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

Answer: (A)

When final image is formed at infinity, then
Length of the tube $=v_o+f_a=v_o+f_e$
$\Rightarrow 15=v_0+3$
$\Rightarrow v_o=12cm$
For objective lens $\frac{1}{f}=\frac{1}{v_o}-\frac{1}{u_o}$
$\Rightarrow \frac{1}{(+2)}=\frac{1}{(+12)}-\frac{1}{u_o}$
$\Rightarrow u_o=-2.4cm$