જ્યારે પીળો પ્રકાશ સમાન જડાઈ ધરાવતા હવાના અને શૂન્યાવકાશના સ્તંભમાંથી પસાર થાય ત્યારે તરંગલંબાઈઓની સંખ્યાનો તફાવત એક મળે છે. તો હવાના સ્તંભની જડાઈ \(....\,{mm}\) હશે. [હવાનો વક્રીભવનાંક \(=1.0003\), શૂન્યાવકાશમાં પીળા પ્રકાશની તરંગલંબાઈ \(=6000 \,\mathring {{A}}\) ]

A \(2\)
B \(4\)
C \(6\)
D \(8\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(2\)

Step-by-step Solution

Detailed explanation

We know Thickness \({t}={n} \lambda\) \({So}, {n} \lambda_{{vac}}=({n}+1) \lambda_{{air}}\) \({n} \lambda=({n}+1) \frac{\lambda}{\mu_{{air}}}\) \(n=\frac{1}{\mu_{\text {air }}-1}=\frac{10^{4}}{3}\) \({t}={n} \lambda\) \(=\frac{10^{4}}{3} \times 6000\, \stackrel{\circ}{{A}}\)…

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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