A sheet of glass having an index of refraction of 1.40 is to be coated by a film of material having an index of refraction of 1.55 in order that green light with a wavelength of 525 nm (in air) will be preferentially transmitted via constructive interference. (a) What is the minimum thickness of the film that will achieve the result? (b) Why are other parts of the visible spectrum not also preferentially transmitted? (c) Will the transmission of any colors be sharply reduced? If so, which colors?