The optical properties of a medium are governed by the relative permittivity  (εr) and relative permeability (μ_r). The refractive index is defined as $\sqrt[]{{\mathit{\mu }}_{\mathit{r}}{\mathit{\epsilon }}_{\mathit{r}}}$ = n.For ordinary material ε_r > 0 and μ_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 εr < 0 and μr < 0. Since then such 'metamaterials' have been produced in the laboratories and their optical properties studied. For such materials n = – $\sqrt[]{{\mathit{\mu }}_{\mathit{r}}{\mathit{\epsilon }}_{\mathit{r}}}$   . 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 θ in 2nd quadrant, them the refracted beam is in the 3rd quadrant.  (ii) Prove that Snell's law holds for such a medium.

The angle between the plane of vibration and plane of polarization is

A uniform thin rope of length 12 m and mass 6 kg hangs vertically from a rigid support and a block of mass 2 kg is attached to its free end. A transverse short wave-train of wavelength 6 cm is produced at the lower end of the rope. What is the wavelength of the wave train (in cm) when it reaches the top of the rope?
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In the Young's double slit experiment, the distance between the slits varies in time as d(t) = d? + a? sin(ωt); where d?, ω and a? are constants. The difference between the largest fringe width and the smallest fringe width obtained over time is given as :

An unpolarised light beam of intensity 2l₀ is passed through a polaroid P and then through another polaroid Q which is oriented is such a way that its passing axis makes an angle of 30° relative to that of P. The intensity of the emergent light is
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In Young’s double slit experiment the two slits are 0.6mm distance apart. Interference pattern is observed on a screen at a distance 80cm from the slits. The first dark fringe is observed on the screen directly opposite to one of the slits. The wavelength of light will be__________nm.