(a) A nearsighted person cannot clearly see beyond `200 cm`. Find the power of the lens needed to see objectes at large distances.
(b) A farsighted person cannot see objects placed closer to `50cm`. Find the power of the lens needed to see the objets at `20cm`.
(c) A person wears glasses of power `-2.5 D`. Is the person farsighted or nearsighted? What is the far point of the person without the glasses?

Explanation

(a) `F.P. = 200cm`
`(1)/(-(F.P.)) -(1)/(-("distance of object")) = (1)/(f)`
`(1)/(-200)-(1)/(oo) = (1)/(f) rArr f=- 200cm`
`P = (100)/(f(cm)) = (100)/(-200) =-0.5D`
(b) `N.P. = 50cm`
`(1)/(-(N.P.)) -(1)/(-("distance of object")) = (1)/(f)`
`(1)/(-50)-(1)/(-20) = (1)/(f) rArr (1)/(f)=(1)/(20) - (1)/(50) = (3)/(100)`
`f = (100)/(3)cm`
`P = (100)/(f(cm)) = (100)/(100//3) = +3D`
(c) `P=- 2.5D` i.e concave lens, the person is nearsighted,
`f = (100)/(-2.5) =- 40`
`(1)/(-(F.P.)) -(1)/(-("distance")) = (1)/(f)`
`(1)/(-(F.P.)) -(1)/(oo)=(1)/(-40) rArr F.P. = 40cm`