Athin 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

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

The refractive index of oil-to-water

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

                 = 212nm

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

moving ball hits still ball. mover stops, hit ball moves. momentum transfer.

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west