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A plane wave of monochromatic light is incident normally on a uniform thin film of oil that covers a glass plate. The wavelength of the source can be varied continuosly. Fully destructive interference of the reflected light is observed for wavelengths of 500 and 700 nm and for no wavelengths in between. If the index of refraction of the oil is 1.30 and that of the glass is 1.50, find the thickness of the oil film.
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there is pie phase shift at both reflections

also t ll be odd half integer

ie 2t = (m + 0.5 ) * lambda

also since no destructive interference hence

m(500) = m(700) +1

hence

2t = {m(500)+ 0.5}(500/1.3) = {m(700)+ 0.5}(700/1.3)

m(700) = 4/2 = 2

m(500) = 3

t = .5(5/2)(700/1.3) = 673 nm
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