How does thin film interference work?

So thin film interference is when light is half-reflected half-refracted then the reflected and refracted wave interfere with each other to produce another color.

What I don't understand is that the waves are off-sync; not on top of each other. So why do they interfere? And doesn't interference change only amplitude? Why does it affect the wavelength?

• Who says it affects the wavelength? – Emilio Pisanty Oct 8 '15 at 12:29
• What you describe as thin-film interference is, at best, confused. Generally, it's incorrect. Are you talking about monochromatic or non-monochromatic light? If monochromatic, there is no color "change" only intensity changes. Go back and re-read your source. – Bill N Oct 8 '15 at 15:49

All the rays are reflected at some point. One is reflected immediately and never enters the thin film. There, it is reflected at an angle $\alpha$, equal to the angle of incidence. Another ray might enter the thin film, being refracted to an angle $\beta$, is then reflected on the inside of the film, and then leaves again on the same side it entered, thereby again being refracted, so it too leaves at an angle $\alpha$. Any other rays might be reflected any (odd) number of times on the inside of the film (each time at an angle $\beta$), but in the end they all leave at the angle $\alpha$ they entered at. Thus, all those rays are indeed "on top of each other" in terms of angle (wave vector), but their relative "optical path lengths" differ depending on how often they have been reflected on the inside.