Answer
(a) $5cm$
(b) $-2.5cm$
(c) increase
Work Step by Step
(a) We know that
$m=-\frac{d_i}{d_{\circ}}$
$0.5=-\frac{d_i}{d_{\circ}}$
$\implies d_i=-\frac{d_{\circ}}{2}$
Now $\frac{1}{f}=\frac{1}{d_{\circ}}+\frac{1}{d_i}$
We plug in the known values to obtain:
$-\frac{1}{5}=\frac{1}{d_{\circ}}+(-\frac{2}{d_{\circ}})$
This simplifies to:
$d_{\circ}=5cm$
(b) We can find the image distance as
$d_i=-\frac{d_{\circ}}{2}$
$d_i=-\frac{5cm}{2}$
$d_i=-2.5cm$
(c) We know that if we move the object closer to the lens, then the magnification of the image increases.