KCET · Physics · Wave Optics

Light from two coherent sources of the same amplitude \(A\) and wavelength \(\lambda\) illuminates the screen. The intensity of the central maximum is \(I_{0}\). If the sources were incoherent, the intensity at the same point will be

A \(4 I_{0}\)
B \(2 I_{0}\)
C \(I_{0}\)
D \(\frac{I_{0}}{2}\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{I_{0}}{2}\)

Step-by-step Solution

Detailed explanation

The rays of light from two coherent sources superimpose each other on the screen forming alternate maxima (with maximum intensity \(I_{0}\) ) and minima (with intensity zero). If two non-coherent sources superimpose, there will be no maxima and minima, instead the intensity will be \(\frac{I_{0}}{2}\) throughout.

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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