Q: An object is 30 cm from a spherical mirror, the central axis. The absolute value of lateral magnification is 1/2. The image produced is inverted. What is the focal length of the mirror ?

Sol: image inverted so it is real u and v both are negative. Magnification is 1/2,therefore,

v = u/2, given,u = -30 cm, v = -15 cm

Using the mirror formula, $\large \frac{1}{v} + \frac{1}{u} = \frac{1}{f} $

$\large \frac{1}{-15} + \frac{1}{-30} = \frac{1}{f} $

$\large – \frac{1}{10} = \frac{1}{f} $

f = – 10 cm

Since focal length is negative the given mirror is concave.