Answer
The lamp should be $~~17~cm~~$ from the mirror.
Work Step by Step
We can find the required distance of the lamp $s$:
$\frac{1}{s}+\frac{1}{s'} = \frac{1}{f}$
$\frac{1}{s}+\frac{1}{s'} = \frac{2}{R}$
$\frac{1}{s} = \frac{2}{R} - \frac{1}{s'}$
$\frac{1}{s} = \frac{2}{30~cm} - \frac{1}{120~cm}$
$\frac{1}{s} = \frac{7}{120~cm}$
$s = \frac{120~cm}{7}$
$s = 17~cm$
The lamp should be $~~17~cm~~$ from the mirror.
