WAEC Physics 2012 Paper

Concept:A convex mirror forms a virtual, erect and diminished image. Use the spherical mirror formula and magnification relation to find the image height.Explanation:For a convex mirror, by sign convention take focal length $f = +10\ \text{cm}$.The object is on the incident side, so object distance $u = -20\ \text{cm}$.Mirror formula: $\frac{1}{u}+\frac{1}{v}=\frac{1}{f}$, so $\frac{1}{v} = \frac{1}{f} - \frac{1}{u}$.Substitute: $\frac{1}{v} = \frac{1}{10} - \frac{1}{(-20)} = \frac{1}{10}+\frac{1}{20} = \frac{3}{20}$.Thus, $v = \frac{20}{3}\ \text{cm} \approx 6.67\ \text{cm}$.The positive value of $v$ shows the image is virtual and located behind the mirror.Magnitude of magnification, $|m| = \frac{|v|}{|u|} = \frac{20/3}{20} = \frac{1}{3}$.Image height, $h_i = |m| h_o = \frac{1}{3}\times 2.5\ \text{cm} \approx 0.83\ \text{cm}$.Answer:The height of the image is approximately $0.83\ \text{cm}$, so none of the listed options is correct.