What minimum thickness of oil (n = 1.50) on the surface of water (n = 1.33) would give constructive interference for 550 nm light at normal incidence?
A) 78.0 nm
B) 80.0 nm
C) 92.0 nm
D) 183 nm
E) 275 nm

Question

Quizplus · Accepted Answer

For constructive interference, the path length difference between the reflected wave from the top of the oil film and the reflected wave from the bottom of the oil film must be equal to an integer multiple of the wavelength in the oil film.
Let the thickness of the oil film be t.
The path length difference is then given by:
2t(n_oil) = mλ
where m is an integer and λ is the wavelength in vacuum (550 nm).
The wavelength of light in the oil can be found using the relation:
n_oilλ = n_waterλ'
where λ' is the wavelength of light in water.
Substituting the given values, we get:
n_oil = λ'/λ = 1.33/1.50 = 0.887
Therefore, λ = λ'/n_oil = (550 nm)/0.887 = 619 nm
Substituting this value in the first equation, we get:
2t(1.50) = m(619 nm)
Solving for t, we get:
t = (m/2)(619 nm)/(1.50) = 206.33 m/2m = 103.17 m
Since we want the minimum thickness for constructive interference, we take the smallest value of m (m = 1).
Therefore, t = (1/2)(619 nm)/(1.50) = 103.17 nm
Rounding to the nearest tenth, we get t = 92.0 nm.

What Minimum Thickness of Oil (N = 1