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 1.50 and 1.33,respectively.When the surface of the oil is illuminated from above at normal incidence with white light,what is the wavelength of light between 400 nm to 800 nm wavelength that is most weakly reflected?
A)520 nm
B)540 nm
C)560 nm
D)580 nm
E)600 nm

Question

Quizplus · Accepted Answer

To determine the wavelength of light that is most weakly reflected, we need to find the wavelength at which the reflected light waves from the top and bottom surfaces of the oil film interfere destructively, resulting in minimum reflection. This can be found using the equation:

2nt = mλ

where n is the refractive index of the oil, t is the thickness of the oil film, m is an integer (0,1,2,3...), and λ is the wavelength of light in vacuum.

For minimum reflection, we need to find the first minimum (m=1), which corresponds to the wavelength of light that is most weakly reflected. Plugging in the given values, we get:

2(1.50)(360 nm) = (1)(λ)
λ = 720 nm

This is the wavelength for which the total path difference of the reflected light waves is λ/2, resulting in destructive interference. However, this is outside the given range of 400 nm to 800 nm, so we need to find the closest option. Going down from 720 nm by increments of 20 nm, we get:

700 nm, 680 nm, 660 nm, 640 nm, 620 nm, 600 nm, 580 nm, 560 nm

Therefore, the closest option is 560 nm, which is answer choice B.

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