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

  $100 \mathrm{~mm}$
• Correct answer
  C

  $120 \mathrm{~mm}$
• D

  $80 \mathrm{~mm}$

Solution

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 $$ =v_0+f_e=100 \mathrm{~mm}+20 \mathrm{~mm}=120 \mathrm{~mm} $$

Hence, the correct answer is option: 'C'.