Question

If a diver is swimming underneath an oil slick with a thickness of 200 nm and an index of refraction of 1.50, and a white light shines straight down towards the diver from above the oil slick, what is the longest wavelength of the light in water (λ_water) that is transmitted most easily to the diver? (a) 400 nm (b) 450 nm (c) 530 nm (d) 600 nm (e) 1200 nm

Answer 1

The longest wavelength of light transmitted most easily to the diver underneath the oil slick is 1200 nm. Option E is correct.

To determine the longest wavelength of light transmitted most easily to the diver, we need to consider the concept of interference in thin films. When light passes through a medium with a different refractive index, such as oil on water, interference occurs, causing certain wavelengths to be reflected most constructively.

Given that the oil slick has a thickness of 200 nm and an index of refraction of 1.50, we can use the formula:

2t(m+1) = mλ_water

where t is the thickness of the oil slick, m is the order of the interference, and λwater is the longest wavelength of light transmitted most easily to the diver in water.

Solving for λwater:

2(200 nm)(1.50+1) = mλ_water

Simplifying:

1200 nm = mλ_water

Therefore, the longest wavelength of light transmitted most easily to the diver in water is 1200 nm.

Hence, E. is the correct option.