Question

A thin film of olive oil (index of refraction n_oil = 1.46) of thickness d is floating on the surface of still water (index of refraction n_water = 1.33). The index of refraction of air is n_air = 1.00.

A red laser of wavelength $LaTeX: \lambda=600\,\text{nm}=6.00\times 10^{-7}\,\mathrm{m}$ λ=600nm=6.00×10−7m is incident on the film of olive oil from above as shown. The laser reflects at the air-oil and oil-water interfaces and interferes with itself.

Answer the following questions:

1. What does the thickness d of the olive oil film have to be for the laser to interfere with itself constructively? Note that n_air < n_oil at the air-oil interface but n_oil > n_water at the oil-water interface. Also note that the wavelength of the laser inside the oil is different from what it is in air.

2. What does the thickness d of the olive oil film have to be for the laser to interfere with itself destructively?

3. What wavelength light (in air) would interfere with itself constructively for the thickness you found in problem 2?

Answer 1

Ans

The laser reflecting at air-oil and oil-water interface will interfere. If the path length of the interfering waves is integer multiple of the wavelength in the film. There will be path difference of half wavelength due to phase shift at air-oil interface