical stability, aluminum-coated mirrors are sometimes used as external reflecting sur-faces protected by optically transparent layers of A12O3, SiO2, MgF2, or ZnS. Usually the layer of aluminum is covered with the same opaque paints and varnishes used in silvering. A certain nonuniformity over the spectrum and the reflectance of aluminum-plated mirrors, which is lower than that of silver-plated mirrors, are justified by the significant saving of silver in the mass production of mirrors.
Mirrors with coatings of most metals, as well as dielectrics, can be produced by the methods of cathode sputtering and thermal vaporization.
Use in science, technology, and medicine. The ability of concave mirrors to focus light beams parallel to their axis is used in reflecting telescopes. The operation of searchlights is based on the reverse phenomenon—the transformation in a mirror of a beam of light from a source located at the focal point into a parallel beam. Mirrors used in combination with lenses form a broad group of catadioptric systems. In lasers, mirrors are used as components of optical cavities. The lack of chromatic aberrations brought about the use of mirrors in monochromators (especially of infrared radiation) and many other devices.
In addition to measuring and optical devices, mirrors are also used in other fields of technology—for example, in solar concentrators, solar power plants, and zone melting apparatus (the operation of these devices is based on the ability of concave mirrors to concentrate the energy of radiation in a small volume). A frontal reflector—a concave mirror with an aperture in the middle that is used to direct a narrow light beam into the eyes, ears, nose, throat, and larynx—is the most widely used mirror in medicine. Mirrors of diverse design and form are also used for research in stomatology, surgery, and gynecology.
REFERENCESSliusarev, G. G. Melody rascheta opticheskikh sistem. Moscow-Leningrad, 1937.
Sonnefeld, A. Vognutye zerkala. Moscow-Leningrad, 1935. (Translated from German.)
Maksutov, D. D. Astronomicheskaia optika. Moscow-Leningrad, 1946.
Vinokurov, V. M. Khimicheskie melody serebreniia zerkal. Moscow, 1950.
Tudorovskii, A. I. Teoriia opticheskikh pribomv, part 2. Moscow-Leningrad, 1952.
Rozenberg, G. V. Optika tonkosloinykh pokrytii. Moscow, 1958.
Danilin, B. S. Vakuumnoe nanesenie tonkikh plenok. Moscow, 1967.
Gluck, I. /vse eto delaiut zerkala. Moscow, 1970. (Translated from English.)
L. I. BORISOVA and V. N. ROZHDESTVENSKII
What does it mean when you dream about a mirror?
The mirror reflects oneself from the inner depths. If the mirror is clear, one is gazing upon one’s true self. This may be a shocking or a pleasant experience, depending upon how many shortcomings or false images the dreamer presents in the real world. A cracked or cloudy mirror reflects the distortions that are projected into the world.
Several operating systems support software disk mirroring or disk-duplexing, e.g. Novell NetWare.
See also Redundant Array of Independent Disks.
Interestingly, when this technique is used with magnetic tape storage systems, it is usually called "twinning".
A less expensive alternative, which only limits the amount of data loss, is to make regular backups from a single disk to magnetic tape.