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Spherometer
A spherometer is an instrument used for the precise measurement of the radius of curvature of a sphere or a curved surface. Originally, these instruments were primarily used by opticians to measure the curvature of the surface of a lens. Background The usual form consists of a fine screw moving in a nut carried on the center of a 3 small legged table or frame; the feet forming the vertices of a triangle. The lower end of the screw and those of the table legs are finely tapered and terminate in hemispheres, so that each rests on a point. If the screw has two turns of the thread to the milli metre the head is usually divided into 50 equal parts, so that differences of 0.01 millimeter may be measured without using a vernier. A lens, however, may be fitted, in order to magnify the scale divisions. A vertical scale fastened to the table indicates the number of whole turns of the screw and serves as an index for reading the divisions on the head. A contact-lever, delicate level or el ...
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Spherometer
A spherometer is an instrument used for the precise measurement of the radius of curvature of a sphere or a curved surface. Originally, these instruments were primarily used by opticians to measure the curvature of the surface of a lens. Background The usual form consists of a fine screw moving in a nut carried on the center of a 3 small legged table or frame; the feet forming the vertices of a triangle. The lower end of the screw and those of the table legs are finely tapered and terminate in hemispheres, so that each rests on a point. If the screw has two turns of the thread to the milli metre the head is usually divided into 50 equal parts, so that differences of 0.01 millimeter may be measured without using a vernier. A lens, however, may be fitted, in order to magnify the scale divisions. A vertical scale fastened to the table indicates the number of whole turns of the screw and serves as an index for reading the divisions on the head. A contact-lever, delicate level or el ...
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Coordinate Geometry
In classical mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system. This contrasts with synthetic geometry. Analytic geometry is used in physics and engineering, and also in aviation, rocketry, space science, and spaceflight. It is the foundation of most modern fields of geometry, including algebraic, differential, discrete and computational geometry. Usually the Cartesian coordinate system is applied to manipulate equations for planes, straight lines, and circles, often in two and sometimes three dimensions. Geometrically, one studies the Euclidean plane (two dimensions) and Euclidean space. As taught in school books, analytic geometry can be explained more simply: it is concerned with defining and representing geometric shapes in a numerical way and extracting numerical information from shapes' numerical definitions and representations. That the algebra of the real numbers can be employed t ...
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Lensometer
A lensmeter or lensometer (sometimes even known as focimeter or vertometer), is an ophthalmic instrument. It is mainly used by optometrists and opticians to measure the back or front vertex power of a spectacle lens and verify the correct prescription in a pair of eyeglasses, to properly orient and mark uncut lenses, and to confirm the correct mounting of lenses in spectacle frames. Lensmeters can also verify the power of contact lenses, if a special lens support is used. The parameters appraised by a lensmeter are the values specified by an ophthalmologist or optometrist on the patient's prescription: sphere, cylinder, axis, add, and in some cases, prism. The lensmeter is also used to check the accuracy of progressive lenses, and is often capable of marking the lens center and various other measurements critical to proper performance of the lens. It may also be used prior to an eye examination to obtain the last prescription the patient was given, in order to expedite the ...
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Lens (optics)
A lens is a transmissive optical device which focuses or disperses a light beam by means of refraction. A simple lens consists of a single piece of transparent material, while a compound lens consists of several simple lenses (''elements''), usually arranged along a common axis. Lenses are made from materials such as glass or plastic, and are ground and polished or molded to a desired shape. A lens can focus light to form an image, unlike a prism, which refracts light without focusing. Devices that similarly focus or disperse waves and radiation other than visible light are also called lenses, such as microwave lenses, electron lenses, acoustic lenses, or explosive lenses. Lenses are used in various imaging devices like telescopes, binoculars and cameras. They are also used as visual aids in glasses to correct defects of vision such as myopia and hypermetropia. History The word ''lens'' comes from '' lēns'', the Latin name of the lentil (a seed of a lent ...
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Lens Clock
A lens clock is a mechanical dial indicator that is used to measure the dioptric power of a lens. It is a specialized version of a spherometer. A lens clock measures the curvature of a surface, but gives the result as an optical power in diopters, assuming the lens is made of a material with a particular refractive index. How it works The lens clock has three pointed probes that make contact with the surface of the lens. The outer two probes are fixed while the center one moves, retracting as the instrument is pressed down on the lens's surface. As the probe retracts, the hand on the face of the dial turns by an amount proportional to the distance. The optical power \phi of the surface is given by :\phi = , where n is the index of refraction of the glass, s is the vertical distance (''sagitta'') between the center and outer probes, and D is the horizontal separation of the outer probes. To calculate \phi in diopters, both s and D must be specified in meters. A typical lens ...
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Lapidary
Lapidary (from the Latin ) is the practice of shaping stone, minerals, or gemstones into decorative items such as cabochons, engraved gems (including cameos), and faceted designs. A person who practices lapidary is known as a lapidarist. A lapidarist uses the lapidary techniques of cutting, grinding, and polishing. Hardstone carving requires specialized carving techniques. In modern contexts, a gemcutter is a person who specializes in cutting diamonds, but in older contexts the term refers to artists who produced hardstone carvings; engraved gems such as jade carvings, a branch of miniature sculpture or ornament in gemstone. By extension, the term ''lapidary'' has sometimes been applied to collectors of and dealers in gems, or to anyone who is knowledgeable in precious stones. Etymology The etymological root of the word 'lapidary' is the Latin word , meaning "stone".Douglas Harper (2014)Lapidary Online Etymology Dictionary In the 14th century, the term evolved from , meani ...
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Right Circular Cylinder
A cylinder (from ) has traditionally been a three-dimensional solid, one of the most basic of curvilinear geometric shapes. In elementary geometry, it is considered a prism with a circle as its base. A cylinder may also be defined as an infinite curvilinear surface in various modern branches of geometry and topology. The shift in the basic meaning—solid versus surface (as in ball and sphere)—has created some ambiguity with terminology. The two concepts may be distinguished by referring to solid cylinders and cylindrical surfaces. In the literature the unadorned term cylinder could refer to either of these or to an even more specialized object, the ''right circular cylinder''. Types The definitions and results in this section are taken from the 1913 text ''Plane and Solid Geometry'' by George Wentworth and David Eugene Smith . A ' is a surface consisting of all the points on all the lines which are parallel to a given line and which pass through a fixed plane curve in a p ...
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Radius Of Curvature (mathematics)
In differential geometry, the radius of curvature, , is the reciprocal of the curvature. For a curve, it equals the radius of the circular arc which best approximates the curve at that point. For surfaces, the radius of curvature is the radius of a circle that best fits a normal section or combinations thereof. Definition In the case of a space curve, the radius of curvature is the length of the curvature vector. In the case of a plane curve, then is the absolute value of : R \equiv \left, \frac \ = \frac, where is the arc length from a fixed point on the curve, is the tangential angle and is the curvature. Formula In 2D If the curve is given in Cartesian coordinates as , i.e., as the graph of a function, then the radius of curvature is (assuming the curve is differentiable up to order 2): : R =\left, \frac \, \qquad\mbox\quad y' = \frac,\quad y'' = \frac, and denotes the absolute value of . If the curve is given parametrically by functions and , then the rad ...
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Aspherical Lens
An aspheric lens or asphere (often labeled ''ASPH'' on eye pieces) is a lens whose surface profiles are not portions of a sphere or cylinder. In photography, a lens assembly that includes an aspheric element is often called an aspherical lens. The asphere's more complex surface profile can reduce or eliminate spherical aberration and also reduce other optical aberrations such as astigmatism, compared to a simple lens. A single aspheric lens can often replace a much more complex multi-lens system. The resulting device is smaller and lighter, and sometimes cheaper than the multi-lens design. Aspheric elements are used in the design of multi-element wide-angle and fast normal lenses to reduce aberrations. They are also used in combination with reflective elements (catadioptric systems) such as the aspherical Schmidt corrector plate used in the Schmidt cameras and the Schmidt–Cassegrain telescopes. Small molded aspheres are often used for collimating diode lasers. Aspheri ...
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Drill Pipe
Drill pipe, is hollow, thin-walled, steel or aluminium alloy piping that is used on drilling rigs. It is hollow to allow drilling fluid to be pumped down the hole through the bit and back up the annulus. It comes in a variety of sizes, strengths, and wall thicknesses, but is typically 27 to 32 feet in length (Range 2). Longer lengths, up to 45 feet, exist (Range 3). Background Drill stems must be designed to transfer drilling torque for combined lengths that often exceed several miles down into the Earth's crust, and also must be able to resist pressure differentials between inside and outside (or vice versa), and have sufficient strength to suspend the total weight of deeper components. For deep wells this requires tempered steel tubes that are expensive, and owners spend considerable efforts to reuse them after finishing a well. A used drill stem is inspected on site, or off location. Ultrasonic testing and modified instruments similar to the spherometer are used at inspecti ...
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Radius Of Curvature
In differential geometry, the radius of curvature, , is the reciprocal of the curvature. For a curve, it equals the radius of the circular arc which best approximates the curve at that point. For surfaces, the radius of curvature is the radius of a circle that best fits a normal section or combinations thereof. Definition In the case of a space curve, the radius of curvature is the length of the curvature vector. In the case of a plane curve, then is the absolute value of : R \equiv \left, \frac \ = \frac, where is the arc length from a fixed point on the curve, is the tangential angle and is the curvature. Formula In 2D If the curve is given in Cartesian coordinates as , i.e., as the graph of a function, then the radius of curvature is (assuming the curve is differentiable up to order 2): : R =\left, \frac \, \qquad\mbox\quad y' = \frac,\quad y'' = \frac, and denotes the absolute value of . If the curve is given parametrically by functions and , then the radiu ...
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Micrometer (device)
A micrometer, sometimes known as a micrometer screw gauge, is a device incorporating a calibrated screw widely used for accurate measurement of components in mechanical engineering and machining as well as most mechanical trades, along with other metrological instruments such as dial, vernier, and digital calipers. Micrometers are usually, but not always, in the form of calipers (opposing ends joined by a frame). The spindle is a very accurately machined screw and the object to be measured is placed between the spindle and the anvil. The spindle is moved by turning the ratchet knob or thimble until the object to be measured is lightly touched by both the spindle and the anvil. Micrometers are also used in telescopes or microscopes to measure the apparent diameter of celestial bodies or microscopic objects. The micrometer used with a telescope was invented about 1638 by William Gascoigne, an English astronomer. History The word ''micrometer'' is a neoclassical coin ...
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