A farsighted eye is corrected by placing a converging lens in front of the eye.

Question

A farsighted eye is corrected by placing a converging lens in front of the eye. This results in a virtual image located at the eye's near point, the distance to the closest object that can be seen clearly in focus by the eye (normally taken to be about 25.0 cm for someone with perfect eyesight). However, if a person has a near point of 79.5 cm, what focal length should contact lenses have to treat this farsightedness? For contact lenses, the distance from the eye to the contact lens is negligible.

Explanation / Answer

Given

near point of the person having farsighted is 79.5 cm

we know that the lens required to correct the farsightedness is converging lenses whose focal lenght is +ve

the object distance s = 25 cm , (that is for a normal eye )

by definition of near point the distant objects are need to be imaged at s' = -79.5 cm

from the formula

1/f = 1/s+1/s'

f = s'*s/(s-s')

f = (25*(-79.5))/(25-79.5) cm

f = 36.468 cm

focal length of 36.468 cm required for the contact lenses to correct the farsightedness

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