Question

A square of side $3cm$ all is located at a distance $25cm$ from a concave mirror of focal length $10cm$. The centre of square is at the axis of the mirror and the plane is normal to rods of mirror. The area enclosed by the image of the square is

• A. $4c{m}^2$
• B. $6c{m}^2$
• C. $16c{m}^2$
• D. $36c{m}^2$

Answer 1

Answer: (A)

$4c{m}^2$

Height of the object $h_o=3cm$
Width of the object $b_o=3cm$
Given : $u=-25cm$ and $f=-10cm$
Using mirror formula $\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$
Or $\frac{1}{v}+\frac{1}{-25}=\frac{1}{-10}$
$⟹v=\frac{-25}{15}cm$
Magnification $\frac{h_i}{h_o}=\frac{-v}{u}$
$\therefore$ $\frac{h_i}{3}=\frac{-25/15}{25}$
$⟹h_i=2cm$
Similarly, $b_i=2cm$
Thus area of image formed $A_i=h_i{b}_i=\left(2\right)\left(2\right)=4c{m}^2$