Light with an average flux of $20\, W / cm ^{2}$ falls on a non-reflecting surface at normal incidence having surface area $20\, cm ^{2} .$ The energy recelved by the surface during time span of $1$ minute is $............J$

A metal sample carrying a current along $X-$ axis with density $J_x$ is subjected to a magnetic field $B_z$ ( along $z-$ axis ). The electric field $E_y$ developed along $Y-$ axis is directly proportional io $J_x$ as well as $B_z$ . The constant of proportionality has $SI\, unit$.

The electric field part of an electromagnetic wave in a medium is represented by

$E_x=0, E_y=2.5 \frac{N}{C}\, cos\,\left[ {\left( {2\pi \;\times\;{{10}^6}\;\frac{{rad}}{s}\;\;} \right)t - \left( {\pi \;\times\;{{10}^{ - 2}}\;\frac{{rad}}{m}} \right)x} \right]$,and  $ E_z=0$ . The wave is

A lamp emits monochromatic green light uniformly in all directions. The lamp is $3%$ efficient in converting electrical power to electromagnetic waves and consumes $100\,W $ of power. The amplitude of the electric field associated with the electromagnetic radiation at a distance of $10m$  from the lamp will be........$V/m$

A flood light is covered with a filter that transmits red light. The electric field of the emerging beam is represented by a sinusoidal plane wave

$E_x=36\,sin\,(1.20 \times 10^7z -3.6 \times 10^{15}\,t)\,V/m$

The average intensity of the beam will be.....$W/m^2$

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.