A simple microscope is rated $5X$ for a normal relaxed eye. What will be its magnifying power for a relaxed farsighted eye whose near point is $40cm$?

The correct option is D $8$
The near point is closest distance at which the eye lens can form a clear image of the object.



When an object is closer than the near point, image formed is blurry. In that case, a magnifier lens is used. The object will be at the magnifier's focal length and the magnifier will converge the light rays, so that the rays reaching the eye lens are parallel.


Magnification of a simple microscope (magnifier)
$m=\frac{D}{f}$

For a normal eye,
$m=5$ (given)
$D=25cm$ (near point of a normal eye)
$\Rightarrow f=\frac{25}{5}=5cm$
(focal length of magnifier lens)

For the hypermetropic eye,
$D=40cm$ (given)
Hence $m=\frac{D}{f}=\frac{40}{5}=8$