In the case of someone who is farsighted, the eye is not able to focus clearly o

Question

In the case of someone who is farsighted, the eye is not able to focus clearly on objects closer than a certain distance. This closest point on which a person’s eye can focus is called the near point.
In this situation the corrective lens is used to make an object closer than the near point produce an image further away from the lens at the near point.
Suppose a person who has a near point of 53.2 cm is trying to view a book at a distance of 25.0 cm. What is the focal length (with correct sign) of a lens that would take the book and make an image on the same side of the lens as the book a distance 53.2 cm from the lens?

Explanation / Answer

d = least distance of distinct vision = 25 cm

x = distance of near point of defactive eye = 53.2 cm

u = object distance = - d

V = image distance = - x

from lens formaula

1/f ( focal length) = 1/V - 1/u

1/f = ( 1/ -x) - ( 1/ -d)

1/f = - 1/x + 1/d

1/f = - 1/ 53.2 + 1/25

f = 46.94 cm

f = +ve , correcting lens will be convex.

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