Question

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

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

Answer 1

The correct option is A ${4cm}^2$

Side of square is 3cm i.e, object length is 1.5cm

$u=-25$ ; $f=-10$

$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$

$\frac{1}{v}-\frac{1}{25}=\frac{-1}{10}$

$v=\frac{-50}{3}$

Magnification=$-\frac{v}{u}=-\frac{\frac{-50}{3}}{-25}=-\frac{2}{3}$

Image height is $1.5\times \frac{2}{3}=1cm$

Side of image square is $1\times 2=2cm$

Area of square is $2\times 2=4c{m}^2$