સંયુક્ત માઇક્રોસ્કોપ માં ઓબ્જેક્ટિવ અને આઈપીસની કેન્દ્રલંબાઈ અનુક્રમે \(1\,cm\) અને \(5\,cm\) છે. તેમની વચ્ચેનું અંતર \(10\,cm\) છે વસ્તુ અને ઓબ્જેક્ટિવ વચ્ચેનું અંતર \(\frac{ n }{40}\, cm\) રાખવાથી આંખ પર તણાવ લઘુતમ થાય તો \(n=\).............

A \(50\)
B \(55\)
C \(60\)
D \(62\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(50\)

Step-by-step Solution

Detailed explanation

Final image at \(\infty\) \(\Rightarrow\) obj. for eye piece at \(5 cm\) \(\Rightarrow\) image for objective at \(5 cm\) \(\frac{1}{v}-\frac{1}{u}=\frac{1}{f}\) \(\frac{1}{5}+\frac{1}{x}=1\) \(\frac{1}{x}=1-\frac{1}{5}=\frac{4}{5} \Rightarrow x=\frac{5}{4}\)

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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