Question

A man with normal near point $25cm$ reads a book with small print using a magnifying glass, a thin convex lens of focal length $5cm$. The closest and farthest distances from the magnifying glass at which he can read the book when viewing through the magnifying glass, respectively are -

• A. $4.17cm,5cm$
• B. $3cm,6cm$
• C. $2cm,3cm$
• D. $5.17cm,6cm$

Answer 1

The correct option is A $4.17cm,5cm$

The magnifying glass must form the image of the book between $25cm$ (least distance of distinct vision) and $\infty$



For image formed at $25cm$ from the eye,
$v=-25cm$ (since magnifying glass is held close to the eye and it forms virtual image)
and given $f=5cm$
Using lens formula, $\frac{1}{u}=\frac{1}{v}-\frac{1}{f}=\frac{1}{-25}-\frac{1}{5}$
$\Rightarrow u=\frac{-25}{6}=-4.17cm$
For image formed at $\infty$, object should be placed at focus i.e at $5cm$ from the lens.
Thus, the book should be placed between $4.17cm$ and $5cm$ from the magnifying glass.