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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 in air?

Options:

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

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

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 in air?
  • 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 in air is given as 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 to get approximately 1.67: 1.67 = m + 1/2.
  • Step 10: Solve for m by subtracting 1/2 from both sides: m = 1.67 - 0.5 = 1.17.
  • Step 11: Since m must be an integer, the possible values for m are 0, 1, 2, etc., that satisfy the condition.
  • 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 the conditions for constructive or destructive interference.
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