Halliday, Resnick & Walker — Interference: Problem 40

40 White light is sent downward onto a horizontal thin film that is sandwiched between two materials. The indexes of refraction are 1.80 for the top material, 1.65 for the thin film, and 1.50 for the bottom material. The film thickness is \(5.00 \times 10^{-7}\text{ m}\). Of the visible wavelengths (400 nm to 700 nm) that result in fully constructive interference at an observer above the film, which is the (a) longer and (b) shorter wavelength? The materials and film are then heated so that the film thickness increases. (c) Does the light resulting in fully constructive interference shift toward longer or shorter wavelengths?