CHAPTER 1

Geometric Optics

Geometric optics is the study of light and images using geometric principles. In contrast, physical optics emphasizes the wave nature of light, and quantum optics (not covered in this text) emphasizes the particle nature of light and the interaction of light and matter. Geometric optics uses linear rays to represent the paths traveled by light.

This introductory chapter discusses the basic concepts of geometric optics that form the foundation for deeper understanding of the topics covered in subsequent chapters. Included are 6 Clinical Examples and 24 end-of-section and end-of-chapter exercises to reinforce these concepts. The chapter starts by discussing rays, refraction, and reflection; object and image characteristics; light propagation and the lensmaker’s equation; vergence and reduced vergence; and ophthalmic lenses. After a set of exercises, the discussion continues with focal lengths and afocal systems, followed by another set of exercises. The final section discusses thick lenses, aberrations, mirrors, spherocylindrical lenses, and prisms. The end-of-chapter exercises are followed by 2 chapter appendixes with additional details.

Rays, Refraction, and Reflection

Introduction

Imagine a point source of light emitting light waves heading away from the point in all directions. If the medium in which the light travels is uniform, such that the wavefronts move at the same speed in all directions heading away from the source, then the expanding wavefronts are spherical. In geometric optics, we consider a ray to be an arrow denoting the direction of propagation of energy perpendicular to a wavefront surface. A ray is not a vector, as we do not attach any meaning to its length. If the medium is not uniform, such that light travels through regions of it at various speeds, then the expanding wavefronts become nonspherical and the rays will not form straight lines (Fig 1-1). This phenomenon explains how, for example, the regions of more and less dense air over a hot desert can form a mirage; to a thirsty observer, the image of a lake appears to come from a place other than where the lake is.

Figure 1-1 Rectilinear propagation of light through uniform medium. Here, the speed of light is constant with spherical wavefronts and straight rays. Note that in nonuniform medium, the speed of light is variable and rays are not straight.

(Illustration developed b y Leon Strauss, MD, PhD.)

Let’s assume that our light travels only in uniform media, so that we do have spherical wavefronts and straight-line rays; we will find that we can analyze the rays to understand what happens when the waves meet the interface between one uniform medium and another, and either travel into the new medium (refraction), bounce back into the first medium (reflection), or are lost as heat (absorption).

Refraction and reflection are called diffuse if the interface is so rough that the direction of the wavefronts is lost; they are called specular if there continues to be an identifiable direction of propagation of the wavefronts (Figs 1-2, 1-3).

Figure 1-3 Light striking a smooth surface is specularly reflected and/or refracted. θi = angle of incidence; θr = angle of

refraction. (Illustration developed b y Edmond H. Thall, MD, and Kevin M. Miller, MD, and rendered b y C. H. Wooley.)