A diver is swimming underneath an oil slick with a thickness of 200 nm and an index of refraction of 1.50. A white light shines straight down towards the diver from above the oil slick. The index of refraction of water is 1.33. What is the longest wavelength of the light in water,?, that is transmitted most easily to the diver?

thickness of oil t = 200 nm

index of refraction μ = 1.5

For transmitted light : ---

path difference = 2μ t

For constructive interference

path difference = n λ, λ is wavelength of light

2μ t = n λ

λ = 2μ t / n

For longest λ, n = 1

λ = 2μ t

= 2 x 1.5 x 200 nm

= 600 nm

Wavelength in water

= 600 / refractive index of water

= 600 / 1.33

= 451.1 nm Ans