Question

A compound microscope consists of an objective lens of focal length $2cm$ and eyepiece of focal length $6.25cm$ separated by a distance of $15cm$. How far (in $cm)$ from the objective lens should an objeçt be placed in order to obtain the final image at the least distance of distinct vision?

Answer 1

Answer: 2.50

For eyepiece:
$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$
$\Rightarrow -\frac{1}{25}-\frac{1}{u}=\frac{1}{6.25}$
$\Rightarrow u=-5cm$
For Objective:
$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$
$\Rightarrow \frac{1}{10}-\frac{1}{u}=\frac{1}{2}$
$\Rightarrow u=-2.5cm$