Oblique Ray Method

4 Key excerpts on "Oblique Ray Method"

• 

  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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  eBook - ePub

  Physics for Students of Science and Engineering

  • A. L. Stanford, J. M. Tanner(Authors)
  • 2014(Publication Date)
  • Academic Press

    (Publisher)

  20

  Light: Geometric Optics

  Publisher Summary

  This chapter discusses geometric optics of light. Optics is the study of phenomena associated with light. The geometric approximation in the analysis of optical systems permits taking advantage of the concept of light rays. Light rays are lines perpendicular to the wavefronts and are directed at every point in the direction of propagation of the light. Geometric optics is the study of how light rays are reflected and refracted, or bent, in passing from one medium to another. In geometric optics, constructions of reflected and refracted light rays are used to analyze the formation of images. When light is incident upon a surface that is an interface between two media, some of the light is reflected and some is transmitted through the interface. Two principles form the theoretical basis of geometric optics. The principle of superposition for electromagnetic waves provides that the intersecting light rays do not alter the path of either ray. As per the second principle, called Fermat’s principle, in traveling from one point to another, light follows a path that requires the minimum time compared to the times that would be required along nearby paths.

  Optics is the study of phenomena associated with light. In Chapter 18 we saw that light is an electromagnetic wave, and we know from everyday experience that waves can bend around the edges of obstructions, an occurrence called diffraction. For example, sound waves that are diffracted around the corners of buildings or hallways can be heard. Light waves may be diffracted, too; in Chapter 21

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  eBook - ePub

  Engineering Optics with MATLAB®

  • Ting-Chung Poon, Taegeun Kim;;;(Authors)
  • 2017(Publication Date)
  • WSPC

    (Publisher)

  In Eq. (1.2-5), ϕ i is the angle of incidence for the incident ray and ϕ t is the angle of transmission (or angle of refraction) for the refracted ray. Both angles are measured from the normal to the surface. Again, as in reflection, the incident ray, the refracted ray, and the normal all lie in the same plane of incidence. Snell’s law shows that when a light ray passes obliquely from a medium of smaller refractive index n 1 into one that has a larger refractive index n 2, or an optically denser medium, it is bent toward the normal. Conversely, if the ray of light travels into a medium with a lower refractive index, it is bent away from the normal. For the latter case, it is possible to visualize a situation where the refracted ray is bent away from the normal by exactly 90°. Under this situation, the angle of incidence is called the critical angle ϕ c, given by When the incident angle is greater than the critical angle, the ray originating in medium 1 is totally reflected back into medium 1. This phenomenon is called total internal reflection. The optical fiber uses this principle of total reflection to guide light, and the mirage on a hot summer day is a phenomenon due to the same principle. 1.3 Ray Propagation in an Inhomogeneous Medium: Ray Equation In the last Section, we have discussed refraction between two media with different refractive indices, possessing a discrete inhomogeneity in the simplest case. For a general inhomogeneous medium, i.e., n (x, y, z), it is instructive to have an equation that can describe the trajectory of a ray. Such an equation is known as the ray equation. The ray equation is analogous to the equations of motion for particles and for rigid bodies in classical mechanics. The equations of motion can be derived from Newtonian mechanics based on Newton’s laws

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  eBook - ePub

  Engineering Optics with MATLAB®

  • Ting-Chung Poon, Taegeun Kim(Authors)
  • 2006(Publication Date)
  • WSPC

    (Publisher)

  OPL between the two end points is along a straight line which assumes the shortest time for the ray to travel.

  1.2 Reflection and Refraction

  When a ray of light is incident on the interface separating two different optical media characterized by n1 and n2 , as shown in Fig. 1.2 , it is well known that part of the light is reflected back into the first medium, while the rest of the light is refracted as it enters the second medium. The directions taken by these rays are described by the laws of reflection and refraction, which can be derived from Fermat's principle.

  In what follows, we demonstrate the use of the principle of least time to derive the law of refraction. Consider a reflecting surface as shown in Fig. 1.3 . Light from point A is reflected from the reflecting surface to point B, forming the angle of incidence ϕi and the angle of reflection ϕr , measured from the normal to the surface. The time required for the ray of light to travel the path AO + OB is given by t = (AO + OB)/ν, where ν is the velocity of light in the medium containing the points AOB. The medium is considered isotropic and homogeneous. From the geometry, we find

  Fig. 1.2 Reflected and refracted rays for light incident at the interface of two media. Fig. 1.3 Incident (AO) and reflected (OB) rays.

  According to the least time principle, light will find a path that extremizes t(z) with respect to variations in z. We thus set dt(z)/dz = 0 to get

  or so that

  which is the law of reflection. We can readily check that the second derivative of t(z) is positive so that the result obtained corresponds to the least time principle. In addition, Fermat's principle also demands that the incident ray, the reflected ray and the normal all be in the same plane, called the plane of incidence

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