AP EAMCET · PHYSICS · Wave Optics

Two point sources \(S_1\) and \(S_2\) separated by a distance \(10 \mu \mathrm{m}\) emit light waves of wavelength \(4 \mu \mathrm{m}\) in phase. A circular wire of radius \(40 \mu \mathrm{m}\) is placed around the sources as shown in figure, then ( \(O\) is the centre of the circle and \(O S_1=O S_2\) )

A points \(A\) and \(B\) are dark and points \(C\) and \(D\) are bright
B points \(A\) and \(B\) are bright and point \(C\) and \(D\) are dark
C points \(A\) and \(C\) are dark and points \(B\) and \(D\) are bright
D points \(A\) and \(C\) are bright and points \(B\) and \(D\) are dark

Verified Solution

Answer & Solution

Correct Answer

(C) points \(A\) and \(C\) are dark and points \(B\) and \(D\) are bright

Step-by-step Solution

Detailed explanation

Path difference at point \(B\), \[ \Delta x_B=S_1 B-S_2 B=0 \] and at point \(D\), \[ \Delta x_D=S_1 D-S_2 D=0 \] Phase difference, \[ \phi=\frac{2 \pi}{\lambda} \times(0)=0 \] So, intensity at points \(B\) and \(D\) \[ I=I_{\max } \cos ^2(\phi / 2)=I_{\max } \] So, points \(B\)…

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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