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In addition to the two “minimum time” paths from 0 to P of Figure 54 (the “direct,” straight line path OP, and the reflected path ORP) that we have discussed in the last lesson, there is yet another of basic importance, insofar as the problem of two beds is concerned, provided that the velocity of propagation, V2, in the lower bed is greater than the velocity, VI, in the upper bed. This third path which we shall now introduce is a refraction path.

We begin by reconsidering the wave fronts involved in these two minimum time paths. As a consequence of the shot explosion at 0 (Figure 56), the energy radiates from that point so that the successive positions of the wave front are spheres and the corresponding paths are the straight lines radiating from O. We consider simply a vertical plane section of this situation and, for the present, also assume the interface 1'1 to be a plane parallel to the surface S'S, so that all vertical sections through 0 are alike.

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