Let the equations of two ellipses be $E_1:\frac{x^2}{3}+\frac{y^2}{2}=1$ and $E_2:\frac{x^2}{16}+\frac{y^2}{b^2}=1$. If the product of their eccentricities is $\frac{1}{2}$ , then the length of the minor axis of ellipse $E_2$ is