Two separate wires $A$ and $B$ are stretched by 2 mm and 4 mm respectively, when they are subjected to a force of 2 N. Assume that both the wires are made up of same material and the radius of wire $B$ is 4 times that of the radius of wire $A$. The length of the wires $A$ and $B$ are in the ratio of $a : b$. Then $\frac { a } { b }$ can be expressed as $\frac { 1 } { x }$, where $x$ is $\_\_\_\_$.