Waves refract at the boundary of shallow and deep water due to a change in their speed and direction as they encounter the varying water depths. Refraction occurs because the speed of a wave is dependent on the depth of the water it travels through.
When a wave approaches a boundary between shallow and deep water at an angle, different portions of the wave encounter varying water depths. The shallow water near the shoreline has a shallower depth compared to the deeper water further offshore.
As the wave moves from deep water to shallow water, the part of the wave that encounters the shallower depth slows down because the speed of the wave is inversely proportional to the depth of the water it travels through. The portion of the wave that first reaches the shallow water experiences a decrease in speed, causing it to slow down, while the rest of the wave in deeper water continues at its original speed.
Since the wave front has a different speed in shallow water compared to deep water, the wave front changes direction at the boundary. This change in direction is called refraction. The wave bends or curves towards the shoreline, with the portion of the wave in shallow water moving slower and closer to the perpendicular to the shoreline.
The bending or refraction of waves at the boundary of shallow and deep water is a result of the wave's attempt to maintain a consistent speed. This phenomenon is responsible for the gradual breaking of waves as they approach the shore, as well as the observed patterns of wave motion and energy distribution along coastlines.