A short-sighted person has a near point of 15 cm and a far point of 40 cm.(a) Can he see clearly an object at a distance of: (i) 5 cm? (ii) 25 cm? (iii) 50 cm?(b) To see clearly an object at infinity, what kind of spectacle lenses does he need?

(a) (i) A short-sighted person with a near point of 15 cm and a far point of 40 cm cannot see an object clearly at a distance of 5 cm because he can see an object only when it is placed at his near point (i.e., 15 cm).

(ii) A short-sighted person with a near point of 15 cm and a far point of 40 cm can see an object clearly at a distance of 25 cm since it the normal near point of the eye. 

(iii) A short-sighted person with a near point of 15 cm and a far point of 40 cm cannot see an object clearly at a distance of 50 cm since it is beyond his far point.

(b) To see clearly an object at infinity, the person should use concave lenses in his spectacles. Because a concave lens first diverges the parallel light rays coming from the object at infinity to form a virtual image at the eye's far point. Then the eye lens easily focuses the rays from the eye's far point to form a clear image on the retina.

Explanation

Myopia, also known as near-sightedness or short-sightedness, is a defect of vision in which a person can't see the distant object clearly (appears blurred), though can see the nearby objects clearly. The far point of a myopic eye is less than infinity.

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

It is corrected by using spectacles containing concave lenses, which should be of such a focal length (or power) that it produces a virtual image of the distant object (lying at infinity) at the far point of the myopic eye.