A.  Constructive and destructive interference

Figure 4-7 shows two "point" sources of light, S and S¢, whose radiating waves maintain a fixed phase relationship with each other as they travel outward. The emerging waves are in effect spherical, but we show them as circular in the two-dimensional drawing. The solid circles represent crests, the dashed circles, troughs.

Earlier, in Figure 4-5a, we saw the effect of constructive interference for waves perfectly in phase and, in Figure 4-5b, the effect of destructive interference for waves perfectly out of phase. In Figure 4-7, along directions OP, OP₂, and OP₂¢ (emphasized by solid dots) crests from S and S¢ meet (as do the troughs), thereby creating a condition of constructive interference. As a result, light striking the screen at points P, P₂, and P₂¢ is at a maximum intensity and a bright spot appears. By contrast, along directions OP₁ and OP₁¢ (emphasized by open circles) crests and troughs meet each other, creating a condition of destructive interference. So at points P₁ and P₁¢ on the screen, no light appears, leaving a dark spot.

Figure 4-7  Wave interference created by overlapping waves from
coherent sources S and S¢

The requirement of coherent sources is a stringent requirement if interference is to be observed. To see this clearly, suppose for a moment that sources S and S¢ in Figure 4-7 are, in fact, two corks bobbing up and down on a quiet pond. As long as the two corks maintain a fixed relationship between their vertical motions, each will produce a series of related crests and troughs, and observable interference patterns in the overlap region will occur. But if the two corks bob up and down in a random, disorganized manner, no series of related, fixed-phase crests and troughs will form and no interference patterns of sufficiently long duration can develop, and so interference will not be observed.