Question

The length of the compound microscope is $18\text{cm}$. Its magnifying power, for the relaxed eye, is $28$. Find the object distance from the objective lens if the focal length of the eyepiece is $4\text{cm}$.

• A. $3.125\text{cm}$
• B. $3.750\text{cm}$
• C. $2.125\text{cm}$
• D. $2.750\text{cm}$

Answer 1

The correct option is A $3.125\text{cm}$

We know that, for the relaxed eye, the final image is formed at infinity.

So, $|u_e|=|f_e|$

Length of the compound microscope,

$L=|v_o|+|u_e|=|v_o|+|f_e|$

$\Rightarrow 18=|v_o|+4$

$\Rightarrow |v_o|=14\text{cm}$

Now, magnifying power for the relaxed eye is,

$m=\frac{v_o}{|u_o|}\left(\frac{D}{f_e}\right)$

$\Rightarrow 28=\frac{14}{|u_o|}\left(\frac{25}{4}\right)$

$\Rightarrow |u_o|=3.125\text{cm}$

Hence, option $\left(A\right)$ is the correct answer.