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A transparent coating of refractive index 1.25 is deposited on a…

Question

A transparent coating of refractive index 1.25 is deposited on a glass plate of higher refractive index. For light of wavelength 500 nm (in vacuum) at normal incidence, find the minimum nonzero thickness (in nm) of the coating that produces a strongly reflected (constructively interfering) beam. Note: because the coating index is less than that of glass beneath it, both reflections undergo the same phase change, so constructive reflection requires 2nt = (m + 1/2)*lambda.

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Step-by-step solution

Both top and bottom reflections occur going into a denser medium, so each gets a pi phase shift; they cancel, leaving the path-difference condition.

For constructive reflection: 2nt = (m + 1/2)*lambda.
Minimum nonzero thickness uses m = 0: t = lambda/(4n) = 500/(4*1.25) = 500/5 = 100 nm.

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