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The optical properties of a medium are governed by the relative permitivity  (εr) and relative permeability (μr). The refractive index is defined as μrεr = n.For ordinary material εr > 0 and μr > 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 = – μrεr . 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.

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(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.

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