Question

A concave mirror of radius of curvature 40 cm produces a real image 5 times the size of object. The distance between object and its image is

• A. 120cm
• B. 144cm
• C. 96cm
• D. 24cm

Answer 1

The correct option is C 96cm

R = -40 cm, $f=\frac{R}{2}=-20cm,m=-5$$-\frac{v}{u}=\frac{h}{h}=-5\left(\because m=-\frac{v}{u}=\frac{h}{h}\right)$$\Rightarrow \frac{v}{u}=5$ .....(i)
Using the mirror formula,
$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}\Rightarrow 1+\frac{v}{u}=\frac{v}{f}\Rightarrow 1+5=\frac{v}{-20}\Rightarrow v=-120cm\Rightarrow u=-24cm[using\; (i)]$
Distance between object and image = |v – u| = |(–120) – (–24)| = 96 cm
Hence, the correct answer is option (c).