A compound microscope consists of an objective

Question:

A compound microscope consists of an objective lens of focal length $1 \mathrm{~cm}$ and an eye piece of focal length $5 \mathrm{~cm}$ with a separation of $10 \mathrm{~cm}$.

The distance between an object and the objective lens, at which the strain on the eye is minimum is $\frac{\mathrm{n}}{40} \mathrm{~cm}$. The value of $\mathrm{n}$ is

Solution:

Final image at $\infty$

$\Rightarrow$ obj. for eye piece at $5 \mathrm{~cm}$

$\Rightarrow$ image for objective at $5 \mathrm{~cm}$

$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$

$\frac{1}{5}+\frac{1}{x}=1$

$\frac{1}{x}=1-\frac{1}{5}=\frac{4}{5} \Rightarrow x=\frac{5}{4}$

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