An oil film (n=1.45) spreads on a flat glass surface (n=1.52) and is viewed in air at normal incidence using monochromatic light of wavelength λ0=600 nm. Initially the film thickness is such that the fifth-order dark fringe is observed in reflection. As the oil gradually evaporates, the film thins by 120 nm.
(a) Determine the interference order (bright or dark and its integer value) that will be observed in the reflected light after the oil has thinned by the stated amount. Show all steps in your reasoning.
(b) The experiment is repeated with light of wavelength λ0=450 nm under identical conditions. Predict whether the same thickness reduction will cause the reflected intensity at that location to increase or decrease. Explain your answer qualitatively without performing explicit numerical calculations.
(c) Discuss how a small decrease in the oil’s index of refraction during evaporation would affect your answer to part (a), keeping all other parameters the same.