Fundamental to the understanding of physical optics is, of course, the concept of light as a wave disturbance. In this first chapter, we examine mathematically the simplest situations in which the wave nature of light manifests itself. Consider, for example, the passage of a light beam through a small opening in an opaque screen. The ray optics description of this situation leads to the conclusion that the size of the spot of light observed on a second screen some distance from the first will be simply proportional to the size of the hole.
This, of course, is an oversimplification. One finds, in fact, that such a proportionality law holds quite well for fairly large holes (the language is purposely vague at this point) but does not apply at all for smaller holes. In fact, if the transition from illuminated to nonilluminated areas is examined carefully, the geometric predictions do not hold even for large holes. Furthermore, as the hole is made smaller, the observed spot of light will actually increase as the diameter of the hole decreases - an attempt to illustrate this point is shown in Fig. 1.1. This figure shows a series of photographs of the intensity distribution recorded in a plane 30 cm behind a series of apertures illuminated with a collimated beam of quasimonochromatic light. The magnification is 20 x and the size of each aperture is indicated. In each case, the letters of the alphabet correspond to each other. Quite clearly, simple geometric predictions are inadequate. This chapter is devoted to obtaining a mathematical description of phenomena such as those illustrated here.
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