Follow these steps to solve this problem: A very thin oil film (noil=1.25) float

Question

Follow these steps to solve this problem: A very thin oil film (noil=1.25) floats on water (nwater=1.33). What is the thinnest film that produces a strong reflection for green light with a wavelength of 500 nm?

1.Which of the following equations should be used to find the minimum thickness t of the oil film that satisfies the conditions of the problem? Let be the wavelength of light in air and n the index of refraction of the thin film

. a. 2t=mn(m=0,1,2,...) for constructive interference.

b.2t=(m+12)n(m=0,1,2,...) for destructive interference.

c.2t=(m+12)n(m=0,1,2,...) for constructive interference.

d. 2t=mn(m=0,1,2,...) for destructive interference.

2. What is the minimum (non-zero) thickness t of the film that produces a strong reflection for green light with a wavelength of 500 nm?

Explanation / Answer

1.When light reflected from oil and water interfere constructively, strong reflection occurs;

If t is thickness of oil, extra distance travelled by light in reflacting from water is 2t, this distance has to be a multiple of wavelength for constructive interference.

Also in material of index n , wavelength decreases by factor of n

these conditions gives us that we should use (a) equation(i.e. 2t = m/n) for solving the problem.

2.For minimum thickness t we put m = 1 => t = /2noil = 500/2.5 = 200nm

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