The optical properties of a medium are governed

Question:

The optical properties of a medium are governed by the relative permittivity (εr) and relative permeability (µr ). The refractive index is defined as √µr εr = 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 the 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

Solution:

(1)

BC = √μrεr (CD-AE)

BC >0; CD > AE

-√μrεr AE = BC – √μrεr CD

BC = √μrεr (CD – AE)

AE > CD

Therefore, BC < 0

(ii) BC = AC sin θi

CD – AE = AC sin θr

BC = √μrεr

AC sin θi = √μrεr AC sin θr

sin θi/sin θr = √μrεr

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