A manufacturer applies a single transparent coating to glass eyeglass lenses to reduce glare at a green design wavelength of 550 nm (measured in air). The coating has an index of refraction of 1.25, which lies between the index of air (1.00) and the index of the glass substrate (1.50).
Answer the following questions about the physical principles that make the coating effective.
(a) For light incident normally from air, state for each of the two reflections (air↔coating surface and coating↔glass surface) whether a half-cycle phase shift occurs upon reflection and justify your choices in terms of changes in optical density.
(b) Explain qualitatively why there exists a specific non-zero coating thickness that produces nearly complete destructive interference between the two reflected rays at the design wavelength.
(c) Describe two reasons, based on optical interference principles, why the index of refraction of the coating must fall between that of air and that of the glass substrate for the coating to function effectively.