Answer:
The phase change of [tex]180^{o}[/tex] 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 [tex]180^{o}[/tex] 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 [tex]180^{o}[/tex] occurs.