A camera lens is made of glass with an index of refraction of 1.6. This le ns is coated with a magnesium fluoride film (n = 1.38) to enhance its light transmission. This film is to produce zero reflection for light of wavelength 540 nm. Treat the lens surface as a flat plane and the film as a uniformly thick flat film.

(a) How thick must the film be to accomplish its objective in the first order?

(b) Would there be destructive interference for any other visible wavelengths?

(c) By what factor would the reflection for light of wavelengths 400 and 700 nm be reduced by this film? Neglect the variation in the reflected light amplitudes from the two surfaces.