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