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Topic: Spherical distance

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	Glossary
		Spherical aberration causes parallel light rays passing through the edge of a lens to converge at a focal point closer to the lens than light rays passing through the center of the lens.
		A point image affected by spherical aberration is sharply formed by light rays near the optical axis but is affected by flare from the peripheral light rays (this flare is also called halo, and its radius is called lateral spherical aberration).
		With general photographic lenses, the overall length of a lens (the distance from the apex of the frontmost lens element to the focal plane) is longer than its focal length.
	www.usa.canon.com /html/eflenses/lens101/glossary/index_s.html (1655 words)

	Great-circle distance - Wikipedia, the free encyclopedia
		The great-circle distance is the shortest distance between any two points on the surface of a sphere measured along a path on the surface of the sphere (as opposed to going through the sphere's interior).
		Because the Earth is approximately spherical, the equations for great-circle distance are important for finding the shortest distance between points of the surface of the Earth, and so has important applications in navigation.
		In the spherical coordinates used by mathematicians and physicists, usually when considering other spheres than the Earth's surface, the great-circle distance is found as follows.
	en.wikipedia.org /wiki/Great_circle_distance (589 words)

	Reflection (Spherical Mirrors)
		The objective of this lab is to observe the reflection of light from a spherical mirror, determine the focal length of the mirror and verify the mirror equation.
		The center of curvature, C, is the center of the spherical surface of which the mirror is a part, it is equal to the radius of the sphere.
		The distance from the focal point to the mirror is called the focal length, it is equal to one half the center of curvature.
	physics.uwstout.edu /colphys2/labs/mirror.htm (677 words)

	Navigation
		For instance, at a distance on the surface of the Earth of 38 cm the relative error of the Law of Cosines -- computed in an Excel spreadsheet -- is -0.85%.
		The distance from the base station is half the travel time of a signal sent by the aircraft to the base station, which then is sent back by the transponder at the base station.
		For a spherical-triangle, the value of the spherical excess E is in the interval [0, 4 pi].
	www.rism.com /Trig/navigation.htm (3552 words)

	United States Patent: 6,512,838
		With multiple cameras, distance to a target point is estimated by software by measuring offset of the pixel images of the same point in two simultaneous frames obtained by two cameras such that a higher offset means a greater distance from target to the cameras.
		The distance may vary depending upon specific applications and optical properties of the camera, but a distance Z in a range of about 1 m to about 3 m is typical for consumer-grade applications, including home use systems.
		When distance values are mapped to planes in a three-dimensional grid, two points with the same distance value may in fact map to different planes on the three-dimensional grid.
	www.roeder-johnson.com /RJDocs/CA-Patent-6512838.html (18562 words)

	Topic 21. Spherical Mirrors, Part 2: image formation
		The image distance varies in the same direction as the object distance — an increase in one produces a corresponding increase in the other.
		However, the maximum image distance is the focal distance when the object is very, very far away, and the minimum image distance is 0 when the object is right at the mirror.
		Since the object and image vectors form the bases of two similar triangles, the magnification is the ratio of the distance of the image to the focal point divided by the distance of the object to the focal point, and this ratio is almost always less than 1.
	www.colorado.edu /physics/phys1230/phys1230_fa01/topic21.html (1072 words)

	Spherical Astronomy without Trig
		Spherical astronomy concerns the directions of celestial objects, and uses the concept of the celestial sphere.
		There is of course the heavy use of spherical trigonometry in most calculations.
		It is the shortest spherical distance between two points.
	ourworld.compuserve.com /homepages/bmoler/spheric.htm (1288 words)

	Levitated \| Spherical Magnfication
		Spherical Magnification is a three dimensional displacement technique that conserves valuable computational resources.
		When the mouse comes within a specified distance of the object, the object is first pushed away, then attracted to the mouse as it draws nearer.
		In addition, the object is magnified by a sinusoidal relationship to the distance from the mouse.
	levitated.net /daily/levTextSphere.html (137 words)

	Coordinates (elementary mathematics) - free-definition (Site not responding. Last check: 2007-10-10)
		The polar coordinate systems are coordinate systems in which a point is identified by a distance from some fixed feature in space and one or more subtended angles.
		To construct a point from its spherical coordinates: from the origin, go ρ along the positive z -axis, rotate φ about y -axis toward the direction of the positive x -axis, and rotate θ about the z -axis toward the direction of the positive y -axis.
		Spherical coordinates are the natural coordinates for physical situations where there is spherical symmetry.
	www.free-definition.com /Coordinates-(elementary-mathematics).html (906 words)

	Spherical Mirrors
		The image of the light was focused onto the screen, and the distance between the screen and mirror as well as the distance between the light and the mirror was determined.
		At each location, the height of the image, the distance from the screen to the mirror, and the distance of the object box to the mirror was noted.
		Since the object was kept in focus, the ratio of the image distance to the object distance should be equal to the ratio of the image height to the object height.
	www.thought.net /jason/phy252/exp25 (706 words)

	JavaScript Distance Calculator (Site not responding. Last check: 2007-10-10)
		Segment d is the distance between these two points, and the vertex of angle c is the center of the earth.
		The distance from the point to the origin is the radius of the earth.
		The calculated distance is based on the assumption that the earth is a perfect sphere and disregards the altitude of the locations and the curvature of the earth.
	marian.creighton.edu /~besser/physics/crop/distance.html (476 words)

	Aberrations and Fiber Optics (Site not responding. Last check: 2007-10-10)
		for a lens with spherical surfaces, the outer regions of the lens are too strong compared to the central region.
		Difference in distance between the paraxial focus and the marginal focus is a measure of the spherical aberration of the lens or more properly longitudinal spherical aberration, LSA, to distinguish it from the closely related transverse spherical aberration, TSA.
		The distance between the red and blue foci on the optical axis is the axial chromatic aberration (ACA).
	www.chm.colostate.edu /erf/teaching/c532/opaberfib.htm (2523 words)

	UNESCO Training Module on GIS - Module B-3
		Meridians are used to measure longitude - that is, the angular distance east or west from the prime meridian.
		Distances and areas must be calculated using spherical geometry and the Earth's radii to the points in question.
		The distance between the geoid and the spheroid is referred to as the geoid-spheroid separation or geoidal undulation.
	gea.zvne.fer.hr /module/module_b/module_b3.html (2029 words)

	Gravity Page - J R Stockton (Site not responding. Last check: 2007-10-10)
		Consider an arbitrary point inside a uniformly-charged spherical surface, and consider both an arbitrary small element of charged area and that second element of area which is marked out by straight lines from the edge of the first area through the point to meet the sphere again on the opposite side of the point.
		That on the probe, being inverse-square dependent on the mass within its current distance from the centre, with that mass being proportional to the cube of the radius, is proportional to the distance from the centre.
		Let the distance of a moon from its planet be r, that of the planet from its Sun be R ; let the mass of the planet be m, and the mass of the Sun be M ; let the orbital speeds of moon and planet around their primaries be v and V.
	www.merlyn.demon.co.uk /gravity-.htm (5709 words)

	Spherical Mirrors
		Glass correcting plates can correct the spherical aberration of a spherical mirror, and this is often a better solution than the use of a parabolic mirror, since it is very difficult to produce a good parabolic surface.
		The geometry for a concave mirror is shown at the left, and the formulas for finding the reflection angle i in terms of the ray height h, and the point at which a ray of angle i crosses the axis; the distance from this point to the vertex V is x.
		If the distance normal to the axis between two neighboring image points is y', and the similar distance for the object points is y, then the (transverse) magnification is the ratio y'/y.
	www.du.edu /~jcalvert/optics/mirror.htm (3195 words)

	SPHERICAL TO PLANAR TRANSFORMATION (Site not responding. Last check: 2007-10-10)
		Law of Sines: sin A sin B sin C ------- = ------- = ------- sin a sin b sin c Where a,b,c are the sides of the spherical triangle, and A, B, C are the opposite angles.
		Distance and bearing from point #2 to point #4: cos D = (sin lat #2.
		APPENDIX E. This appendix tabulates the results of the calculations described in, "Relationship of Spherical Facet to Planar Facet," the procedure for translating any point in a spherical triangle to a planar triangle.
	www.academic.marist.edu /~jwg9/dymaxion/appendix.htm (697 words)

	Spherical mirrors; and Refraction
		When the image distance is positive, the image is on the same side of the mirror as the object, and it is real and inverted.
		When the image distance is negative, the image is behind the mirror, so the image is virtual and upright.
		The image distance is positive, meaning that it is on the same side of the mirror as the object.
	physics.bu.edu /py106/notes/Spherical.html (1154 words)

	Reaction-less E-field thrusters (Site not responding. Last check: 2007-10-10)
		To illustrate the phenomena let us examine a spherical condenser when both electrodes are charged with identical amounts of charge Q of opposite polarity, and with vacuum between the electrodes as shown on fig.
		If the two electrodes of the spherical condenser are charged with the same amount of elementary charges, then there will be no E-field within the inner sphere, nor outside the bigger sphere.
		This principle is valid not only for spherical condensers but also for cylindrical and other arced condensers with plates of different curvature and surface area, that causes asymmetrical charge density distribution on the two electrodes.
	www.gyogyitokezek.hu /fe/newton.htm (1475 words)

	Lab 5.1.2
		A spherical mirror is a portion of the surface of a hollow sphere as shown in figure 1.
		The distance, OF, is known as the focal length of the concave mirror.
		In the case of the diverging mirror the parallel rays of light appear to diverge from F and it is known as a virtual focus.
	www.usd.edu /phys/labs/Optics/5_1_2/5_1_2c.html (1107 words)

	Spherical Coordinates
		In the last module we looked at cylindrical coordinates -- a system of coordinates that is very useful when the important things about a three-dimensional point are its distance from the z-axis and its angle from the positive xz-plane.
		In this module we look at situations in which the important things about a point are its distance from the origin and, using terms from geography, its latitude and longitude.
		in the denominator comes from the fact that the light intensity at a point is inversely proportional to the area of the hemisphere centered at the origin whose radius is the distance from the point to the origin.
	www.math.montana.edu /frankw/ccp/multiworld/multipleIVP/spherical/body.htm (1849 words)

	Math Forum - Ask Dr. Math
		The intermediate result c is the great circle distance in radians.
		The great circle distance d will be in the same units as R. Most computers require the arguments of trigonometric functions to be expressed in radians.
		The distance we get should be multiplied by R, the radius of the earth.
	www.mathforum.org /library/drmath/view/51879.html (1355 words)

	Perpendicular Distance Calculator
		Distance sampling is a widely-used group of closely related methods for estimating the density and/or abundance of a biological population (Thomas et al., 2002).
		Spherical computations require the geographic coordinates (i.e., latitude and longitude) of the observer or survey platform at the time of initial detection in addition to a detection angle and detection distance.
		In order to calculate perpendicular distance using spherical methods, three pairs of coordinates are needed; the geographic coordinates for the start and the end of each transect and the derived coordinates for each sighting or object of interest.
	geospatial.amnh.org /open_source/pdc/documentation.html (2026 words)

	KryssTal : Spherical Trigonometry
		The Cosine Rule allows the length of one of the arcs of a spherical triangle to be evaluated if the other two arcs and the angle opposite the arc are known.
		c is is the Polar Distance of London: 90° minus the Latitude of London (90° - 51.30° = 38.70°).
		The angle TOS is the Altitude, measured in degrees from the horizon.
	www.krysstal.com /sphertrig.html (4264 words)

	Close-up Lens Selection (Site not responding. Last check: 2007-10-10)
		It is when the book is held at this distance and then pushed just a little further away, so that the print is slightly blurred, that the maximum relaxing effect on the ciliary muscles of the eyes is achieved.
		Small amounts of astigmatism are usually ignored, allowing the use of spherical lenses without a cylindrical correction.
		That means that the spherical component and the astigmatic component which follows it are ground on the same lens.
	www.myopia.org /closeuplensselection.htm (443 words)

	Spherical Measures without Spherical Trigonometry (Site not responding. Last check: 2007-10-10)
		This is the chord distance between the two points, penetrating the sphere.
		The chord distance between the two points can be considered to be one side of a triangle, with origin at the center of a circle, whose other two sides have a length equal to the radius of the sphere.
		Twice this angle is the angle that spans the distance between the two points, that is, it is the angular separation of the points on the sphere.
	www-personal.umich.edu /~sarhaus/image/solstice/win01/tobler/tobler.html (590 words)

	ConeSound (Java 3D API)
		The distance is measured as the angle in radians between the ConeSound's direction vector and the vector from the sound source position to the listener.
		If angular distance from the listener-sound-position vector and a sound's direction vector is less than the first distance in the array, only the first gain scale factor and first filter are applied to the sound source.
		If the distance from the listener-sound-position vector and the sound's direction vector is greater than the last distance in the array, the last gain scale factor and last filter are applied to the sound source.
	java.sun.com /products/java-media/3D/forDevelopers/J3D_1_3_API/j3dapi/javax/media/j3d/ConeSound.html (3604 words)

	Optometric Management
		It incorporates a spherical center zone surrounded by an aspheric intermediate zone with another spherical zone in the periphery.
		The distance-centered lens integrates a 2.3 mm spherical distance prescription; the near-centered lens has a 1.7 mm spherical near prescription in the center.
		The distance center lens design usually needs a +0.25 added to the distance prescription while the near-centered lens requires -0.25 added to the distance prescription.
	www.optometric.com /article.aspx?article=70376 (1690 words)

	spherical geometry (Site not responding. Last check: 2007-10-10)
		of the early geometry of the Babylonians, Arabs, and Greeks was spherical geometry --the study of...
		Spherica l Geometry -- from MathWorld Spherical Geometry -- from MathWorld The study of figures on the surface of a sphere (such as the spherical triangle and spherical polygon), as opposed to the type of geometry studied in plane geometry or...
		Spherical geometry is the geometry of the two-dimensional surface of a sphere...
	learning-gd.com /articles/275/spherical-geometry.html (241 words)

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