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

The minimum nonzero thickness of an oil layer with a refractive index of 1.25 to strongly reflect green light (530 nm) is 212 nm. This calculation considers the path length difference for constructive interference, adjusted for the phase shift occurring at the boundary.

Step-by-step explanation:

The question concerns the phenomenon of thin film interference in Physics, specifically the case where an oil film is on the surface of water. When a thin film of a substance with a different refractive index than its surroundings is present, light waves can reflect off both the top and the bottom surfaces of the film, leading to interference. In this case, we are interested in the interference that causes strong reflection at a green wavelength of 530 nm for an oil layer with a refractive index of 1.25 floating on water with a refractive index of 1.33.

To achieve strong reflection or constructive interference, the path length difference between the light reflected from the top and the bottom of the film must be an integer multiple of the wavelength (λ/n, where n is the refractive index of the film) for the two waves to be in phase. However, since there is a π radian phase shift when light reflects from a medium of higher to lower refractive index, the first strong reflection occurs when the film thickness is equal to λ/(4n). For the given green light wavelength (λ = 530 nm) and the refractive index of oil (n = 1.25), we can calculate the minimum nonzero thickness (t) required:

1. 
   
3. 
   
5. 
   

So the minimum nonzero thickness of the oil layer for strong reflection of green light is 212 nm.

Answer 2

C) 212nm

Step-by-step 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
`= (1.0)/(1.25)`

The refractive index of oil-to-water
`= (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 = ( 530 nm)/(2.5)`

= 212nm

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