Lesson No. 17: Snell’s Law—Principle of Least Time
Published:January 01, 1959
A fundamental result in the mathematical discussion of wave propagation is the concept known as Fermat*#x0027;s Principle. Stated for our purposes, it runs somewhat like this: The study of the propagation of waves may be reduced to the study of wave paths which are defined as the paths along which the travel-times are minimal. We proceed to expand on this subject.
Consider a moving wave front. Corresponding to it is a family of wave paths (see Lesson No.1). Choose any two points lying on anyone of these wave paths. Of all possible paths joining those two points, the wave path is that for which the travel-time is least. In other words, the travel-time along any other path (within suitable limits) joining those two points would be greater than along the wave path.
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Lessons in Seismic Computing
“An elementary text and problem book containing 44 lessons in seismology arranged for selection or combination to cover the normal 36-week course, or for condensation into an 18-week course. The lessons begin without assuming more than secondary school mathematics. An elementary knowledge of calculus is desirable, though not required, for the last half of the book.”