White light is sent downward onto a horizontal thin film that is sandwiched betw

Question

White light is sent downward onto a horizontal thin film that is sandwiched between two materials. The indexes of refraction are 1.80 for the top material, 1.69 for the thin film, and 1.50 for the bottom material. The film thickness is 5.31 times 10^-7 m. (a) Of the visible wavelengths (400 to 700 nm) that result in fully constructive interference at an observer above the film, which is the longer wavelength? nm (b) Which is the shorter wavelength? nm (c) The materials and him art then cooled so that the film thickness decrease. Is there a change in the wavelengths of light resulting in fully constructive interference? Yes, there is a shift towards shorter wavelengths. Yes, there is a shift towards longer wavelengths. No.

Explanation / Answer

t = 5.31 * 10-7 m

constuctive interference 2 n t = m * lambda

wavelength lambda = 2 n t / m

for m = 1 , lambda = (2 * 1.69 * 5.31 * 10-7) / (1) = 1795 nm

for m = 2 , lambda = (2 * 1.69 * 5.31 * 10-7) / (2) = 897 nm

for m = 3 , lambda = (2 * 1.69 * 5.31 * 10-7) / (3) = 598 nm

for m = 4 , lambda = (2 * 1.69 * 5.31 * 10-7) / (4) = 448.75 nm

a) The longer wavelength in region between 400 to 700 nm

lambda = 598 nm

b) The shorter wavelength in region between 400 to 700 nm

lambda = 448.75 nm

c) Yes, there is a shift towards shorter wavelengths

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