A thin, non-absorbing horizontal oil film of refractive index nf=1.40 floats on the surface of water of refractive index nw=1.33. Monochromatic light of vacuum wavelength λ=540nm is incident vertically downward from air (nair≈1.00) onto the film.
(a) For normal incidence, determine whether the wave reflected at the air–oil interface experiences a 180∘ phase change. Make a separate determination for the wave reflected at the oil–water interface. In each case, justify your answer on the basis of wave propagation speed in the adjoining media.
(b) Using your conclusions from part (a), derive an expression for the minimum non-zero thickness tmin of the oil film that results in constructive interference in the reflected light for wavelength λ.
(c) Calculate the numerical value of tmin for λ=540nm, expressing your answer in nanometres.