Question

An object is placed at a distance $2f$ from the pole of a convex mirror of focal length $f$ . The linear magnification is:

• A. $\frac{1}{3}$
• B. $\frac{2}{3}$
• C. $\frac{3}{4}$
• D. $1$

Answer 1

The correct option is A $\frac{1}{3}$

Here,

Object distance, $u=-2f$

Image distance, $v=$?

From mirror formula,

$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$

$\frac{1}{v}+\frac{1}{-2f}=\frac{1}{f}$

$\frac{1}{v}=\frac{3}{2f}$

$v=\frac{2f}{3}$

Now,
Magnification, $M=\frac{-v}{u}$

$=-\frac{\frac{2f}{3}}{(-2f)}$

$=\frac{1}{3}$

(M is positive for convex mirror)