Question

If the distance between object and its two times magnified virtual image produced by a curved mirror is 15 cm focal length of the mirror must be:

• A. -10 cm
• B. 10/3 cm
• C. -12 cm
• D. 15 cm

Answer 1

Answer: (A)

-10 cm

Answer 2

For a curved mirror, the magnification is

$m=-\frac{v}{u}$ and given $m=2$.

This gives

$-\frac{v}{u}=2 \Rightarrow v=-2u$.

The distance between the object and image is

$|v-u|=15 \Rightarrow |-2u-u|=3|u|=15 \Rightarrow |u|=5\,\text{cm}$.

Taking $u=-5$ (object in front), then $v=10$ cm. Using the mirror formula,

$\frac{1}{f}=\frac{1}{u}+\frac{1}{v}=\frac{1}{-5} +\frac{1}{10}=-\frac{2}{10}+\frac{1}{10}=-\frac{1}{10}$,

so

$f=-10\,\text{cm}$.