Oscillations and Waves > Wave propagation > Problem 3.7.14

Statement

A plane wave is incident on a plane interface with sound velocity at angle to the normal. Find the direction of propagation of the reflected and refracted wave if the velocity of the wave in the second medium is equal to .

Solution

The blue lines in the figure are the same wavefront at different equally-spaced time points. The incident angle is . When the wavefront reaches the interface of the two media at , , , these points become sources of new spherical waves. (The figure shows the moment when the wavefront has just reached .) Since the red spherical wave originating from is tangent to the first blue line and the reflected wavefront (as the speed of the wavefront equals the speed of sound), we have . Thus, the reflected angle .

The ratio of the radii of the red and green spherical waves originating from is . Consequently,

Therefore, the refracted angle is

Answer

Reflected angle = .

Refracted angle = .