The electric field part of an electromagnetic wave in a medium is represented by $E_x = 0\,;$

${E_y} = 2.5\,\frac{N}{C}\,\,\cos \,\left[ {\left( {2\pi \, \times \,{{10}^6}\,\frac{{rad}}{m}} \right)t – \left( {\pi  \times {{10}^{ – 2}}\frac{{rad}}{s}} \right)x} \right];$

$E_z = 0$. The wave is

A light wave is incident normally on a glass slab of refractive index $1.5$. If $4\%$ of light gets reflected and the amplitude of the electric field of the incident light is $30\, V/m$, then the amplitude of the electric field for the wave propagating in the glass medium will be…….$ V/m$

An electron is constrained to move along the $y-$axis with a speed of $0.1\, c$ (c is the speed of light) in the presence of electromagnetic wave, whose electric field is $\overrightarrow{ E }=30 \hat{ j } \sin \left(1.5 \times 10^{7} t -5 \times 10^{-2} x \right)\, V / m$ The maximum magnetic force experienced by the electron will be: (given $c=3 \times 10^{8}\, ms ^{-1}$ and electron charge $\left.=1.6 \times 10^{-19} C \right)$

If ${\varepsilon _0}$ and ${\mu _0}$ are respectively, the electric permittivity and the magnetic permeability of free space. $\varepsilon $ and $\mu $ the corresponding quantities in a medium, the refractive index of the medium is

The optical properties of a medium are governed by the relative permitivity $({ \in _r})$ and relative permeability $(\mu _r)$. The refractive index is defined as $n = \sqrt {{ \in _r}{\mu _r}} $. For ordinary material ${ \in _r} > 0$ and $\mu _r> 0$ and the positive sign is taken for the square root. In $1964$, a Russian scientist V. Veselago postulated the existence of material with $\in _r < 0$ and $u_r < 0$. Since then such 'metamaterials' have been produced in the laboratories and their optical properties studied. For such materials $n =  – \sqrt {{ \in _r}{\mu _r}} $. As light enters a medium of such refractive index the phases travel away from the direction of propagation.

$(i) $ According to the description above show that if rays of light enter such a medium from air (refractive index $=1)$  at an angle $\theta $ in $2^{nd}$ quadrant, then the refracted beam is in the $3^{rd}$ quadrant.

$(ii)$ Prove that Snell's law holds for such a medium.