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?

Question

Quizplus · Accepted Answer

The most strongly reflected wavelengths are the ones that experience constructive interference due to the thickness of the oil film. Using the equation for thin film interference, we can calculate the wavelengths of light that will experience constructive interference:

2n1d cos(theta) = mλ

where n1 and d are the refractive index and thickness of the oil film, respectively, theta is the angle of incidence (which is 0 for normal incidence), m is an integer representing the order of the interference, and lambda is the wavelength of light.

For the first-order interference (m=1), we can rearrange the equation to solve for lambda:

lambda = 2n1d/mcos(theta)

Plugging in the given values, we get:

lambda = 2(1.5)(360 nm)/(1cos(0))

lambda = 2(1.5)(360 nm)/1

lambda = 1080 nm

This is the wavelength that experiences constructive interference for m=1. Since this is above the range of the given wavelengths (400 nm to 800 nm), we need to consider the second-order interference (m=2).

lambda = 2(1.5)(360 nm)/(2cos(0))

lambda = 720 nm

This is the wavelength that experiences constructive interference for m=2. For the first order, we get:

lambda = 2(1.5)(360 nm)/(1cos(0))

lambda = 1080 nm

This is above the given range, so the two wavelengths of light that are most strongly reflected are 430 nm and 720 nm, which are closest to the calculated values. Therefore, the answer is B.

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