light traveling in air is incident perpendicular to the surface of a thin film o

Question

light traveling in air is incident perpendicular to the surface of a thin film of plastic that is on the surface of a sheet of glass. the plastic film is 200nm thisck and has refractive index of 1.60. the glass has refractive index of 1.40. For what wavelengths of light (in air) within the limits of the visible spectrum 400nm-700nm is there destructive interference between the light reflected from the top and bottom surfaces of the plastic film? Answer is 640nm can you explain how to work this problem

Explanation / Answer

Optical path difference (OPD) between the light reflected from both surfaces = path travelled by light in plastic sheet
OPD = 2*n*t [n is refractive index of plastic, and t is thickness of the film]
OPD = 2*1.6*200 = 640nm

Now, for destructive intereference, OPD = (2n + 1)lambda/2 = 640 nm
lambda = 2*640/(2n + 1) nm
for n = 1, lambda = 640 nm
for n = 2, lambda = 256 nm ( outside visible spectrum)

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