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Near the Horizon: An Invitation to Geometric Optics
 
Near the Horizon
MAA Press: An Imprint of the American Mathematical Society
Hardcover ISBN:  978-0-88385-142-5
Product Code:  CAR/33
List Price: $75.00
MAA Member Price: $56.25
AMS Member Price: $56.25
eBook ISBN:  978-1-61444-030-7
Product Code:  CAR/33.E
List Price: $70.00
MAA Member Price: $52.50
AMS Member Price: $52.50
Hardcover ISBN:  978-0-88385-142-5
eBook: ISBN:  978-1-61444-030-7
Product Code:  CAR/33.B
List Price: $145.00 $110.00
MAA Member Price: $108.75 $82.50
AMS Member Price: $108.75 $82.50
Near the Horizon
Click above image for expanded view
Near the Horizon: An Invitation to Geometric Optics
MAA Press: An Imprint of the American Mathematical Society
Hardcover ISBN:  978-0-88385-142-5
Product Code:  CAR/33
List Price: $75.00
MAA Member Price: $56.25
AMS Member Price: $56.25
eBook ISBN:  978-1-61444-030-7
Product Code:  CAR/33.E
List Price: $70.00
MAA Member Price: $52.50
AMS Member Price: $52.50
Hardcover ISBN:  978-0-88385-142-5
eBook ISBN:  978-1-61444-030-7
Product Code:  CAR/33.B
List Price: $145.00 $110.00
MAA Member Price: $108.75 $82.50
AMS Member Price: $108.75 $82.50
  • Book Details
     
     
    The Carus Mathematical Monographs
    Volume: 332016; 163 pp

    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.

    The book is written in a very personal and engaging style. Broer is passionate about the subject and its history, and his passion helps carry the reader along. The result is readable and charming.

  • Table of Contents
     
     
    • Chapters
    • Chapter 1. Introduction and Overview
    • I. Geometry of light rays in the atmosphere
    • Chapter 2. Geometric optics
    • Chapter 3. Atmospheric optics
    • Chapter 4. Light and the cycloid
    • II. Light rays as geodesics
    • Chapter 5. The principles of Fermat and Hamilton
    • Chapter 6. The brachistochrone revisited
    • Chapter 7. Light rays as geodesics on a surface of revolution
    • Chapter 8. Scholium generale
  • Additional Material
     
     
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 332016; 163 pp

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.

The book is written in a very personal and engaging style. Broer is passionate about the subject and its history, and his passion helps carry the reader along. The result is readable and charming.

  • Chapters
  • Chapter 1. Introduction and Overview
  • I. Geometry of light rays in the atmosphere
  • Chapter 2. Geometric optics
  • Chapter 3. Atmospheric optics
  • Chapter 4. Light and the cycloid
  • II. Light rays as geodesics
  • Chapter 5. The principles of Fermat and Hamilton
  • Chapter 6. The brachistochrone revisited
  • Chapter 7. Light rays as geodesics on a surface of revolution
  • Chapter 8. Scholium generale
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.