A 360-nm thick oil film floats on the surface of a pool of water 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 nm
B)430 nm and 720 nm
C)450 nm and 740 nm
D)470 nm and 760 nm
E)490 nm and 780 nm

Question

Quizplus · Accepted Answer

The condition for constructive interference is given by:
2nt = mλ, where n is the refractive index, t is the thickness of the oil film, m is an integer and λ is the wavelength in the medium outside the oil film (in this case, air).

For maximum reflection, we need a high contrast in the refractive indices of the two media, which occurs at normal incidence. Therefore, we consider the wavelengths within the visible spectrum (400 nm to 800 nm).

Using the given values:
n1 = 1.5 (refractive index of oil)
n2 = 1.33 (refractive index of water)
t = 360 nm

For the first maximum (m=1), we have:
2n1t = λ1n2
λ1 = 2n1t/n2 = 430 nm

For the second maximum (m=2), we have:
2n1t = λ2n2
λ2 = 2n1t/2n2 = 720 nm

Therefore, the two wavelengths that are most strongly reflected are 430 nm and 720 nm, which corresponds to option B.

A 360-Nm Thick Oil Film Floats on the Surface of a Pool