A scientist designs a thin transparent coating of uniform thickness t on a semiconductor wafer. Light in the visible range (400 nm≤λ0≤700 nm in air) strikes the coating at normal incidence. The coating index of refraction is nc=2.00, and the underlying semiconductor has index ns=3.50.
(a) Derive a general expression for the set of vacuum wavelengths that will experience maximum reflection from the coating as a function of t and integer order m. State clearly any conditions regarding phase reversals at the two interfaces.
(b) For a coating thickness of 90 nm, determine how many distinct wavelengths within the visible range will exhibit maximum reflection. List the vacuum wavelength(s) to the nearest nanometer.
(c) The scientist wishes to adjust the coating so that exactly two visible wavelengths produce maximum reflection. Determine the range of thicknesses for which this is possible and state one specific thickness value that satisfies the requirement. Explain your reasoning.