Answer:
A thin layer of oil with index of refraction ng = 1.47 is floating above the water. The index of refraction of water is nw = 1.3. The index of refraction of air is na= 1. A light with wavelength λ = 775 nm goes in from the air to oil and water.
Part (a) Express the wavelength of the light in the oil, λ₀, in terms of λ and n⁰ (b) Express the minimum thickness of the film that will result in destructive interference, t min, in terms of λ o
(c) Express tmin in terms of λ and no.
(d) Solve for the numerical value of tmin in nm.
Explanation:
n₀ = 1.47
refraction of water = 1.3
refraction of air = 1
wavelength λ = 775 nm
(a) wavelength of light in water ⇒ λ₀ = λ / n₀
(b) minimum thickness of the film that will result in destructive interference
t(min) = λ₀ / 2
(c) the express t(min)
t = λ /2n₀
(d) the thickness is
t = 775 / 2(1.47)
= 263.61 nm
