Answer
$16cm$
Work Step by Step
We know that the object distance for the secondary mirror is given as
$d_{os}=x-d_{ip}$
$d_{os}=43cm-50cm=-7cm$
and the image distance for the secondary mirror is given as
$d_{is}=x+x^{\prime}$
$d_{is}=43cm+8cm=51cm$
Now $\frac{1}{f_2}=\frac{1}{d_{os}}+\frac{1}{d_{is}}$
We plug in the known values to obtain:
$\frac{-2}{R}=\frac{1}{-7cm}+\frac{1}{51cm}$
This simplifies to:
$R=16cm$
