What is the minimum thickness of a thin film required for constructive interference in the reflected light from it?
Answers
It depends on the indices of refraction of the film and the surface on
which it resides: Assuming the incident beam is in air; then if the index of refraction of the film is less than the substrate on which the film rests then there will be a 180 deg phase change at both the air-film and the film-substrate.
As an example, if a film of oil with n0 = 1.4 rests on a glass substrate with an index of refraction 1.5 there is a phase change at both interfaces. Since the total path difference must be a full wavelength for constructive interference then the thickness of the film would have to be 1/2 wavelength (1/2 wavelength of the incident beam in oil and 1/2 wavelength of the reflected beam in oil) for a total path difference of a full wavelength with the incident beam on the oil.
If the oil with n = 1.4 was floating on water with an index of refraction of 1.33 then you still have the 180 deg phase change at the air-oil interface but no phase change at oil-water interface because the index of refraction of the oil is less than that of water. So the film would only need to be 1/4 wavelength in thickness for constructive interference. This may be a little long-winded but if n(incident) > n(reflected) --- no phase change
n(reflected) > n(incident) -- phase change