Two persons, both of height $h$, are standing at a distance of $h$ from each other. The shadow of one person cast by a vertical lamp-post placed between the two persons is double the length of the shadow of the other. If the sum of the lengths of the shadows is $h$, then the height of the lamp post is\\
(A) $\frac{\sqrt{3}}{2}h$\\
(B) $2h$\\
(C) $\left(\frac{1 + \sqrt{2}}{2}\right)h$\\
(D) $\left(\frac{\sqrt{3} + 1}{2\sqrt{2}}\right)h$.