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) Here, `f = 5 cm, u = ?`
For the closest distance , `v = -25 cm`
As `(1)/(f)=(1)/(v)-(1)/(u) :. (1)/(u)=(1)/(v)-(1)/(f) = (1)/(-25)-(1)/(5) = (-1 - 5)/(25)`
`u = (25)/(-6) = -4.2 cm`
This is the closest distance at which he can read the book.
For the farthest distance, `v' = oo, u' = ?`
As `(1)/(f)=(1)/(v')-(1)/(u') :. (1)/(u')=(1)/(v')-(1)/(f)=(1)/(oo)-(1)/(5)=-(1)/(5)`
`u' = -5 cm`
This is the farthest distance at which he can read the book.
(b) Max. angular magnification `m=(d)/(u)=(25)/(25//6) = 6`, Min. angular magnification `m' = (d)/(u')=(25)/(5) = 5`.