The near point of a long-sighted person is 50 cm from the eye.(a) Can she see clearly an object at: (i) a distance of 20 cm? (ii) at infinity?(b) To read a book held at a distance of 25 cm, will she need converging or perging spectacle lenses?

(a) (i) A long-sighted person with a near point of 50 cm from the eye cannot see an object clearly kept at a distance of 20 cm because she can see an object only when it is placed at her near point (i.e., 50 cm).

(ii)  A long-sighted person with a near point of 50 cm from the eye can see an object clearly kept at infinity because a long-sighted person cannot see nearby objects, but can see distant objects, clearly. 

(b) To read a book held at a distance of 25 cm, the person needs converging lenses as she is long-sighted. Because a convex lens first converges the diverging light rays coming from the nearby object to form a virtual image at the eye's near point. Then the eye lens easily focuses the rays from the eye's near point to form a clear image on the retina.

Explanation

Hypermetropia, also known as long-sightedness or far-sightedness, is a defect of vision in which a person can't see the nearby object clearly (appears blurred), though can see the distant objects clearly. The near point of a hypermetropic eye is more than 25 cm away.

This defect occurs either due to the low converging power of the eye lens, (because of its large focal length). Or, due to the eye-ball being too short, which causes light to focus beyond the retina, instead of directly on the retina. 

It is corrected by using spectacles containing convex lenses, which should be of such a focal length (or power) that it forms a virtual image of the object (lying at the normal near point N of 25 cm) at the near point 'N' of the hypermetropic eye.