[UPSC IFoS 2010] Electromagnetic Theory (Q380, 10M)

Consider a perfectly conducting half-space as shown below :

A uniform plane wave given by \begin{align*} \vec{E}^i &= \hat{x} E_0 e^{-j k z} \ \vec{H}^i &= \hat{y} \frac{E_0}{\eta_0} e^{-j k z} \quad \eta_0 = 120\pi\text{ ohm} \end{align*} is incident normally on the boundary. Write down the expressions for the reflected electric and magnetic fields.