Distance between an object and three times magnified real image is 40 cm . The focal length of the m

Question

Distance between an object and three times magnified real image is 40 cm . The focal length of the mirror used is $\_\_\_\_$ cm .

Professor PC Thomas Classes · Answer

A real, magnified image is formed by a concave mirror. The magnification is $m = \frac{-v}{u} = -3$, which means $v = 3u$. The distance between the object and the real image is $|v - u| = 3u - u = 2u$. We are given $2u = 40 	ext{ cm} \implies u = 20 	ext{ cm}$. By the Cartesian sign convention, $u = -20 	ext{ cm}$ and $v = -60 	ext{ cm}$. Applying the mirror formula: $\frac{1}{f} = \frac{1}{v} + \frac{1}{u} = -\frac{1}{60} - \frac{1}{20} = \frac{-1-3}{60} = -\frac{4}{60} = -\frac{1}{15}$. Thus, $f = -15 	ext{ cm}$.