Question

A thin layer of oil (n = 1.25) is floating on water (n = 1.33). What is the minimum nonzero thickness of the oil in the region that strongly reflects green light (λ = 530 nm)?

A) 500 nm

B) 285 nm

C) 212 nm

Answer 1

Answer:

C) 212nm

Explanation:

For a thin layer of oil floating on water, there is an air-oil interface and oil-water interface. When light ray is incident on the thin layer of oil floating on the water, there is an interference which occur from the reflected ray from air-oil interface and oil-water interface. There is phase shift of 180° between the two rays due to reflections, then the interference is constructive.

Given:

Refractive index of oil (n₁) = 1.25

Refractive index of water (n₂) = 1.33

Refractive index of air (n₃) = 1.00

The wavelength of  light = 530nm

Let thickness = t

The refractive index of air-to-oil $= \frac{1.0}{1.25}$

The refractive index of oil-to-water $= \frac{1.25}{1.33}$

Since the refractive index of air-to-oil is lesser than the refractive index of oil-to-water, constructive interference occurs when:

        2t =    λ      

                   n₁

 

        t  =   λ      

              2 x n₁

        t =   530      

              2 x 1.25

       $t = \frac{ 530 nm}{2.5}$

                 = 212nm

The minimum nonzero thickness of the oil in the region that strongly reflects green light  = 212nm