Question

A pool of water is covered with a film of oil which is 256 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

Wavelength of visible light (in air) will the reflected light constructively interfere which given as :

Assume that the incident light is normal to the surface of the oil.

using an equation,

2 d = (m + 1/2) / n

where, d = thickness of oil layer = 256 x 10^-9 m

n = refractive index of oil = 1.65

m = positive integer = 1

inserting these values in above eq.

2 (256 x 10^-9 m) = [1 + (1/2)] / (1.65)

(844.8 x 10^-9 m) = (3 / 2)

= (844.8 x 10^-9 m) / (1.5)

= 563.2 x 10^-9 m

= 563.2 nm