Phase of reflected and transmitted waves

[carllacan]

I'm reading the EM waves chapter on Griffiths, and, after getting the complex amplitudes of the reflected and transmitted waves he obtains the real amplitudes by (apparently) just "disregarding" the exponential part, which is equivalent to assuming that the phase of both waves is equal to the phase of the incident wave (except for the minus charge in the reflected wave if v2 < v1). Why does he assume this?

 

[blue_leaf77]

Can you provide the equation related to what you describe there?
Besides, the presence of minus implies that the phase has been flipped 180 degree, that is the phase is not omitted.

 

[Blackberg]

Not familiar with the Griffiths book, but what you are describing seems like the most elementary thing about how waves behave at an interface. I'd say it's assumed as a hypothesis, because he knows it turns out to be true. What is the author coming to at the end of the demonstration?