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Q.

The refractive index and permeability of a medium are $1.5$ and $5 \times 10^{- 7} {Hm}^{- 1}$ respectively. The relative permittivity of the medium is nearly:

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a

$15$

b

$25$

c

$6$

d

$10$

answer is D.

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Detailed Solution

velocity in the medium, $v = \frac{c}{n} = \frac{3 \times 10^{8}}{1.5} = 2 \times 10^{8} {ms}^{- 1}$

Here, $μ = 5 \times 10^{- 7} {Hm}^{- 1} ∴ v = \frac{1}{\sqrt{με}} = \frac{1}{\sqrt{{με}_{0} ε_{r}}}$

$ε_{r} = \frac{1}{v^{2} {με}_{0}} = \frac{1}{{(2 \times 10^{8})}^{2} \times (5 \times 10^{- 7}) \times (8.85 \times 10^{- 12})} = 5.65 ≃ 6$

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The refractive index and permeability of a medium are 1.5 and 5×10−7 Hm−1respectively. The relative permittivity of the medium is nearly: