A simple microscope has a magnifying power of 3.0 when the image is formed at the near point (25 cm) of a normal eye. (a) What is its focal length? (b) What will be its magnifying power if the image is formed at infinity?

For the simple microscope, we have:
Least distance of clear vision, D = 25 cm
Magnifying power, m = 3
Now,
Let the focal length be f.

(a) When the image is formed at D = 25 cm, the magnifying power of the simple microscope is given by
$$\begin{gathered} m=1+\left(\frac{D}{f}\right) \\ \Rightarrow 3=1+\left(\frac{25}{f}\right) \end{gathered}$$
$$\begin{gathered} \Rightarrow \frac{25}{f}=2 \\ \Rightarrow f=\frac{25}{2}=12.5\mathrm{cm} \end{gathered}$$

(b) When the image is formed at infinity in normal adjustment, the magnifying power is given by
$m=\frac{D}{f}=\frac{25}{12.5}=2.0$

So, the magnifying power is 2 if the image is formed at infinity.