Question

A square wire of side $3.0cm$ is placed $25cm$ in front of a concave mirror of focal length $10cm$, with its centre on the axis of the mirror and its plane normal to the axis. The area enclosed by the image of the wire is :

• A. 7.5 cm${}^2$
• B. 6.0 cm${}^2$
• C. 4.0 cm${}^2$
• D. 3.0 cm${}^2$

Answer 1

The correct option is C 4.0 cm${}^2$

We know that the magnification of a concave mirror is given as $m=\frac{f}{f-u}$.
So, we get: $m=\frac{-10}{-10-(-25)}=-\frac{2}{3}$
Thus the length of the side gets magnified by this factor. The image length is thus $\frac{2}{3}\times 3=2cm$
Area of the image is thus $2\times 2=4c{m}^2$