A compound microscope consists of an objective lens of focal length $1\; cm$ and an eye piece of focal length $\inline 5\; cm$ with a seperation of $\inline 10\; cm$.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 ______. Option: 1 50 Option: 2 100 Option: 3 150 Option: 4 200

$\\ \text{Image by objective is formed at the focus of eye-piece} \\ \therefore For objective, v=5, u, f=1 \mathrm{~cm}$

\begin{aligned} \frac{1}{5}-\frac{1}{u}=\frac{1}{1} \Rightarrow \frac{1}{5}-1=\frac{1}{u} \\ \therefore \quad|u|=\frac{5}{4} c m \Rightarrow|u|=\frac{50}{40} c m \\ \therefore \quad n=50 \end{aligned}

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