Question

An object of height $2\text{cm}$ is placed on the principal axis of a concave mirror at a distance of $12\text{cm}$ from the pole. If the image is real, inverted and $5\text{cm}$ high, then location of the image and the focal length of the mirror is

• A. $30\text{cm},8.6\text{cm}$
• B. $30\text{cm},7.6\text{cm}$
• C. $25\text{cm},8.6\text{cm}$
• D. $25\text{cm},7.6\text{cm}$

Answer 1

The correct option is A $30\text{cm},8.6\text{cm}$

Given:
Height of object, $h_o=+2\text{cm}$
Height of image, $h_i=-5\text{cm}$
Distance of object, $u=-12\text{cm}$
So, $m=\frac{h_i}{h_o}=\frac{-v}{u}$
$\Rightarrow \frac{-5}{+2}=\frac{-v}{-12}$
$\Rightarrow v=-30\text{cm}$
Applying mirror formula,
$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$
$\Rightarrow \frac{-1}{30}-\frac{1}{12}=\frac{1}{f}$
$\Rightarrow \frac{1}{f}=\frac{-7}{60}$
$\Rightarrow f=-8.6\text{cm}$