Consider a ray incident at an angle i. A part of this ray is reflected from the air-film interface and a part refracted inside. This is partly reflected at the film-glass interface and a part transmitted. A part of the reflected ray is reflected at the film-air interface and a part transmitted as r2 parallel to r1. Of course succesive reflections and transmissions will keep on decreasing the amplitude of the wave. Hence rays r1 and r2 shall dominate the behavior. If incident light is to be transmitted through the lens, r1 and r2 should interfere destructively. Both the reflections at A and D are from lower to higher refractive index and hence there is no phase change on reflection. The optical path difference between r2 and r1 is n (AD + CD) – AB.
If d is the thickness of the film, then
For these waves to interefere destructively this must be λ/2.
For a camera lens, the sources are in the vertical plane and hence
i = r = 0