Answer
$d_i=1.707r$
$m=-2.41$
Work Step by Step
$r=d_o+d_i$
$d_o=r-d_i$
$d_i=\frac{1}{\frac{1}{f}-\frac{1}{d_o}}=\frac{1}{\frac{2}{r}-\frac{1}{d_o}}=\frac{1}{\frac{2}{r}-\frac{1}{r-d_i}}=\frac{r^2-rd_i}{3r-2d_i}$
$r^2-4rd_i+2di^2=0$
$d_i=1.707r$
$d_i=0.293r$ The first solution is the answer
$m=-\frac{d_i}{d_o}=-\frac{d_i}{r-d_i}=-2.41$