Question 291 of 295

We wish to make a microscope with the help of two positive lenses both with a focal length of 20 $\mathrm{mm}$ each and the object is positioned $25 \mathrm{~mm}$ from the objective lens. How far apart the lenses should be so that the final image is formed at infinity?

A$20 \mathrm{~mm}$B$100 \mathrm{~mm}$C$120 \mathrm{~mm}$D$80 \mathrm{~mm}$

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Answer: (C) $120 \mathrm{~mm}$

To obtain final image at infinity, object which is the image formed by objective should be at focal distance of eye-piece. By lens formula (for objective)
$$\begin{aligned} & \frac{1}{v_0}-\frac{1}{u_0}=\frac{1}{f_0} \\ \text { or, } \quad & \frac{1}{v_0}-\frac{1}{-25}=\frac{1}{20} \\ \Rightarrow \quad & \frac{1}{v_0}=\frac{1}{20}-\frac{1}{25}=\frac{5-4}{100}=\frac{1}{100} \mathrm{~mm} \\ \therefore \quad & v_0=100 \mathrm{~mm} \end{aligned}$$
Therefore the distance between the lenses
$$=v_0+f_e=100 \mathrm{~mm}+20 \mathrm{~mm}=120 \mathrm{~mm}$$