chapter 1, Geometrical Optics

Excerpt

In this chapter we will introduce most of the basic concepts of geometrical optics, although it is likely that most readers will be familiar with these concepts from a study of more elementary texts.

Although all of the basic principles of geometrical optics can be derived from a knowledge of the wave nature of light, we will not follow this approach here. Except in special cases, an understanding of the rigorous derivations of these principles is not helpful in lens design.

However, we will discuss the limitations of geometrical optics when they are relevant to lens design, because there are situations in which an understanding of physical optics is absolutely essential. In lens design, as in other branches of applied science, it is most helpful to use the simplest approximation that can be used for any given task.

Geometrical optics can be considered to describe, with a high degree of accuracy, the properties of lenses as the wavelength of the radiation, λ, approaches zero. In this situation, diffraction effects disappear. So geometrical optics will be quite accurate for the design of short-wavelength x-ray imaging systems (if the wavelength is short enough). On the other hand, geometrical optics is rarely completely adequate for the design of thermal imaging systems operating at wavelengths around 10 μm. In the visible waveband, some lenses can be designed and evaluated completely by using geometrical optics, while the evaluation of other lenses must use physical optics. However, in almost all cases, lenses are actually designed using the results of geometrical optics.

1.1 Coordinate system and notation

In this book we discuss primarily the design of centered optical systems. We define the optical axis of a lens to be the z-axis, with the y-axis in the plane of the diagram, in Fig. 1.1. The x-axis is orthogonal to the y- and z-axes; in a right-handed coordinate system the x-axis is positive into the diagram. In the case of lenses that are centered, the z-axis represents the common optical axis of the refracting and reflecting surfaces.

In many equations in geometrical optics, we are concerned with quantities that are affected by refraction or reflection at a surface or at a lens. In these cases, we represent quantities after refraction or reflection as primed quantities; for example, we shall see that we write n′ for the refractive index after a surface in Eq. (1.1) below.