Question

A pool of water is covered with a film of oil which is 234 nm thick. For what wavelength of visible light (in air) will the reflected light constructively interfere? The index of refraction of the oil is 1.65. Visible light (in air) has wavelengths between 430 nm (blue) and 770 nm (red) in air. Assume that the incident light is normal to the surface of the oil.

Answer 1

given,

thickness of the oil film = 234 n m

refractive index of oil = n = 1.65

Visible light (in air) has wavelengths between 430 nm (blue) and 770 nm (red)

λ = ?

condition of constructive interference

2 n t + λ/2 = k λ

now,

`\lambda = (4nt)/(2k - 1)`

at k = 1

`\lambda = (4* 1.65 * 234)/(2(1) - 1)`

`\lambda = 1603.8\ nm`

not between the visible range

at k =2

`\lambda = (4* 1.65 * 234)/(2(2) - 1)`

`\lambda = 535\ nm`

above wavelength is in the visible range.