In this lesson we will consider the propagation of waves. Fermat's Principle states that the propagation of waves can be reduced to the study of wave paths along which the travel time is minimal. Wave paths are curves that represent the direction of travel of a wave. Wave paths intersect the wave fronts at right angles. Fermat's principle states that of all possible paths joining two given points on a wave path, the wave path has actual least travel time. The travel time along any other path joining these points will be greater than the travel time along the wave path. This is why Fermat's Principle is also known as the principle of least time.
In a medium in which the velocity is constant the wave paths are straight lines. The travel time t is then
where L is the length of the line joining the two points and v is the velocity.