दो पतले छिद्रों जो \(1\, mm\) दूरी से पृथक हैं को प्रकाश स्रोत \((\lambda=632.8\, nm )\) से प्रतिदिप्त किया जाता है तो पदे पर व्यतिकरण फ्रिंज प्राप्त होता है। पदे से छिद्र की दूरी \(100\, cm\) है। यदि केन्द्रिय दिप्त फ्रिंज से \(1.27\, mm\) की दूरी पर पदे पर दिप्त फ्रिंज प्राप्त होता है तो छिद्र से इस बिन्दु तक पहुँच रहे तरंगों का पथान्तर ........\(\mu m\) है

A \(1.27\)
B \(2\)
C \(2.87\)
D \(2.05\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(1.27\)

Step-by-step Solution

Detailed explanation

\(y=\frac{n D \lambda}{d}\) \(n=\frac{y d}{D \lambda}=\frac{1.27 \times 10^{-3} \times 10^{-3}}{1 \times 632.8 \times 10^{-9}}=2\) Path difference \(\Delta x=n \lambda\) \(=2 \times 632.8 nm\) \(=1265.6 nm\) \(=1.27 \mu m\)

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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