(a) A `40`-year-old professor requires eyeglasses with lenses of `2D` power to read a book at `25cm`. What is his near point?
(b) After `10` years he finds that while wearing same specks he must hold the book `40cm` from his eyes. What is his near point now, what power lens does he require now to read a book again at `25cm`?

Explanation

(a) `f = (100)/(P)= (100)/(2) = 50 cm`
`(1)/(-(N.P.)) -(1)/(-("distance of object")) = (1)/(f)`
`(1)/(-(N.P)) - (1)/(-25) = (1)/(50) rArr N.P = 50 cm`
(b) New `N.P.`
`(1)/(-(N.P.)') -(1)/(-("distance of object")) = (1)/(f)`
`(1)/(-(N.P.)') - (1)/(-40)=(1)/(50) rArr (1)/((N.P)') = (1)/(40)-(1)/(50) = (1)/(200)`
`(N.P') = 200 cm `
New lens
`(1)/(-200)-(1)/(-25)=(1)/(f')`
`(1)/(f') = (1)/(25)-(1)/(200)=(7)/(200) rArr f' = (200)/(7) cm`
`P = (100)/(f'(cm)) = (100)/(200//7) =+3.5D`