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Chapter 9:
Diffraction and Interference
Abstract
Interference describes the phenomenon of wave superposition in which the resulting wave has an amplitude that depends on the phase of the component waves. This is commonly demonstrated in physics when two waves of the same amplitude and frequency meet at a point in space. The two waves will superimpose at that point, and the result will be either a diminishment or an enhancement of the wave. When the crest of one wave and the trough of another wave meet, the two waves are out of phase by 180 deg, and they will cancel each other, while when two crests or two troughs meet each other, they are in phase, and the waves will reinforce each other.1–5 However, this is just one example; waves of differing frequency and amplitude will also interfere, although the resulting wave can take a very complicated form. Diffraction, which is caused by the interaction of waves with an object (or its inverse such as a slit), will cause the light to bend into the region of shadow. The resulting waves will superimpose, resulting in an interference pattern. Diffraction thus can be considered as a generator of interference patterns caused by a wave passing by an object. Since interference and diffraction are so tightly related, it is good to recognize that interference is used to describe the effect of the superposition of waves, while diffraction refers to the effects of waves passing an obstacle or a slit. One other phenomenon that drives the manner in which light interacts is coherence, which describes how waves relate to each other both spatially and temporally. In particular, coherent waves will have a constant phase difference within themselves and with respect to other waves of interest. These three concepts, diffraction, interference, and coherence drive many of the optical phenomena that we deal with in optical design and engineering. Changes to any one of these concepts leads to a new and interesting result. Many early physics experiments in optics dealt with these three concepts, of which the single- and double-slit experiments can be used to gain considerable insight. In this chapter we will explore different calculations related to these effects.