A manufacturer deposits a transparent polymer film (nf=1.30) onto a glass substrate (ns=1.60) to create an antireflection layer for normally incident light.
Assume air (na=1.00) above the film. The film thickness can be precisely controlled during deposition.
(a) Derive a general expression for the set of film thicknesses tm(m=0,1,2,…) that yields minimum reflected intensity for normally incident monochromatic light of wavelength λ in air. Your expression should be in terms of m,nf, and λ. State clearly any phase considerations at each interface that you employ in the derivation.
(b) Using your expression, calculate the two smallest non-zero thicknesses that minimize reflections for green light of wavelength 560nm in air. Express each thickness to three significant figures.
(c) Suppose a film is deposited with thickness 210nm. Predict the single visible wavelength (in the range 400–700nm) that will be most strongly reflected. Explain your reasoning, citing the interference condition you use.