\(0.2 \mathrm{~mm}\) પહોળાઈ ધરાવતી સ્લિટ પરથી \(400 \mathrm{~nm}\) તરંગલંબાઈ ધરાવતા પ્રકાશથી વિવર્તન માટે મળતી વિવર્તન ભાત ને \(100 \mathrm{~cm}\) કેન્દ્રલંબાઈના બહિર્ગોળ લેન્સની મદદથી મુખ્ય સમતલ પર કેન્દ્રિત કરવામાં આવે છે. તો પ્રથમ ગૌણ મહત્તમની પહોળાઈ _________થશે.

A \(2 \mathrm{~mm}\)
B \(2 \mathrm{~cm}\)
C \(0.02 \mathrm{~mm}\)
D \(0.2 \mathrm{~mm}\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(2 \mathrm{~mm}\)

Step-by-step Solution

Detailed explanation

Width of \(1^{\text {st }}\) secondary maxima \(=\frac{\lambda}{a} \cdot D\) Here \( a=0.2 \times 10^{-3} \mathrm{~m} \) \( \lambda=400 \times 10^{-9} \mathrm{~m} \) \( D=100 \times 10^{-2}\) Width of \(1^{\text {st }}\) secondary maxima…

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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