Answer
$16cm$
Work Step by Step
Power of objective $Po=+100D$
Power of eye piece $Pe=+50D$
Total desired magnification $=-200X$
Respective focal lengths
$fe=\frac{1}{P}=\frac{1}{50}=2cm$
$fo=\frac{1}{P}=\frac{1}{100}=1cm$
$m_{total}=-\frac{25\times(cm)L}{fofe}$
or, $-200=-\frac{25\times L}{1\times 2}$
or, $L=16cm$