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In a thin film of oil on water, if the thickness of the film is 500 nm, what is

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Question: In a thin film of oil on water, if the thickness of the film is 500 nm, what is the condition for destructive interference for light of wavelength 600 nm?

Options:

  1. 2t = (m + 1/2)λ
  2. 2t = mλ
  3. t = (m + 1/2)λ
  4. t = mλ

Correct Answer: 2t = (m + 1/2)λ

Solution: 

For destructive interference in a thin film, the condition is 2t = (m + 1/2)λ, where m is an integer.

In a thin film of oil on water, if the thickness of the film is 500 nm, what is

Practice Questions

Q1
In a thin film of oil on water, if the thickness of the film is 500 nm, what is the condition for destructive interference for light of wavelength 600 nm?
  1. 2t = (m + 1/2)λ
  2. 2t = mλ
  3. t = (m + 1/2)λ
  4. t = mλ

Questions & Step-by-Step Solutions

In a thin film of oil on water, if the thickness of the film is 500 nm, what is the condition for destructive interference for light of wavelength 600 nm?
  • Step 1: Understand that we are dealing with a thin film of oil on water.
  • Step 2: Know that the thickness of the oil film is given as 500 nm.
  • Step 3: Recognize that the wavelength of light we are considering is 600 nm.
  • Step 4: Recall the formula for destructive interference in a thin film: 2t = (m + 1/2)λ.
  • Step 5: Identify 't' as the thickness of the film, which is 500 nm.
  • Step 6: Substitute the values into the formula: 2(500 nm) = (m + 1/2)(600 nm).
  • Step 7: Simplify the left side: 1000 nm = (m + 1/2)(600 nm).
  • Step 8: Divide both sides by 600 nm to isolate (m + 1/2): (1000 nm / 600 nm) = m + 1/2.
  • Step 9: Calculate 1000/600, which simplifies to 5/3 or approximately 1.67.
  • Step 10: Set up the equation: 1.67 = m + 1/2.
  • Step 11: Solve for m: m = 1.67 - 0.5 = 1.17.
  • Step 12: Since m must be an integer, the closest integer values for m are 1 or 2, which can be tested for destructive interference.
  • Thin Film Interference – Destructive interference occurs when the path difference between light waves reflected from the top and bottom surfaces of a thin film leads to a phase difference of half a wavelength.
  • Wavelength and Thickness Relationship – The relationship between the thickness of the film, the wavelength of light, and the order of interference (m) is crucial for determining conditions for constructive or destructive interference.
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