A puddle of water (n = 1.33)is covered with a very thin layer of oil (n = 1.20).How thick is the oil in the region that strongly reflects light with a wavelength of 636 nm?

Question

Quizplus · Accepted Answer

When light travels from a medium with higher refractive index to a medium with lower refractive index, it reflects partially. The condition for constructive interference is given as 2nt = mλ, where n is the refractive index of the medium, t is the thickness of the layer, m is an integer, and λ is the wavelength of the light.
In this case, the oil layer is the thinner medium, and the incident light is travelling from air (which has a refractive index close to 1). Therefore, we can use 2nt = λ to find the thickness of the oil layer that strongly reflects the given wavelength of light. 
2nt = λ
t = λ/2n
t = (636 nm)/(2 x 1.20)
t = 265 nm
Therefore, the thickness of the oil layer in the region that strongly reflects light with a wavelength of 636 nm is 265 nm.

A Puddle of Water (N = 1