[wave]兀(pie)phrase change

I think you ask why there is a phase change of pi when waves are reflected on a denser medium.
You could read the following web-pages which contain answer to your question:
http://www.madsci.org/posts/archives/1998-05/895429359.Ph.q.html
http://www.madsci.org/posts/archives/1998-05/895429359.Ph.r.html
Basically, the principle is that particles in the denser medium are not as free as those in the less dense one, so that forced vibrations of dense medium particles by the incident wave cannot follow so easily the vibrations of paticles in the less dense medium. That is to say, there is a "lag-behind" of vibrations. As a result, the reflected wave will suffer a phase change which indicates the "lagging behind phenomenon" of the reflected wave.
But you have to make use of Maxwell's electromagnetic equations to prove the lag-behind of the reflected wave is exavtly equal to half a wavelength, i.e. a phase change pi.