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 `prop` and 25 cm respectively so for magnifier `V_(max) = - prop` and `V_(min) = - 23 cm` . 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= minimum =- 23 cm
`i.e., (u) _(min)= (5)/(-(5//25)-1) = - (25)/( 6) = - 4.17 cm`
Ans will be maximum when v= maximum `= prop`
i.e., `u_(max) = (5)/( (5)/(prop)-1) = - 5 cm`
So the closet and fartest distance of the book from the magnifier (or eye) for clear viewing are 4.17 cm and 5 cm respectively .
( b) As in case of simple magnifier `MP= (D//u) . ` So MP will be minimum when u= maximum = 5 cm
`i.e., (MP)_(min) = (-25)/(-5) = 5 , [ (D )/(f )]`
And MP will be maximum
when u= minimum `=(25 //6)` cm ,
`i.e., (MP)_(max) = (-25)/(-(25//6)) = 6 [=1+ (D )/( f )]`