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.

Near the Horizon

Author : Hendrik Wolter Broer
Publisher :
ISBN 13 : 9781614440307
Total Pages : pages
Book Rating : 4.4/5 (43 download)

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Book Synopsis Near the Horizon by : Hendrik Wolter Broer

Download or read book Near the Horizon written by Hendrik Wolter Broer and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

A Treatise on Geometrical Optics

Author : Robert Alfred Herman
Publisher :
ISBN 13 :
Total Pages : 366 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis A Treatise on Geometrical Optics by : Robert Alfred Herman

Download or read book A Treatise on Geometrical Optics written by Robert Alfred Herman and published by . This book was released on 1900 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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.

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."

Teaching about Geometric Optics

Author : Jane Bray Nelson
Publisher :
ISBN 13 : 9780735422148
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:

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:

Modern Geometrical Optics

Author : Max Herzberger
Publisher :
ISBN 13 :
Total Pages : 524 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Modern Geometrical Optics by : Max Herzberger

Download or read book Modern Geometrical Optics written by Max Herzberger and published by . This book was released on 1958 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Geometric Optics

Author : Allen Nussbaum
Publisher : Addison-Wesley
ISBN 13 :
Total Pages : 148 pages
Book Rating : 4.:/5 (319 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 Addison-Wesley. This book was released on 1968 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Geometrical Optics

Author : John Lighton Synge
Publisher :
ISBN 13 :
Total Pages : 110 pages
Book Rating : 4.:/5 (758 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 1937 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Teaching About Geometric Optics

Author : Jane Bray Nelson
Publisher :
ISBN 13 : 9780735422759
Total Pages : 336 pages
Book Rating : 4.4/5 (227 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 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Teaching About Geometric Optics: Teacher’s Notes 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.

Geometrical Optics

Author : John Lighton Synge
Publisher :
ISBN 13 :
Total Pages : 110 pages
Book Rating : 4.:/5 (462 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 1937 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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).

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

The Optical Unconscious

Author : Rosalind E. Krauss
Publisher : MIT Press
ISBN 13 : 9780262611053
Total Pages : 374 pages
Book Rating : 4.6/5 (11 download)

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Book Synopsis The Optical Unconscious by : Rosalind E. Krauss

Download or read book The Optical Unconscious written by Rosalind E. Krauss and published by MIT Press. This book was released on 1994-07-25 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Optical Unconscious is a pointed protest against the official story of modernism and against the critical tradition that attempted to define modern art according to certain sacred commandments and self-fulfilling truths. The account of modernism presented here challenges the vaunted principle of "vision itself." And it is a very different story than we have ever read, not only because its insurgent plot and characters rise from below the calm surface of the known and law-like field of modernist painting, but because the voice is unlike anything we have heard before. Just as the artists of the optical unconscious assaulted the idea of autonomy and visual mastery, Rosalind Krauss abandons the historian's voice of objective detachment and forges a new style of writing in this book: art history that insinuates diary and art theory, and that has the gait and tone of fiction. The Optical Unconscious will be deeply vexing to modernism's standard-bearers, and to readers who have accepted the foundational principles on which their aesthetic is based. Krauss also gives us the story that Alfred Barr, Meyer Shapiro, and Clement Greenberg repressed, the story of a small, disparate group of artists who defied modernism's most cherished self-descriptions, giving rise to an unruly, disruptive force that persistently haunted the field of modernism from the 1920s to the 1950s and continues to disrupt it today. In order to understand why modernism had to repress the optical unconscious, Krauss eavesdrops on Roger Fry in the salons of Bloomsbury, and spies on the toddler John Ruskin as he amuses himself with the patterns of a rug; we find her in the living room of Clement Greenberg as he complains about "smart Jewish girls with their typewriters" in the 1960s, and in colloquy with Michael Fried about Frank Stella's love of baseball. Along the way, there are also narrative encounters with Freud, Jacques Lacan, Georges Bataille, Roger Caillois, Gilles Deleuze, and Jean-François Lyotard. To embody this optical unconscious, Krauss turns to the pages of Max Ernst's collage novels, to Marcel Duchamp's hypnotic Rotoreliefs, to Eva Hesse's luminous sculptures, and to Cy Twombly's, Andy Warhol's, and Robert Morris's scandalous decoding of Jackson Pollock's drip pictures as "Anti-Form." These artists introduced a new set of values into the field of twentieth-century art, offering ready-made images of obsessional fantasy in place of modernism's intentionality and unexamined compulsions.