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?
 A: Everything is explained in wikipedia at "thin film interference". What do you mean by "off-sync" ? In classical images like the wikipedia one (see below)  only one ray is drawn, but in practice there are an infinity of parallele rays, so superimposition do occurs.
But if by "off-sync" you mean there is a phase difference in the "2" superimposed rays, this is the whole point: phases will positively or negatively (or intermediatly) interfere based on this phase difference. And since the phase corresponds to wavelength/offset, the phase difference varies with wavelength.

A: 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.
The color one sees depends on the thickness of the film. The two phase boundaries act as a resonance cavity. This effect is used in so-called Fabry-Perot interferometers. It is not that the color of the light changes, but rather light of certain wave lengths is enhanced by the interference (constructive, large amplitude) whilst all the other wave lengths interfere destructively (small amplitude). Thus, if you shine white light on such a film, you will only see the colors which resonate with the films thickness. The variety of color in, say, a soap bubble is due to variations in the thickness of the film.
