Near the Horizon: An Invitation to Geometric Optics PDF Download
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Author: Henk W. Broer
Publisher: American Mathematical Soc.
ISBN: 0883851423
Category : Mathematics
Languages : en
Pages : 178
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Book Description
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.
Author: Henk W. Broer
Publisher: American Mathematical Soc.
ISBN: 0883851423
Category : Mathematics
Languages : en
Pages : 178
Get Book Here
Book Description
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.
Author: Hendrik Wolter Broer
Publisher:
ISBN: 9781614440307
Category :
Languages : en
Pages :
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Book Description
Author: Rocco Sinisgalli
Publisher: Cambridge University Press
ISBN: 1139561162
Category : Art
Languages : en
Pages : 209
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Book Description
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.
Author: Henk Broer
Publisher: Springer
ISBN: 354036398X
Category : Mathematics
Languages : en
Pages : 178
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Book Description
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.
Author: Rosalind E. Krauss
Publisher: MIT Press
ISBN: 9780262611053
Category : Design
Languages : en
Pages : 374
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Book Description
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.
Author: Friedrich W Hehl
Publisher: Springer
ISBN: 9783642957345
Category : Science
Languages : en
Pages : 389
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Book Description
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.
Author: Oliver Bimber
Publisher: CRC Press
ISBN: 1439864942
Category : Computers
Languages : en
Pages : 386
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Book Description
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
Author: Freddy Dumortier
Publisher: World Scientific
ISBN: 9814480916
Category : Mathematics
Languages : en
Pages : 1180
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Book Description
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
Author: Martin Harwit
Publisher: Springer Science & Business Media
ISBN: 147572019X
Category : Science
Languages : en
Pages : 642
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Book Description
My principal aim in writing this book was to present a wide range of astrophysical topics in sufficient depth to give the reader a general quantitative understanding of the subject. The book outlines cosmic events but does not portray them in detail-it provides aseries of astrophysical sketches. I think this approach befits the present uncertainties and changing views in astrophysics. The material is based on notes I prepared for a course aimed at seniors and beginning graduate students in physics and astronomy at Cornell. This course defined the level at which the book is written. For readers who are versed in physics but are unfamiliar with astronomical terminology, Appendix A is included. It gives a brief background of astronomical concepts and should be read before starting the main text. The first few chapters outline the scope of modern astrophysics and deal with elementary problems concerning the size and mass of cosmic objects. However, it soon becomes apparent that a broad foundation in physics is needed to proceed. This base is developed in Chapters 4 to 7 by using, as ex am pIes, specific astronomi cal situations. Chapters 8 to 10 enlarge on the topics first outlined in Chapter I and show how we can obtain quantitative insights into the structure and evolution of stars, the dynamics of co~mic gases, and the large-scale behavior of the universe.
Author: Abraham Rees
Publisher:
ISBN:
Category : Encyclopedias and dictionaries
Languages : en
Pages : 838
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Book Description
