Question

The focal lengths of objective and eyepiece of a compound microscope are $5cm$, $6.25cm$ respectively. When an object is placed in front of the objective at a distance of $6.25cm$, the final image is formed at least distance of distinct vision. The length of a microscope is :

• A. $22.5cm$
• B. $25.0cm$
• C. $30.0cm$
• D. $31.25cm$

Answer 1

Answer: (C)

$30.0cm$

Focal length of the objective, $f_o=5cm$

Focal length of eye-piece, $f_e=6.25cm$

Object distance, $u_o=6.25cm$

$r_e=D$

$L_D=?$

From lens formula, $\frac{1}{v_o}-\frac{1}{u_o}=\frac{1}{f_o}$

$\frac{1}{r_o}-\frac{1}{6.25}=\frac{-1}{5}$ $\Rightarrow \frac{1}{v_o}=\frac{1}{25}$ $\Rightarrow v_o=25$

Length of microscope, $L_D=r_o+\frac{D{f}_e}{D+f_e}$

$=25+\left(\frac{25\times 6.25}{25+6.25}\right)$

$=25+5=30cm$