A compound microscope consists of an objective lens of focal length \(1 \,cm\) and an eye piece of focal length \(5 \,cm\) with a separation of \(10 \,cm\) The distance between an object and the objective lens, at which the strain on the eye is minimum is \(\frac{ n }{40}\, cm .\) The value of \(n\) is\(....\)

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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 \(5 cm\)

\(\frac{1}{v}-\frac{1}{u}=\frac{1}{f}\)

\(\frac{1}{5}+\frac{1}{x}=1\)

\(\frac{1}{x}=1-\frac{1}{5}=\frac{4}{5} \Rightarrow x=\frac{5}{4}\)

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