Question

The optical properties of a medium are governed by the relative permitivity  (ε_r) and relative permeability (μ_r). The refractive index is defined as √μ_rε_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 ε_r < 0 and μ_r < 0. Since then such ‘metamaterials’ have been produced in the laboratories and their optical properties studied. For such materials n = – √μ_rε_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 2^nd quadrant, them the refracted beam is in the 3^rd quadrant. 

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

Answer 1

(i) Suppose the postulate is true, then two parallel rays would proceed as shown in Fig. 1. Assuming ED 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)

showing that this is not possible. Hence the postalate is correct.

(ii) From Fig. 1.