The optical properties of a medium are governed by the relative permitivity and relative permeability (. The refractive index is defined as . For ordinary material and and the positive sign is taken for the square root.
In 1964, a Russian scientist V. Veselago postulated the existence of material with and . Since then such ‘metamaterials’ have been produced in the laboratories and their optical properties studied.
For such materials . 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 in quadrant, then the refracted beam is in the quadrant.
(ii) Prove that Snell’s law holds for such a medium.
Suppose the postulate is true, then two parallel rays would proceed as shown in Figure. Assuming shows a wave front then all points on this must have the same phase. All points with the same optical path length must have the same phase.
As showing that the postulate is reasonable. If however, the light proceeded in the sense it does for ordinary material (viz. in the fourth quadrant, Fig. 2)
As , showing that this is not possible. Hence the postulate is correct.