ABSTRACT
Geometrical optics is a branch of optics that typically examines the transfer of light from a source to some destination via an optical system. These systems can be composed of multiple lenses, mirrors, prisms, and windows. Consequently, geometrical optics concerns itself with the refraction and reflection of light at interfaces and its propagation through various media. Light exhibits wave phenomenon such as interference and diffraction (treated in Chapter 5). However, the description of refraction, reflection, and propagation of waves is mathematically intensive. Geometrical optics makes a series of approximations that vastly
simplifies the analysis. These approximations are valid for incoherent light. The main approximation of geometrical optics is to replace the wavefront with a series of rays and analyze how the rays move through space and interact with objects. Rays represent the local normals to wavefronts and illustrate the direction of propagation of the wave at a given point. In homogeneous materials, rays will travel in a straight line until they reach a boundary. At the boundary, the rays will refract and reflect and then continue their straight-line propagation in the ensuing material. This simplification enables optical systems to be designed and analyzed in a straightforward manner leading to systems for illumination or imaging having the desired properties of the designer. This chapter examines the basic description of the properties of rays and their interaction with optical elements
3.1.1 What is geometrical optics? 27 3.1.2 Sign convention 28 3.1.3 Wavelength, speed of light, and refractive index 28
3.2 Waves, rays 28 3.2.1 Vergence 28 3.2.2 Rays and wavefronts 29
3.3 Laws of refraction and reflection 29 3.3.1 Reflection from a planar surface 29 3.3.2 Snell’s law at an interface 29 3.3.3 Total internal reflection 30 3.3.4 Prisms 30
3.4 Refraction and reflection from a spherical surface 30 3.4.1 Refraction from a spherical surface 30 3.4.2 Reflection from a spherical mirror 31
3.5 Gaussian imaging equation 32 3.5.1 Thick lenses and Gaussian imaging 32 3.5.2 Cardinal points 33 3.5.3 Aperture stop and pupils 34 3.5.4 Chief and marginal rays 34
3.6 Cylindrical and toric surfaces 34 3.6.1 Power and axis of a cylindrical lens 34 3.6.2 Toric and spherocylindrical surfaces 34
3.7 Visual instruments 37 3.7.1 Simple magnifier and magnifying power 37 3.7.2 Microscopes 37 3.7.3 Telescopes and angular magnification 38
3.8 Summary 38
such as lenses and prisms. In addition, definitions for the various properties of optical systems are provided.
