A transparent film with index of refraction n=1.30 is deposited on a glass substrate (n=1.52). Light is incident from air at normal incidence, and the film thickness is chosen so that a particular vacuum wavelength experiences nearly zero reflection. Which of the following best explains why a thickness equal to one-quarter of that wavelength (in the film) produces destructive interference of the reflected light?
a) Because the film introduces a 90∘ phase shift solely at the air–film surface, the two reflected rays cancel.
b) Both reflected rays undergo identical 180∘ phase reversals, so they always cancel regardless of film thickness.
c) The second reflected ray travels an extra half-wavelength in the film, and because both reflections introduce the same 180∘ phase shift, the two reflected rays return 180∘ out of phase and interfere destructively.
d) With a λ/4 coating the second ray’s round-trip is one full wavelength, so the two reflected waves return 360∘ out of phase and cancel.