A lady cannot see objects closer than `40cm` from the left eye and closer than `100cm` from the right eye. While on a mountaineering trip, she is lose from her team. She tries to make an astronomical trip, form her reading glasses to look fro her teammates. (a) Which glass should she use as the eyepiece? (b) What magnification can she get with relaxed eye?

Explanation

The near point for left eye is `40cm` and for right eye is `100cm`.
Left eye:
`(1)/(-(N.P.)) -(1)/(-("distance of object")) = (1)/(f_(1))`
`(1)/(-40)-(1)/(-25)= (1)/(f_(1))`
`(1)/(f_(1)) = (1)/(25)-(1)/(40)=(8-5)/(200) rArr f_(1) = (200)/(3)cm`
Right eye:
`(1)/(-100) - (1)/(-25) = (1)/(f_(2))`
`(1)/(f_(2)) = (1)/(25)-(1)/(100) = (4-1)/(100) rArr f_(2) = (100)/(3)cm`
(a) For astronomical telescope
`|m| = (f_(0))/(f_(e))`, for `|m|gt1, f_(0) gt f_(e)`
Since `f_(1) gt f_(2)`, left eye lens as objective, right eye lens as eye-piece.
(b) `m=- (f_(0))/(f_(e)) = -(f_(1))/(f_(2)) =- (200//3)/(100//3)=- 2`