લેન્સના સંયોજન દ્વારા રચાતા પ્રતિબિંબનું સ્થાન _______ છે. \(\mathrm{f}_1=10 \mathrm{~cm} \quad \mathrm{f}_2=10 \quad \mathrm{f}_3=30 \mathrm{~cm}\)

A \(30 \mathrm{~cm}\) (ત્રીજા લેન્સની જમણી બાજુએ)
B \(15 \mathrm{~cm}\) (બીજા લેન્સની ડાબી બાજુએ)
C \(30 \mathrm{~cm}\) (ત્રીજા લેન્સની ડાબી બાજુએ)
D \(15 \mathrm{~cm}\) (બીજા લેન્સની જમણી બાજુએ)

Verified Solution

Answer & Solution

Correct Answer

(A) \(30 \mathrm{~cm}\) (ત્રીજા લેન્સની જમણી બાજુએ)

Step-by-step Solution

Detailed explanation

લેન્સ 1 માટે: \(f_1=10, u=-30, v=\) ? \(v=\frac{u f}{u+f}=\frac{-30 \times 10}{-30+10}=15\) લેન્સ 2 માટે: \(f_1=-10, u=10, v=\) ? \(\mathrm{v}=\frac{\\mathrm{uf}}{\mathrm{u}+\mathrm{f}}=\frac{10 \times-10}{10-10}=\infty\) લેન્સ 3 માટે: \(f=30, u=-\infty, v=\) ? તેથી v 30 થશે.

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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