Question

An object of height $2cm$ is placed at a distance $20cm$ in front of a concave mirror of focal length $12cm$. Which of the following is true about image?

• A. The position of image is $30cm$ in front of mirror
• B. Size of the image is $3cm$
• C. The image is real, inverted and magnified
• D. All the above are true

Answer 1

The correct option is D All the above are true

Size of object $h_o=2cm$
Size of the object $h_i=?$
Focal length $f=-12cm$
Object distance $u=-20cm$
Image distance $v=?$
Using mirror formula
$\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$
$\frac{1}{-12}=\frac{1}{v}+\frac{1}{-20}$
$\frac{1}{v}=\frac{-5+3}{60}$
$v=-30cm$
Magnification (M)$=\frac{h_i}{h_o}=\frac{-v}{u}=\frac{30}{-20}=-1.5$
$h_i=-1.5\times 2=-3cm$
Image will be real, inverted and magnified.