Question

Why does a wave undergo a 180° phase change at a fixed boundary?

Answer 1

Answer:

The phase change of $180^{o}$ can be theoretically understood as follows:

For transmission or propagation of waves between media the wave motion should maintain a principle of continuity meaning that the wave function at the interface should be continuous and diffrentiable at the interface.

At the point of incidence there are 2 types of waves reflected wave and the incident wave. Now the principle of continuity dictates that the sum of the phases of the above 2 waves should be same as that of transmitted wave. If we use these relations we notice that the reflected wave shall either change it's phase by $180^{o}$ or will not change it's phase depending on the relationship between the refractive indices of the incident and the reflecting medium. For a solid boundary a phase change of $180^{o}$ occurs.