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`.
(a) What are the closest and the farthest distances at which he can read the book when viewing through the magnifying glass ?
(b) What is the maximum and the minimum angular magnifications (magnifying powers) possible using the above simple microscope ?

Explanation

(a) As for normal eye far and near point are `oo` and `25` cm respectively, so for magnifier `v_(max) -oo "and" v_(min) = -25"cm"` . However , for a lens as `(1)/(v) - (1)/(u) = (1)/(f) implies u = (f)/((f//v)-1)`
So u will be minimum when v= minimum = `-25 "cm i.e.," (u)_(min) = (5)/(-(5//25)-1) = -(25)/(6) = -4.17 "cm"`
Ans u will be maximum when v= maximum =`oo` i.e., `u_(max) = (5)/(((5)/(oo)-1)) = -5` cm
So the closest and farthest distance of the book from the magnifier (or eye) for clear viewing are `4.17 "cm and " 5` cm respectively.