A man with normal near point (25 cm) reads a book with small print using a magnifying glass : a thin convex lens of focal length `5 cm`.
What are the closest and the farthest distances at which he can read the book when viewing through the magnifying glass ?

Explanation

(a) As for normal eye far and near points are `oo` and 25 cm respectively, so for magnifier
`v_(max)=-ooandv_(min)=-25cm`
However, for a lens as `1/v-1/u=1/f`
i.e., `u=f/((f//v)-1)`, So u will be minimum
when v = min = -25 cm i.e.,
`(u)_(min)=5/(-(5//25)-1)=(-25)/6=-4.17cm` and u will be maximum when v = max = `oo`
i.e., `(u)_(max)=5/((5//oo)-1)=-5cm`
So the closest and farthest distances of the book from the magnifier (or eye) for clear viewing are 4.17 cm and 5cm respectively.
(b) As in case of simple magnifier MP = (D/u). So MP will be minimum when u= max = 5 cm
i.e., `(MP)_(min)=(-25)/(-5)=5" "[=D/f]`
And MP will be maximum when u = min = (25/6)cm
`(MP)_(min)=(-25)/(-(25//6))=6" "[=1+D/f]`