Question:
\(n\) identical waves each of intensity \(I_0\) interfere with each other. The ratio of maximum intensities if the interference is (i) coherent and (ii) incoherent is :
\(n\) identical waves each of intensity \(I_0\) interfere with each other. The ratio of maximum intensities if the interference is (i) coherent and (ii) incoherent is :
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Coherent waves add amplitudes; incoherent waves add intensities.
Updated On: Oct 31, 2026
- \(n^2\)
- \(\frac{1}{n}\)
- \(\frac{1}{n^2}\)
- \(n\)
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The Correct Option is D
Solution and Explanation
Each wave has intensity \(I_0\propto A^2\).
(i) Coherent: the maximum occurs when all waves are in phase; amplitudes add: \(A_{res}=nA\), so \(I_{coh}=n^2A^2\propto n^2I_0\).
(ii) Incoherent: intensities add: \(I_{incoh}=nI_0\).
Ratio \(\dfrac{I_{coh}}{I_{incoh}}=\dfrac{n^2I_0}{nI_0}=n\).
Answer: (4) \(n\)
(i) Coherent: the maximum occurs when all waves are in phase; amplitudes add: \(A_{res}=nA\), so \(I_{coh}=n^2A^2\propto n^2I_0\).
(ii) Incoherent: intensities add: \(I_{incoh}=nI_0\).
Ratio \(\dfrac{I_{coh}}{I_{incoh}}=\dfrac{n^2I_0}{nI_0}=n\).
Answer: (4) \(n\)
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