Question

A card sheet divided into square each of size 1 mm² is being viewed at a distance of 9 cm through a magnifying glass (a converging lens of focal length 10 cm) held close to the eye. What is the magnification produced by the lens?

• A. 10/19
• B. 9
• C. 10
• D. 5

Answer 1

Answer: (C)

10

Answer 2

The problem asks for the magnification produced by a magnifying glass. We are given:

• Object distance, $u = -9$ cm (negative by sign convention as the object is placed in front of the lens).
• Focal length of the converging lens, $f = 10$ cm.

First, we find the position of the image using the lens formula: $\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$ Substituting the given values: $\frac{1}{10 \text{ cm}} = \frac{1}{v} - \frac{1}{-9 \text{ cm}}$ $\frac{1}{10} = \frac{1}{v} + \frac{1}{9}$ $\frac{1}{v} = \frac{1}{10} - \frac{1}{9}$ $\frac{1}{v} = \frac{9 - 10}{90} = -\frac{1}{90}$ $v = -90 \text{ cm}$

The linear magnification ($m$) is given by: $m = \frac{v}{u}$ Substituting the values of $v$ and $u$: $m = \frac{-90 \text{ cm}}{-9 \text{ cm}}$ $m = 10$