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) (i) Closest distance at which the person can read the book :
`"Image distnace, "v=-25cm`
`"Focal length of lens, "f=5cm`
From lens formula
`(1)/(u_("min"))=(1)/(v)-(1)/(f)=-(1)/(25)-(1)/(5)=-(6)/(25)`
`rArr" "u_("min")=-(25)/(6)cm =-4.16cm`
(ii) Farthest distance at which the person can read the book :
Image distnace, `v=-oo, f=5cm`
From lens formula
`(1)/(u_("max"))=(1)/(v)-(1)/(f)=(-1)/(oo)-(1)/(5)=(-1)/(5)`
`rArr u_("max")=-5cm`
(b) Maximum angular magnification `=(D)/(u_("min"))`
`=(25)/(25//6)=6`
Minimum angular magnification `=(D)/(u_("max"))`
`=(25)/(5)=5`
`"Ratio "=(6)/(5)`