An engineer wishes to reduce reflections from the front element of a smartphone camera lens at a design wavelength of 550 nm (in air). The glass lens has an index of refraction of 1.70. A thin magnesium-fluoride coating with an index of 1.38 will be deposited on the lens surface.
(a) Calculate the least non-zero thickness of the coating that minimizes the intensity of light reflected back into air at the design wavelength.
(b) If the same coating thickness is used, describe qualitatively whether the reflected intensity at 450 nm (in air) will increase, decrease, or remain approximately the same compared with that at 550 nm. Support your answer with physical reasoning related to path difference and phase.