Question

How far an object must be placed in front of a converging lens of focal length 10 cm in order to produce an erect image of linear magnification 4?

• A. 15.8 cm
• B. 2.5 cm
• C. 12.5 cm
• D. 7.5 cm

Answer 1

The correct option is D 7.5 cm

$Answer:-$ $d_o=7.5$ cm

The lens equation expresses the quantitative relationship between the object distance $d_o$, the image distance $d_i$, and the focal length $\left(f\right)$. The equation is stated as follows:

$\frac{1}{f}=\frac{1}{d_o}+\frac{1}{d_i}$

The magnification equation relates the ratio of the image distance and object distance:-

$M=-\frac{d_i}{d_o}$

$4=-\frac{d_i}{d_o}$

$d_i=-4d_o$ ------eqn (1)

$\frac{1}{10}=\frac{1}{d_o}+\frac{1}{d_i}$ -----eqn(2)

using eqn(1) and (2) solve for $d_o$

$d_o=7.5$ cm