JAMB Physics 2018 Paper

Concept:For a convex mirror, the image is virtual, erect, and located behind the mirror, so the image distance and focal length are negative.Explanation:Given: $v = -6\, \mathrm{cm}$ (virtual image behind the mirror) and magnification $m = 0.6$.Use the magnification formula for mirrors:$$m = \frac{-v}{u}$$Substitute values:$$0.6 = \frac{-(-6)}{u} = \frac{6}{u}$$Solve for the object distance:$$u = \frac{6}{0.6} = 10\, \mathrm{cm}$$Apply the mirror formula:$$\frac{1}{f} = \frac{1}{u} + \frac{1}{v}$$Substitute $u = 10\, \mathrm{cm}$ and $v = -6\, \mathrm{cm}$:$$\frac{1}{f} = \frac{1}{10} + \frac{1}{-6} = \frac{3 - 5}{30} = -\frac{2}{30} = -\frac{1}{15}$$Therefore, the focal length is:$$f = -15\, \mathrm{cm}$$The negative sign confirms the convex mirror.Answer:D. $-15.00\, \mathrm{cm}$