A uniform plane wave having parallel polarization is obliquely incident on an air - dielectric interface as shown in Fig. If the wave has an electric field $$E = 10\,\,V/m$$, find
(i) The angle of incidence $${\theta _i}$$ for which there is no reflection of the wave.
(ii) The surface charge density at the interface.

A wave traveling in the $$+Z$$-direction, is the resultant of two linearly polarized components, $${E_x}\,\,\, = \,\,\,\,\,\,3$$ $$\,\,\,\,\cos \omega t$$ and $$\,{E_y}\,\,\,\, = \,\,\,2\,\cos \,\left( {\omega t + {{45}^ \circ }} \right)$$

Determine
(1) The axial ratio
(2) The angle between the major axis of the polarization ellipse and the $$+x$$-axis.

Match the following descriptions with each of the diagrams given in Fig. Fields are near the interface, but on opposite sides of the boundary. Vectors are drawn to scale.

(a) Medium $$1$$ and medium $$2$$ are dielectrics with $${\varepsilon _1} > {\varepsilon _2}$$
(b) Medium $$1$$ and medium $$2$$ are dielectrics with $${\varepsilon _1} < {\varepsilon _2}$$
(c) Medium $$2$$ is a perfect conductor
(d) Impossible
(e) Medium $$1$$ is a perfect conduct