Question

Water (n = 1.33) in a shallow pan is covered with a thin film of oil that is 450 nm thick and has an index of refraction of 1.45. What visible wavelengths will not be present in the reflected light when the pan is illuminated with white light and viewed from straight above?

Answer 1

n = index of refraction of = 1.45

t = thickness = 450 nm

m = order

for a wavelength not to be present , the interference must be destructive. hence

2 nt = m $\lambda$

for m = 2

2 (1.45) (450) = 2 $\lambda$

$\lambda$ = 652.5 nm

for m = 3

2 (1.45) (450) = 3 $\lambda$

$\lambda$ = 435 nm