A 500 nm light is reflected constructively from a thin layer of oil of index of refraction 1.25, which rests on the top of water of index of refraction 1.33. What is the minimum thickness of the layer of oil?
A) 100 nm
B) 150 nm
C) 175 nm
D) 200 nm
E) 225 nm

Question

Quizplus · Accepted Answer

For constructive interference, the path difference between the reflected waves from the top and bottom of the oil layer should be an integer multiple of the wavelength. Let the minimum thickness of the oil layer be 't'. Then the path difference is given by 2t(n2-n1)/λ, where n1 and n2 are the refractive indices of water and oil, respectively. For constructive interference, this path difference should be equal to mλ, where m is an integer.
Thus, we have 2t(n2-n1)/λ = mλ
or t = mλ/(2(n2-n1))
The minimum value of t occurs when m=1, which gives t = λ/(2(n2-n1)). Substituting the given values, we get:
t = 500/(2(1.33-1.25)) = 200 nm
Hence, the minimum thickness of the oil layer is 200 nm.

A 500 Nm Light Is Reflected Constructively from a Thin