 # A man with normal near point (25 cm) reads a book with small print using a magnifying glass

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.
(i) What is the closest and the farthest distance at which he should keep the lens from the page, so that he can read the book when viewing through the magnifying glass?
(ii) What is the maximum and the minimum angular magnification (magnifying power) possible using the above simple microscope?

(i) Focal length f = +5 cm, v = -25 cm
It is for the closest distance.
Using the lens formula,
1/f = 1/v -1/u
===> 1/5 = 1/-25 -1/u
====> 1/u = -1/25-1/5 = -1-5/25 = -6/25
u = -25/6 = -4.2 cm
For the farthest distance, v’ = ∞ and f = 5cm
1/f = 1/v’ -1/u’
===> 1/5 = 1/∞ - 1/u’
u’ = -5cm
Thus the closest and the farthest distances are -4.2cm and -5 cm respectively.

(ii) Maximum angular magnification,
\$m_{ max }\$ = D/u = 25/25/6=6
Minimum angular magnification is at the farthest distance,
\$m_{ min }\$ = D/u’ = 25/5 =5