A thin soap film (index of refraction nf=1.36) floats on the surface of water (nw=1.33) and is illuminated from above by white light in air at normal incidence. An observer looks straight down at the film and notices that some regions appear vividly colored while others look dark.
(a) Identify for each of the two reflected rays (the one from the top surface of the film and the one that reflects after first entering the film) whether a half-wavelength phase shift occurs upon reflection. Justify your answer in terms of the relative indices of refraction at each interface.
(b) Explain qualitatively how the integer order m determines which wavelengths experience constructive or destructive interference in the reflected light.
(c) A particular spot on the film has a thickness of about 300 nm. Using your reasoning from parts (a) and (b), predict whether light of wavelength 600 nm in air will be enhanced or suppressed in the reflected spectrum at that spot. Clearly state the reasoning steps that lead to your conclusion, but do not perform any explicit numerical calculation of path difference.