એક પાતળા \(f\) કેન્દ્રલંબાઈ ધરાવતા બહિર્ગોળ લેન્સને એક સમતલ અરિસાની સામે આકૃતિમાં દર્શાવ્યા પ્રમાણે મુકેલ છે. જ્યારે વસ્તુને આ તંત્રથી \(a\) અંતરે મૂકવામાં આવે ત્યારે તેનું પ્રતિબિંબ તંત્રની સામે \(\frac{a}{3}\) અંતરે માળાતું હોય તો \(a\) કેટલું હશે?

A \(3f\)
B \(\frac{3}{2}f\)
C \(f\)
D \(2f\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(2f\)

Step-by-step Solution

Detailed explanation

When object is keept at a distance \('a'\) from thin covex lens By lens formula: \(\frac{1}{v}-\frac{1}{u}=\frac{1}{f}\) \(\frac{1}{V}-\frac{1}{(-a)}=\frac{1}{f}\) or, \(\frac{1}{v}=\frac{1}{f}-\frac{1}{a}\) ...... \((i)\) Mirror forms image at equal distance from mirror Now,…

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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