3. A monochromatic plane EM wave travels in the negative z direction, and is incident on
the surface of a lake at z=0. The electric field of the incident wave at the lake's
surface is given by
$\vec{E}_i (z=0,t) = E_0 \cos \omega t \hat{x}$,
where $E_0$ is the amplitude and $\omega$ is the angular frequency. Part of the EM wave is
reflected by the lake's surface. The magnetic field of the reflected wave at the lake's
surface is given by
$\vec{B}_r (z=0,t) = \frac{E_0}{c} \cos \omega t \hat{y}$
PHYS 2041 University Physics III
(a) Write down the expression $\vec{E}_i (z,t)$, $\vec{B}_i (z,t)$ of the electric field and magnetic
field for the incident wave for z >0. Explain your answer. What is the wavelength
of the wave?
(b) Write down the expression $\vec{E}_r (z,t)$, $\vec{B}_r (z,t)$ of the electric field and magnetic
field for the reflected wave for z> 0.
(c) Find the time averaged Poynting vectors of the incident and reflected waves
respectively. What is the physical meaning of the Poynting vector?
(d) Find the fraction of EM wave energy reflected by the lake.
