Ray Diagrams

4 Key excerpts on "Ray Diagrams"

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  eBook - ePub

  Understanding Physics

  • Michael M. Mansfield, Colm O'Sullivan(Authors)
  • 2020(Publication Date)
  • Wiley

    (Publisher)

  23 Geometrical optics

  AIMS

  • to introduce the ray model and to ascertain how it explains the phenomena of reflection and refraction
  • to describe how the ray model explains image formation in mirrors and lenses
  • to explain the operation of certain optical instruments
  • to discuss dispersion of light in transparent media

  23.1 The ray model: geometrical optics

  Consider a geometrical area which is a long way from a source of waves as shown shaded in Figure 23.1 . The spherical wavefronts that pass through such an area emerge almost parallel. These waves, therefore, can be approximated to plane waves and, in the limit of the shaded area in Figure 23.1 becoming very small, may be considered to travel in an infinitesimally narrow beam.

  Figure 23.1

  A ray of light as the limit of a very narrow beam of plane waves.

  Figure 23.2

  Rays from a point source of light; the figure shows just a few of the infinite number of such rays envisaged in the ray model.

  In such a situation the energy of the wave may be considered to propagate in straight lines, as it does in the case of particles. This model of wave propagation leads to the concept of a light ray in geometrical optics, the ray being always perpendicular to the wavefront. Thus, a point source of light may be considered to be a source of rays emanating radially from the source in all directions (Figure 23.2

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  Rays, Waves, and Scattering

  Topics in Classical Mathematical Physics

  • John Adam(Author)
  • 2017(Publication Date)
  • Princeton University Press

    (Publisher)

  PART I Rays Chapter Two Introduction to the “Physics” of Rays It is common physical knowledge that wavefields (acoustic, electromagnetic, etc.) rather than rays are a physical reality. Nonetheless, the traditions to endow rays with certain physical properties, traced back to Descartes’ times, have been deeply enrooted in natural science. Rays are discussed as if they were real objects. This handling of rays is justified when rays can be localized in space. [174] 2.1 WHAT IS A RAY ? In optics, a ray is a mathematical idealization of an infinitesimally narrow beam of light. In other words, it doesn’t exist in the physical world, only in a mathematical realm. They are mathematical models that, like many models, can be extremely valuable despite their shortcomings. Specifically, they are geometrical objects as opposed to physical ones, and this gives rise to the subject of geometrical optics . As we shall see, rays may (usually) be regarded as normals to wavefronts (or to surfaces of constant phase). Clearly at this point the more an attempt is made to describe rays, the more things that have to be described! We shall therefore proceed as if rays were real physical entities. In this spirit, rays have positions, directions, and speeds, and they “carry” energy, while the “density” of rays is a measure of power per unit area. They can propagate in homogeneous or inhomogeneous media, but in the former they do so in straight lines, these being mathematical models of the path in which light travels in such media. In the latter, if the properties of the medium vary continuously, the rays paths of light are in general curved; if the properties of the medium are discontinuous the rays will undergo reflection (and possibly refraction). It is particularly important to note that ray paths are reversible.

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  eBook - ePub

  Fundamentals of Photonics

  • Bahaa E. A. Saleh, Malvin Carl Teich(Authors)
  • 2020(Publication Date)
  • Wiley

    (Publisher)

  Chapter 1 RAY OPTICS

  1. 1.1 POSTULATES OF RAY OPTICS
  2. 1.2 SIMPLE OPTICAL COMPONENTS
     1. A. Mirrors
     2. B. Planar Boundaries
     3. C. Spherical Boundaries and Lenses
     4. D. Light Guides
  3. 1.3 GRADED-INDEX OPTICS
     1. A. The Ray Equation
     2. B. Graded-Index Optical Components
     3. *C. The Eikonal Equation
  4. 1.4 MATRIX OPTICS
     1. A. The Ray-Transfer Matrix
     2. B. Matrices of Simple Optical Components
     3. C. Matrices of Cascaded Optical Components
     4. D. Periodic Optical Systems

  Sir Isaac Newton (1642–1727) set forth a theory of optics in which light emissions consist of collections of corpuscles that propagate rectilinearly.

  Pierre de Fermat (1601–1665) enunciated a rule, known as Fermat’s Principle, in which light rays travels along the path of least time relative to neighboring paths.

  Light can be described as an electromagnetic wave phenomenon governed by the same theoretical principles that govern all other forms of electromagnetic radiation, such as radio waves and X-rays. This conception of light is called electromagnetic optics. Electromagnetic radiation propagates in the form of two mutually coupled vector waves, an electric-field wave and a magnetic-field wave. Nevertheless, it is possible to describe many optical phenomena using a simplified scalar wave theory in which light is described by a single scalar wavefunction. This approximate way of treating light is called scalar wave optics, or simply wave optics.

  When light waves propagate through and around objects whose dimensions are much greater than the wavelength of the light, the wave nature is not readily discerned and the behavior of light can be adequately described by rays obeying a set of geometrical rules. This model of light is called ray optics. From a mathematical perspective, ray optics is the limit of wave optics when the wavelength is infinitesimally small.

  Thus, electromagnetic optics encompasses wave optics, which in turn encompasses ray optics, as illustrated in Fig. 1.0-1

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  Gratings, Mirrors and Slits

  Beamline Design for Soft X-Ray Synchrotron Radiation Sources

  • WB Peatman(Author)
  • 2018(Publication Date)
  • Routledge

    (Publisher)

  3.2 RAY TRACING Just as Fermat's principle attempts to describe natural principles with words, a ray trace program is designed to put the ideas of the beamline designer into plots and numbers. The basic idea of a ray trace program is simple: optical paths, or rays, are traced through a system of optical elements, the laws of geometrical optics being observed at all times. In the vacuum ultraviolet and soft x-ray portion of the spectrum only three optical principles are required for a basic ray trace program: a) the optical path between physical elements of the optical system is a straight line, b) the angle of reflection is equal to the angle of incidence and c) diffraction phenomena are governed by Bragg's law. With these three relationships the behavior of many optical systems for photon energies from, say, 10 to 2000 eV can be quantitatively scrutinized. Over the course of recent years many ray trace programs have been written to assist in beamline design. Most of these have been for personal use and not intended for others. Hence, they have been designed for some specific application and need only be understood by their respective authors. There are, however, at least two ray trace programs that have been written for general use in beamline design which are capable of dealing with almost all of the optical elements and possible situations that one may encounter at synchrotron radiation laboratories. In addition, they have been continually debugged and improved over many years and great effort has been made by their authors to make them understandable and easily usable. They are SHADOW [1.3] and RAY [1.4]. These programs are available from their authors and the reader is urged to contact them for details. Regardless of the particular program used, a ray trace program of some sort is essential for the design of beamlines for synchrotron radiation. The conventional definitions of the toroid, the parabola and the ellipse, a.

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