Question

In a compound microscope, the focal lengths of the two lenses are $1.5cm$ and $6.25$cm. If an object is placed at $2cm$ from objective and the final image is formed at $25$ cm from the eye lens, the distance between the two lenses is :

• A. $6.00cm$
• B. $7.75cm$
• C. $9.25cm$
• D. $11.00cm$

Answer 1

Answer: (D)

$11.00cm$

Focal length of objective, $f_0=1.5cm$

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

Object distance, $v_o=2cm$

Image distance, $v_e=25cm$

Distance between the lenses, $L=?$

From lens formula:
$\frac{1}{v_0}-\frac{1}{(-2)}=\frac{1}{1.5}$

$\frac{1}{v_0}=\frac{1}{\left(6\right)}\Rightarrow v_0=6cm$

By using tubelength formula for the Microscope:
$L=v_0+\frac{Dfe}{D+fe}$
$\Rightarrow 6+\frac{25\times 6.25}{31.25}$ $=6+5=11cm$
So, the correct option will be $\left(D\right)$