Consider a rectangular coordinate system \( (x, y, z) \) with unit vectors \( \hat{a}_x, \hat{a}_y, \hat{a}_z \). A plane wave traveling in the region \( z \geq 0 \) with electric field vector
\[
E = 10 \cos(2 \times 10^8 t + \beta z) \hat{a}_y
\]
\text{is incident normally on the plane at } z = 0, \text{ where } \beta \text{ is the phase constant. The region } z \geq 0 \text{ is in free space and the region } z<0 \text{ is filled with a lossless medium (permittivity } \varepsilon = \varepsilon_0, \text{ permeability } \mu = 4\mu_0, \text{ where } \varepsilon_0 = 8.85 \times 10^{-12} \text{ F/m and } \mu_0 = 4\pi \times 10^{-7} \text{ H/m). The value of the reflection coefficient is:}