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Radius Of Curvature (optics)
Radius of curvature (ROC) has specific meaning and sign convention in optical design. A spherical lens or mirror surface has a center of curvature located either along or decentered from the system local optical axis. The vertex of the lens surface is located on the local optical axis. The distance from the vertex to the center of curvature is the radius of curvature of the surface. The sign convention for the optical radius of curvature is as follows: * If the vertex lies to the left of the center of curvature, the radius of curvature is positive. * If the vertex lies to the right of the center of curvature, the radius of curvature is negative. Thus when viewing a biconvex lens from the side, the left surface radius of curvature is positive, and the right radius of curvature is negative. Note however that ''in areas of optics other than design'', other sign conventions are sometimes used. In particular, many undergraduate physics textbooks use the Gaussian sign conve ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lens Radii Sign Conventions
A lens is a transmissive optics, 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 lenses, compound lens consists of several simple lenses (''elements''), usually arranged along a common Optical axis, axis. Lenses are made from materials such as glass or plastic, and are Grinding (abrasive cutting), ground and Polishing, polished or Molding (process), molded to a desired shape. A lens can focus light to form an image, unlike a Prism (optics), 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 Near-sightedness, myopia and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Optic Axis
An optical axis is a line along which there is some degree of rotational symmetry in an optical system such as a camera lens, microscope or telescopic sight. The optical axis is an imaginary line that defines the path along which light propagates through the system, up to first approximation. For a system composed of simple lenses and mirrors, the axis passes through the center of curvature of each surface, and coincides with the axis of rotational symmetry. The optical axis is often coincident with the system's mechanical axis, but not always, as in the case of off-axis optical systems. For an optical fiber, the optical axis is along the center of the fiber core, and is also known as the ''fiber axis''. See also * Ray (optics) * Cardinal point (optics) In Gaussian optics, the cardinal points consist of three pairs of points located on the optical axis of a rotationally symmetric, focal, optical system. These are the '' focal points'', the principal points, and the nodal p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vergence (optics)
In optics, vergence is the angle formed by rays of light that are not perfectly parallel to one another. Rays that move closer to the optical axis as they propagate are said to be ''converging'', while rays that move away from the axis are ''diverging''. These imaginary rays are always perpendicular to the wavefront of the light, thus the vergence of the light is directly related to the radii of curvature of the wavefronts. A convex lens or concave mirror will cause parallel rays to focus, converging toward a point. Beyond that focal point, the rays diverge. Conversely, a concave lens or convex mirror will cause parallel rays to diverge. Light does not actually consist of imaginary rays and light sources are not single-point sources, thus vergence is typically limited to simple ray modeling of optical systems. In a real system, the vergence is a product of the diameter of a light source, its distance from the optics, and the curvature of the optical surfaces. An increase in c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cardinal Point (optics)
In Gaussian optics, the cardinal points consist of three pairs of points located on the optical axis of a rotationally symmetric, focal, optical system. These are the '' focal points'', the principal points, and the nodal points. For ''ideal'' systems, the basic imaging properties such as image size, location, and orientation are completely determined by the locations of the cardinal points; in fact only four points are necessary: the focal points and either the principal or nodal points. The only ideal system that has been achieved in practice is the plane mirror, however the cardinal points are widely used to ''approximate'' the behavior of real optical systems. Cardinal points provide a way to analytically simplify a system with many components, allowing the imaging characteristics of the system to be approximately determined with simple calculations. Explanation The cardinal points lie on the optical axis of the optical system. Each point is defined by the effect the optica ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Base Curve Radius
Base curve radius, or simply base curve, abbreviated BCR or BC, is the measure of an important parameter of a lens in optometry. On a spectacle lens, it is the flatter curvature of the front surface. On a contact lens it is the curvature of the back surface and is sometimes referred to as the back central optic radius (abbreviated BCOR). Typical values for a contact lens are from 8.0 to 10.0 mm. The base curve is the radius of the sphere of the back of the lens that the prescription describes (the lower the number, the steeper the curve of the cornea and the lens, the higher the number, the flatter the curve of the cornea and the lens). This number is important in order to allow the contact lens to fit well to the wearer's cornea for comfort, to facilitate tear exchange, and to allow oxygen transmission. See also * Lens shape *Radius of curvature (optics) Radius of curvature (ROC) has specific meaning and sign convention in optical design. A spherical lens ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Radius
In classical geometry, a radius ( : radii) of a circle or sphere is any of the line segments from its center to its perimeter, and in more modern usage, it is also their length. The name comes from the latin ''radius'', meaning ray but also the spoke of a chariot wheel. as a function of axial position ../nowiki>" Spherical coordinates In a spherical coordinate system, the radius describes the distance of a point from a fixed origin. Its position if further defined by the polar angle measured between the radial direction and a fixed zenith direction, and the azimuth angle, the angle between the orthogonal projection of the radial direction on a reference plane that passes through the origin and is orthogonal to the zenith, and a fixed reference direction in that plane. See also *Bend radius *Filling radius in Riemannian geometry *Radius of convergence *Radius of convexity * Radius of curvature *Radius of gyration ''Radius of gyration'' or gyradius of a body about the axis of ro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Radius Of Curvature (applications)
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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quadric Surface
In mathematics, a quadric or quadric surface (quadric hypersurface in higher dimensions), is a generalization of conic sections ( ellipses, parabolas, and hyperbolas). It is a hypersurface (of dimension ''D'') in a -dimensional space, and it is defined as the zero set of an irreducible polynomial of degree two in ''D'' + 1 variables; for example, in the case of conic sections. When the defining polynomial is not absolutely irreducible, the zero set is generally not considered a quadric, although it is often called a ''degenerate quadric'' or a ''reducible quadric''. In coordinates , the general quadric is thus defined by the algebraic equationSilvio LevQuadricsin "Geometry Formulas and Facts", excerpted from 30th Edition of ''CRC Standard Mathematical Tables and Formulas'', CRC Press, from The Geometry Center at University of Minnesota : \sum_^ x_i Q_ x_j + \sum_^ P_i x_i + R = 0 which may be compactly written in vector and matrix notation as: : x Q x^\mathrm + P x^\m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Axial Symmetry
Axial symmetry is symmetry around an axis; an object is axially symmetric if its appearance is unchanged if rotated around an axis. glossary of meteorology. Retrieved 2010-04-08. For example, a without trademark or other design, or a plain white tea saucer, looks the same if it is rotated by any angle about the line passing lengthwise through its center, so it is axially symmetric. Axial symmetry can also be [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conic Constant
In geometry, the conic constant (or Schwarzschild constant, after Karl Schwarzschild) is a quantity describing conic sections, and is represented by the letter ''K''. The constant is given by K = -e^2, where is the eccentricity of the conic section. The equation for a conic section with apex at the origin Origin(s) or The Origin may refer to: Arts, entertainment, and media Comics and manga * Origin (comics), ''Origin'' (comics), a Wolverine comic book mini-series published by Marvel Comics in 2002 * The Origin (Buffy comic), ''The Origin'' (Bu ... and tangent to the y axis is y^2-2Rx+(K+1)x^2 = 0 alternately x = \dfrac where ''R'' is the radius of curvature at . This formulation is used in geometric optics to specify oblate elliptical (), spherical (), prolate elliptical (), parabolic (), and hyperbolic () lens and mirror surfaces. When the paraxial approximation is valid, the optical surface can be treated as a spherical surface with the same radius. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Displacement (vector)
In geometry and mechanics, a displacement is a vector whose length is the shortest distance from the initial to the final position of a point P undergoing motion. It quantifies both the distance and direction of the net or total motion along a straight line from the initial position to the final position of the point trajectory. A displacement may be identified with the translation that maps the initial position to the final position. A displacement may be also described as a ''relative position'' (resulting from the motion), that is, as the final position of a point relative to its initial position . The corresponding displacement vector can be defined as the difference between the final and initial positions: s = x_\textrm - x_\textrm = \Delta In considering motions of objects over time, the instantaneous velocity of the object is the rate of change of the displacement as a function of time. The instantaneous speed, then, is distinct from velocity, or the time rate of cha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aspheric Lens
An aspheric lens or asphere (often labeled ''ASPH'' on eye pieces) is a lens (optics), lens whose surface profiles are not portions of a sphere or Cylinder (geometry), cylinder. In photography, a camera lens, 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 Aberration in optical systems, optical aberrations such as Astigmatism (optical systems), 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 lens, 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
