Q. 22

# The optical properties of a medium are governed by the relative permittivity (ε_{r}) and relative permeability (μ_{r} ). The refractive index is defined as 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 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 2nd quadrant, them the refracted beam is in the 3rd quadrant.

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

Answer :

(i) Let’s assume the given postulate is true, then if A and B be two parallel rays entering to such a medium from air the refracted diagram will be **FIG (1)**

Here incidence angle is θi and refracted angle is θr . AB shows the incident wave front and ED shows the refracted wave front, then all the points on ED will have the same phase.

We know all the points with the same optical path length must have the same phase.

**FIG (1)**

Given n2=

n_{2}AE=BC+ n_{2}CD

If BC>0,

CD should be greater than 0, which is true according postulate diagram, which means rays of light enter such a medium from air (refractive index = 1) at an angle in 2nd quadrant, then the refracted beam is in the 3rd quadrant.

Let us consider the normal case where light entering 2^{nd} quadrant refracting in 4rth quadrant as in **FIG (2)**, then

n_{2}AE=BC+ n_{2}CD

,

which means if AE>CD, BC <0 which is not possible

the postulate is true

**FIG (2)**

(ii) From **FIG (1)**

--Hence Snell’s law is proved

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