1. Thin film interference (35 pts) (a) A thin film of refractive index no and thickness d is in between two media with refractive indices m and no. Light is incident on the thin film from medium 1 at an incident angle of @. Consider the interference of the two reflected rays from the front and back of the thin film. Show that the phase difference between the two rays due to their path length difference (i.e. only the geometrical contribution) is given by the expression below, where do is the wavelength in vacuum: 6 = Inad cos At 1 3 (b) Consider n1 = 1 (air), no = 1.4 (some type of oil), na = 1.5 (glass). At normal incidence, what is the smallest non-zero thickness d such that green light (No = 500 nm) is reflected strongly? (c) Consider m = 1 (air), ny = 1.4 (oil), n3 = 1.3 (water). At normal incidence, what is the smallest non-zero thickness d such that green light (Xo = 500 nm) is reflected strongly? (d) Following the conditions in (c), where the thin oil film is floating on water. At the thickness you calculated, white light normally incident on the oil film will appear green in reflection. Now a gust of wind passes through, creating waves on the surface of the water. Making use of the result in (a), how will the color of the reflected light change: will it shift towards blue or red