GATE 2021 EC – Question 25

Consider a rectangular coordinate system $(x,y,z)$ with unit vectors $\mathbf a_x,\mathbf a_y$, and $\mathbf a_z$. A plane wave traveling in the region $z\ge0$ with electric field vector $\mathbf E=10\cos(2\times10^8t+\beta z)\mathbf a_y$ is incident normally on the plane at $z=0$, where $\beta$ is the phase constant. The region $z\ge0$ is in free space and the region $z<0$ is filled with a lossless medium (permittivity $\varepsilon=\varepsilon_0$, permeability $\mu=4\mu_0$, where $\varepsilon_0=8.85\times10^{-12}$ F/m and $\mu_0=4\pi\times10^{-7}$ H/m). The value of the reflection coefficient is