Question

The focal lengths of the objective and the eye-piece of a compound microscope are $2.0 \,cm$ and $3.0 \,cm$ respectively. The distance between the objective and the eye-piece is $15.0\, cm$. The final image formed by the eye-piece is at infinity. The two lenses are thin. The distances in $cm$ of the object and the image produced by the objective measured from the objective lens are respectively

• A. 2.4 and 12.0
• B. 2.4 and 15.0
• C. 2.3 and 12.0
• D. 2.3 and 3.0

Answer 1

Answer: (A)

When final image is formed at infinity, then
Length of the tube $=v_{o}+f_{a}=v_{o}+f_{e}$
$\Rightarrow 15=v_{0}+3 $
$\Rightarrow v_{o}=12\,cm$
For objective lens $\frac{1}{f}=\frac{1}{v_{o}}-\frac{1}{u_{o}}$
$\Rightarrow \frac{1}{(+2)}=\frac{1}{(+12)}-\frac{1}{u_{o}} $
$\Rightarrow u_{o}=-2.4 \,cm$