A man with a normal near point (25 cm) reads a book with small print using a magnifying glass of focal length 5 cm. The closest distance at which he can keep the book when viewing through the magnifying glass would be about-
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 4.2 cm
The book is closest to the lens when the virtual image is formed at the near point, 25 cm from the eye (lens held close to the eye). Using the lens formula with the Cartesian sign convention (distances on the object side negative):
\( f = +5\,\mathrm{cm} \)
\( v = -25\,\mathrm{cm} \)
\( \displaystyle \frac{1}{v} - \frac{1}{u} = \frac{1}{f} \)
\( \displaystyle \frac{1}{u} = \frac{1}{v} - \frac{1}{f} = -\frac{1}{25} - \frac{1}{5} = -\frac{6}{25} \)
\( \displaystyle u = -\frac{25}{6}\,\mathrm{cm} \approx -4.2\,\mathrm{cm} \)
The book must be about 4.2 cm from the lens.