Near The Horizon An Invitation To Geometric Optics

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Near the Horizon: An Invitation to Geometric Optics

Author : Henk W. Broer
Publisher : American Mathematical Soc.
ISBN 13 : 0883851423
Total Pages : 163 pages
Book Rating : 4.8/5 (838 download)

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Book Synopsis Near the Horizon: An Invitation to Geometric Optics by : Henk W. Broer

Download or read book Near the Horizon: An Invitation to Geometric Optics written by Henk W. Broer and published by American Mathematical Soc.. This book was released on 2016-12-31 with total page 163 pages. Available in PDF, EPUB and Kindle. Book excerpt: Near the Horizon starts out by considering several optical phenomena that can occur when the sun is near the horizon. One can sometimes see objects that are actually below the horizon. Sometimes there seems to be a dark strip in the middle of the solar disk. These are a result of the way that the atmosphere affects the geometry of light rays. Broer starts his book with the Fermat principle (rays of light take least-time paths) and deduces from it laws for refraction and reflection; by expressing these as conservation laws, he can handle both the case of inhomogeneous layers of air and the case of continuous variation in the refraction index. A surprising application is the brachistochrone problem, in which the path of fastest descent is determined by studying how a light ray would behave in a “flat earth” atmosphere whose refraction index is determined by the gravitational potential. This leads to a very interesting chapter on the cycloid and its properties. The final chapters move from the elementary theory to a more sophisticated version in which the Fermat Principle leads to a Riemannian metric whose geodesics are the paths of light rays. This gives us an optics which is geometric in a new sense, and serves as a nice demonstration of the physical applicability of Riemannian geometry.

Mathematical Theory of Optics

Author : R. K. Luneburg
Publisher : University of California Press
ISBN 13 : 0520328256
Total Pages : 480 pages
Book Rating : 4.5/5 (23 download)

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Book Synopsis Mathematical Theory of Optics by : R. K. Luneburg

Download or read book Mathematical Theory of Optics written by R. K. Luneburg and published by University of California Press. This book was released on 2021-01-08 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1964.

Geometrical Optics

Author : J. L. Synge
Publisher : CUP Archive
ISBN 13 :
Total Pages : 132 pages
Book Rating : 4./5 ( download)

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Book Synopsis Geometrical Optics by : J. L. Synge

Download or read book Geometrical Optics written by J. L. Synge and published by CUP Archive. This book was released on 1937-01-02 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is by no means easy for the applied mathematician to decide how much importance he should attach to the more abstract and aesthetic side of his work ... To all appearances, Sir William Rowan Hamilton (1850-1865) attached little importance to the practical applications of his method, and it was only with the publication of his Mathematical Papers that it was possible to form a more correct and balanced judgement of Hamilton as an applied mathematician.

Geometric Optics

Author : J. Warren Blaker
Publisher :
ISBN 13 :
Total Pages : 154 pages
Book Rating : 4.3/5 (97 download)

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Book Synopsis Geometric Optics by : J. Warren Blaker

Download or read book Geometric Optics written by J. Warren Blaker and published by . This book was released on 1971 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Geometrical Optics and Related Topics

Author : Ferrucio Colombini
Publisher : Springer Science & Business Media
ISBN 13 : 1461220149
Total Pages : 365 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Geometrical Optics and Related Topics by : Ferrucio Colombini

Download or read book Geometrical Optics and Related Topics written by Ferrucio Colombini and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains fourteen research papers which are expanded versions of conferences given at a meeting held in September 1996 in Cortona, Italy. The topics include blowup questions for quasilinear equations in two dimensions, time decay of waves in LP, uniqueness results for systems of conservation laws in one dimension, concentra tion effects for critical nonlinear wave equations, diffraction of nonlin ear waves, propagation of singularities in scattering theory, caustics for semi-linear oscillations. Other topics linked to microlocal analysis are Sobolev embedding theorems in Weyl-Hormander calculus, local solv ability for pseudodifferential equations, hypoellipticity for highly degen erate operators. The book also contains a result on uniqueness for the Cauchy problem under partial analyticity assumptions and an article on the regularity of solutions for characteristic initial-boundary value problems. On each topic listed above, one will find new results as well as a description of the state of the art. Various methods related to nonlinear geometrical optics are a transversal theme of several articles. Pseu dodifferential techniques are used to tackle classical PDE problems like Cauchy uniqueness. We are pleased to thank the speakers for their contributions to the meeting: Serge Alinhac, Mike Beals, Alberto Bressan, Jean-Yves Chemin, Christophe Cheverry, Daniele Del Santo, Nils Dencker, Patrick Gerard, Lars Hormander, John Hunter, Richard Melrose, Guy Metivier, Yoshinori Morimoto, and Tatsuo Nishitani. The meeting was made possible in part by the financial support of a European commission pro gram, "Human capital and mobility CHRX-CT94-044."

Geometric Optics

Author : Antonio Romano
Publisher : Birkhäuser
ISBN 13 : 3319437321
Total Pages : 289 pages
Book Rating : 4.3/5 (194 download)

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Book Synopsis Geometric Optics by : Antonio Romano

Download or read book Geometric Optics written by Antonio Romano and published by Birkhäuser. This book was released on 2016-09-26 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book—unique in the literature—provides readers with the mathematical background needed to design many of the optical combinations that are used in astronomical telescopes and cameras. The results presented in the work were obtained by using a different approach to third-order aberration theory as well as the extensive use of the software package Mathematica®. Replete with workout examples and exercises, Geometric Optics is an excellent reference for advanced graduate students, researchers, and practitioners in applied mathematics, engineering, astronomy, and astronomical optics. The work may be used as a supplementary textbook for graduate-level courses in astronomical optics, optical design, optical engineering, programming with Mathematica, or geometric optics.

Mathematical Theory of Optics

Author : Rudolf Karl Luneburg
Publisher : Univ of California Press
ISBN 13 :
Total Pages : 484 pages
Book Rating : 4./5 ( download)

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Book Synopsis Mathematical Theory of Optics by : Rudolf Karl Luneburg

Download or read book Mathematical Theory of Optics written by Rudolf Karl Luneburg and published by Univ of California Press. This book was released on 1964 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Geometric Optics on Phase Space

Author : Kurt Bernardo Wolf
Publisher : Springer
ISBN 13 : 9783642060366
Total Pages : 376 pages
Book Rating : 4.0/5 (63 download)

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Book Synopsis Geometric Optics on Phase Space by : Kurt Bernardo Wolf

Download or read book Geometric Optics on Phase Space written by Kurt Bernardo Wolf and published by Springer. This book was released on 2010-12-01 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: Symplectic geometry, well known as the basic structure of Hamiltonian mechanics, is also the foundation of optics. In fact, optical systems (geometric or wave) have an even richer symmetry structure than mechanical ones (classical or quantum). The symmetries underlying the geometric model of light are based on the symplectic group. Geometric Optics on Phase Space develops both geometric optics and group theory from first principles in their Hamiltonian formulation on phase space. This treatise provides the mathematical background and also collects a host of useful methods of practical importance, particularly the fractional Fourier transform currently used for image processing. The reader will appreciate the beautiful similarities between Hamilton's mechanics and this approach to optics. The appendices link the geometry thus introduced to wave optics through Lie methods. The book addresses researchers and graduate students.

Geometrical Optics

Author : John Lighton Synge
Publisher :
ISBN 13 :
Total Pages : 110 pages
Book Rating : 4.:/5 (974 download)

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Book Synopsis Geometrical Optics by : John Lighton Synge

Download or read book Geometrical Optics written by John Lighton Synge and published by . This book was released on 1962 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Teaching About Geometric Optics

Author : Jane Bray Nelson
Publisher :
ISBN 13 : 9780735422155
Total Pages : 280 pages
Book Rating : 4.4/5 (221 download)

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Book Synopsis Teaching About Geometric Optics by : Jane Bray Nelson

Download or read book Teaching About Geometric Optics written by Jane Bray Nelson and published by . This book was released on 2020 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: Teaching About Geometric Optics guides physics teachers to help students develop a foundational understanding of geometric optics. The cornerstone of photonics systems, geometric optics, have applications in a wide range of industries including technology, medical, and military sectors. This book covers the basics of light propagation, reflection and refraction and the use of simple optical elements such as mirrors, prisms, lenses, and optical fibers.

A Note on the Expansion Coefficient of Geometrical Optics

Author : Morris Kline
Publisher :
ISBN 13 :
Total Pages : 1 pages
Book Rating : 4.:/5 (227 download)

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Book Synopsis A Note on the Expansion Coefficient of Geometrical Optics by : Morris Kline

Download or read book A Note on the Expansion Coefficient of Geometrical Optics written by Morris Kline and published by . This book was released on 1961 with total page 1 pages. Available in PDF, EPUB and Kindle. Book excerpt: The expansion coefficient of geometrical optics is a measure of the cross section os, New York U., N.Y.A NOTE ON THE EXPANSION COEFFICIENT OF GEOMETRICAL OPTICS, by Morris Kline. 1961, 12p. (Research rept. no. EM-166) (Contract AF 19(604)5238) Unclassified report DESCRIPTORS: *Optics, *Electromagnetic theory, *Differential geometry, Light, Electron optics, Series, Geometry. The expansion coefficient of geometrical optics is a measure of the cross section of a tube of rays and has the physical significance of measuring the intensity of the light propagating along the tube. Strictly, it is a point concept and measures the intensity along an individual ray. This paper presents a convenient expression for the expansion coefficient. The mathematics involved is merely an application of known differential geometry but the expression derived seems to be new and is apparently unknown to workers in electromagnetic theory. The new feature of this paper is that the formula given for the variation of the expansion coefficient holds in inhomogeneous isotropic media and reduces immediately to the widely known expression for the expansion coefficient in homogeneous media, which involves the Gauss curvature of the wave front. (Author).

Geometric Optics

Author : Allen Nussbaum
Publisher :
ISBN 13 :
Total Pages : 132 pages
Book Rating : 4.:/5 (314 download)

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Book Synopsis Geometric Optics by : Allen Nussbaum

Download or read book Geometric Optics written by Allen Nussbaum and published by . This book was released on 1968 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Relativity and Scientific Computing

Author : Friedrich W Hehl
Publisher : Springer Science & Business Media
ISBN 13 : 3642957323
Total Pages : 405 pages
Book Rating : 4.6/5 (429 download)

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Book Synopsis Relativity and Scientific Computing by : Friedrich W Hehl

Download or read book Relativity and Scientific Computing written by Friedrich W Hehl and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: For this set of lectures we assumed that the reader has a reasonable back ground in physics and some knowledge of general relativity, the modern theory of gravity in macrophysics, and cosmology. Computer methods are present ed by leading experts in the three main domains: in numerics, in computer algebra, and in visualization. The idea was that each of these subdisciplines is introduced by an extended set of main lectures and that each is conceived as being of comparable 'importance. Therefpre we believe that the book represents a good introduction into scientific I computing for any student who wants to specialize in relativity, gravitation, and/or astrophysics. We took great care to select lecturers who teach in a comprehensible way and who are, at the same time, at the research front of their respective field. In numerics we had the privilege of having a lecturer from the National Center for Supercomputing Applications (NCSA, Champaign, IL, USA) and some from other leading institutions of the world; visualization was taught by a visualization expert from Boeing; and in com puter algebra we took recourse to practitioners of different computer algebra systems as applied to classical general relativity up to quantum gravity and differential geometry.

Bifurcations in Hamiltonian Systems

Author : Henk Broer
Publisher : Springer
ISBN 13 : 354036398X
Total Pages : 178 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Bifurcations in Hamiltonian Systems by : Henk Broer

Download or read book Bifurcations in Hamiltonian Systems written by Henk Broer and published by Springer. This book was released on 2003-01-01 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors consider applications of singularity theory and computer algebra to bifurcations of Hamiltonian dynamical systems. They restrict themselves to the case were the following simplification is possible. Near the equilibrium or (quasi-) periodic solution under consideration the linear part allows approximation by a normalized Hamiltonian system with a torus symmetry. It is assumed that reduction by this symmetry leads to a system with one degree of freedom. The volume focuses on two such reduction methods, the planar reduction (or polar coordinates) method and the reduction by the energy momentum mapping. The one-degree-of-freedom system then is tackled by singularity theory, where computer algebra, in particular, Gröbner basis techniques, are applied. The readership addressed consists of advanced graduate students and researchers in dynamical systems.

Perspective in the Visual Culture of Classical Antiquity

Author : Rocco Sinisgalli
Publisher : Cambridge University Press
ISBN 13 : 1139561162
Total Pages : 209 pages
Book Rating : 4.1/5 (395 download)

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Book Synopsis Perspective in the Visual Culture of Classical Antiquity by : Rocco Sinisgalli

Download or read book Perspective in the Visual Culture of Classical Antiquity written by Rocco Sinisgalli and published by Cambridge University Press. This book was released on 2012-09-17 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear perspective is a science that represents objects in space upon a plane, projecting them from a point of view. This concept was known in classical antiquity. In this book, Rocco Sinisgalli investigates theories of linear perspective in the classical era. Departing from the received understanding of perspective in the ancient world, he argues that ancient theories of perspective were primarily based on the study of objects in mirrors, rather than the study of optics and the workings of the human eye. In support of this argument, Sinisgalli analyzes, and offers new insights into, some of the key classical texts on this topic, including Euclid's De speculis, Lucretius' De rerum natura, Vitruvius' De architectura and Ptolemy's De opticis. Key concepts throughout the book are clarified and enhanced by detailed illustrations.

Spatial Augmented Reality

Author : Oliver Bimber
Publisher : CRC Press
ISBN 13 : 1439864942
Total Pages : 386 pages
Book Rating : 4.4/5 (398 download)

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Book Synopsis Spatial Augmented Reality by : Oliver Bimber

Download or read book Spatial Augmented Reality written by Oliver Bimber and published by CRC Press. This book was released on 2005-08-08 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: Like virtual reality, augmented reality is becoming an emerging platform in new application areas for museums, edutainment, home entertainment, research, industry, and the art communities using novel approaches which have taken augmented reality beyond traditional eye-worn or hand-held displays. In this book, the authors discuss spatial augmented r

EQUADIFF 2003

Author : Freddy Dumortier
Publisher : World Scientific
ISBN 13 : 9814480916
Total Pages : 1184 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis EQUADIFF 2003 by : Freddy Dumortier

Download or read book EQUADIFF 2003 written by Freddy Dumortier and published by World Scientific. This book was released on 2005-02-23 with total page 1184 pages. Available in PDF, EPUB and Kindle. Book excerpt: ' This comprehensive volume contains the state of the art on ODE's and PDE's of different nature, functional differential equations, delay equations, and others, mostly from the dynamical systems point of view. A broad range of topics are treated through contributions by leading experts of their fields, presenting the most recent developments. A large variety of techniques are being used, stressing geometric, topological, ergodic and numerical aspects. The scope of the book is wide, ranging from pure mathematics to various applied fields. Examples of the latter are provided by subjects from earth and life sciences, classical mechanics and quantum-mechanics, among others. The proceedings have been selected for coverage in: • Index to Scientific & Technical Proceedings® (ISTP® / ISI Proceedings) • Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings) • CC Proceedings — Engineering & Physical Sciences Contents: Computational Aspects of Differential Equations and ApplicationsWater WavesTopological and Variational MethodsQualitative Theory of Nonlinear Parabolic and Elliptic EquationsAround Hilbert's 16th ProblemNavier–Stokes Equations and Reaction Diffusion EquationsHyperbolic Dynamics and BeyondSymmetry and MechanicsShock Waves and Conservation LawsNonlinear Elliptic Partial Differential EquationsAlgebraic Aspects and Optimisation in Dynamical SystemsCase Studies in Theoretical Interpretation of Numerical ExperimentsInfinite-Dimensional DynamicsQuasiperiodicityDelay EquationsWave Stability and Pattern FormationNonautonomous DynamicsNormal Forms and Invariant ManifoldsSingular PerturbationsDifferential Geometric Foliations and FlowsHomoclinic and Heteroclinic DynamicsMathematical Aspects of Celestical Mechanics Readership: Graduate students and researchers in mathematics, especially in ODE and PDE areas. Keywords:Differential Equations;Dynamical Systems;ODE;PDE;Delay Equations;Water Waves;Hilbert''s 16th Problem'