How does interference occur in thin films?Why is it important that the films be thin? Why don’t you get these effects with a relatively thick...

Thin film interference exists when the thickness of the
coating is approximately the same as a multiple of a quarter wavelength of light.
Reflections of light can be made to add destructively by choosing a film thickness that
is one-quarter of a wavelength. A quarter wavelength is choosen because a wave reflected
from the second boundary traverses the length of the coating twice-- forward, and then
backward. Hence, when returns to the first boundary, it is one-half of a wavelength (180
degrees) out of phase with the reflection from the first boundary. Thus the reflected
light, which is much weaker than the transmitted/incident light, is canceled out. Note
that thin film interference is very dependant on the incident angle of the light, since
light at oblique angles will travel farther within the thin film, and exit the coating
at a different point than where it entered. Both these factors introduce a
phase-shift-error relative to the quarter-wave matching
criterion.

Note that the interference of the two
reflections (one at the top of the coating and one from the bottom of the coating)
results in a wave with zero amplitude only if the intensities of the two waves are
equal. Thus, destructive interference will only occur if a) the second reflection is not
attenuated in the coating material and b) slight deviations from normal incidence do not
result in severe phase-shift errors. It is this latter restriction that limits the
thickness of an anti-reflection coating in most instances. Typically, this limits the
thickness of the film to less than that of a wavelength. Hence, the response to your
criteria defining the boundary between "thick" and "thin" films is likely whether they
are thicker than the wavelength of the light, typically near quarter-wavelength
thickness.