(a) (i)
`u = oo, v = 2cm`
`(1)/(v)-(1)/(u)=(1)/(f) rArr f = v = 2cm`
`P = (100)/(f(cm)) = (100)/(2) = 50D`
(ii)
`(1)/(f)=(1)/(v)-(1)/(u)=(1)/(2)-(1)/(-25) = (17)/(50) rArr f = 50//27`
`P = (100)/(f(cm)) = (100)/(50//27) = 54D`
(b)
`(1)/(f)=(1)/(v)-(1)/(u)=(1)/(2)-(1)/(-100)=(50+1)/(100)=(51)/(100) rArr f=(100)/(51)cm`
`P = (100)/(f(cm)) =(100)/(100//51) = 51D`
`(1)/(f)=(1)/(v)-(1)/(u)=(1)/(2)-(1)/(-10)=(6)/(10) rArr f = (10)/(6)=(5)/(3)cm`
`P = (100)/(f(cm)) = (100)/(5//3) = 60D`
Range: `51D` to `60D`
(c) when the eye is most relaxed, focal length is maximum or power is minimum hence in most relaxed case, `P = 50D`,
`f = (100)/(P)=(100)/(50) = 2cm`. The rays coming from infinite are focused at retina, hence `v = 2 cm = f`
`(1)/(v)-(1)/(u)=(1)/(f) rArr (1)/(v)-(1)/(oo)=(1)/(2) rArr v = 2cm`
Distance of retina from lens `d =v=2cm`
The eye is most strained when object is at near point. Hence focal length is minimum or power is maximum i.e `60 D`,
`f = (100)/(60) = (5)/(3)cm`. The image is formed at retina.
`(1)/(v)-(1)/(u)=(1)/(f)`
`(1)/(2)-(1)/(u)=(1)/(5//3) rArr (1)/(u)=(1)/(2)-(3)/(5)=(5-6)/(10) rArr u =- 10cm`
`N.P. = 10cm`