A section of roadway is coated by a thin, non-volatile film of gasoline (ng=1.40) that has a uniform thickness of 300nm over water (nw=1.33). Sunlight, which can be treated as containing all visible wavelengths uniformly, strikes the film at normal incidence.
Observers note vivid colors in the reflected light.
(a) Taking into account phase changes on reflection, derive the condition that must be satisfied by wavelengths of visible light that are constructively reflected from this film.
(b) Using the condition derived in part (a), determine all wavelengths in the visible range 400–700nm that will be strongly reflected for the stated film thickness. List the wavelengths to the nearest nanometer.
(c) Based on your results in part (b), predict the predominant color that an observer would perceive when viewing the reflected light. Justify your answer by relating the set of reflected wavelengths to the human perception of color.
(d) If the film gradually thins by evaporation, describe qualitatively how the observed colors will change over time. Your explanation should reference the dependence of interference on film thickness.