If the distance between the foci of an ellipse is half the length of its latus recturn , then the eccentricity of the ellipse is :

Question

$\begin{array}{1 1} \frac{1}{2} \\ \frac{2 \sqrt 2-1}{-2} \\ \sqrt 2 -1 \\ \frac{\sqrt 2-1}{2} \end{array}$