Question

You are given two converging lenses of focal lengths, $1.25\text{cm}$ and $5\text{cm}$ to design a compound microscope. It is desired to have a magnification of $30$ in case of normal adjustment. Find out the separation between the objective lens and the eyepiece.

• A. $7.5\text{cm}$
• B. $6.5\text{cm}$
• C. $5.5\text{cm}$
• D. $4.5\text{cm}$

Answer 1

The correct option is A $7.5\text{cm}$

Given:
$f_o=1.25\text{cm}$
$f_e=5\text{cm}$
$m=30$

We know that, in normal adjustment, the final image is formed at infinity.

So, $|u_e|=|f_e|$

Now, magnifying power,

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

$\Rightarrow m=\frac{L}{f_o}\left(\frac{D}{f_e}\right)$

$\Rightarrow 30=\frac{L}{1.25}\left(\frac{25}{5}\right)$

$\Rightarrow L=7.5\text{cm}$

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