Light waves reflect from the surfaces of two plastic sheets separated by a thin air gap. These light waves meet after reflecting from the two surfaces. When two waves meet, they can add together, cancel each other, or partially cancel each other. This adding and canceling of light waves—called constructive interference and destructive interference—creates the rainbow-colored patterns you see.
White light is made up of all different colors mixed together. When light waves of a particular color meet and cancel each other, that color is subtracted from white light. For example, if the blue light waves cancel, you see what is left of white light after the blue has been removed, which is yellow, the complementary color of blue.
When you place a red filter in front of the light source, only red and black fringes will appear. Where destructive interference takes place, there is no red light left to reach your eyes, so you see black. Where the waves constructively interfere, you see red.
The thickness of the gap between the plates determines which colors of light cancel out at any one point. For example, if the separation of the plates is roughly equal to one-half the wavelength of blue light (or some multiple of it), the crests of waves of blue light reflected from the top surface of the air gap will match up with the troughs of waves reflected from the bottom surface, causing the blue light to cancel out.
This is what happens: Imagine that the distance between the two plates is one-half the wavelength of blue light. When a wave hits the top of the air layer, part reflects and part continues on. Compared to the part that reflects from the top of the air layer, the part that continues on and reflects from the bottom travels an extra wavelength through the air layer (half a wavelength down and half a wavelength back). In addition, the wave that reflects from the bottom is inverted. The net effect is that the blue light waves reflected from the two surfaces recombine trough-to-peak and cancel each other out. (See diagram; click to enlarge.)
Because the interference pattern depends on the amount of separation between the plates, what you’re actually seeing is a topographical map of the distance between plates.