Question

A 360-nm thick oil film floats on the surface of a pool of water. the indices of refraction of the oil and the water are 1.5 and 1.33, respectively. when the surface of the oil is illuminated from above at normal incidence with white light, what are the two wavelengths of light between 400 nm to 800 nm wavelength that are most strongly reflected?a) 410 nm and 700 nmb) 430 nm and 720 nmc) 450 nm and 740 nmd) 470 nm and 760 nme) 490 nm and 780 nm

Answer 1

The correct answer is 432, and 720.
The thickness of a film is t= 360nm
the refractive index of oil n₀t = (m +1/2) λ
For m =0
λ = 4n₀t
= 4(1.50)(360)
= 2160nm
for m = 1
λ = 4n₀t
= 4(1.50)(360)/3
= 720nm
m = 2
λ = 4n₀t/5 = 4(1.50)(360)/5
= 432nm
The wavelength which are most strongly reflected are
432nm, 720nm.