Question

The focal lengths of the objective and the eye-piece of a compound microscope are $2.0cm$ and $3.0cm$ respectively. The distance between the objective and the eye-piece is $15.0cm$. 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

The correct option is A $2.4$ and $12.0$

When final image is formed at infitinity,
length of the tube $=v_0+f_e$
$\Rightarrow 15=v_0+3\Rightarrow v_0=12cm$
For objective lens $\frac{1}{f_0}=\frac{1}{v_0}-\frac{1}{u_0}$
$\Rightarrow \frac{1}{(+2)}=\frac{1}{(+12)}-\frac{1}{u_0}\Rightarrow u_0=-2.4cm$