A plane electromagnetic wave of wave intensity $6\,W/m^2$ strike a small mirror of area $30\,cm^2$ , held perpendicular to a approching wave. The momentum transmitted in $kg\, m/s$ by the wave to the mirror each second will be

The energy of an electromagnetic wave contained in a small volume oscillates with

The electric field in an electromagnetic wave is given as $\vec{E}=20 \sin \omega\left(t-\frac{x}{c}\right) \vec{j} NC ^{-1}$ Where $\omega$ and $c$ are angular frequency and velocity of electromagnetic wave respectively. The energy contained in a volume of $5 \times 10^{-4}\, m ^3$ will be $.....\times 10^{-13}\,J$

(Given $\varepsilon_0=8.85 \times 10^{-12}\,C ^2 / Nm ^2$ )

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. 

A charged particle oscillates about its mean equilibrium position with a frequency of $10^9 \;Hz$. What is the frequency of the electromagnetic waves produced by the oscillator?

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