Question

Choose the correct answer from the alternatives given.
The refractive index and permeability of a medium are 1.5 and $5\times {10}^{-7}H{m}^{-1}$ respectively. The relative permittivity of the medium nearly

• A. 25
• B. 15
• C. 10
• D. 6

Answer 1

The correct option is D 6

Given: Refractive index of the medium is $1.5$.

The permeability of the medium is $5\times {10}^{-7}H{m}^{-1}$.

To find: The relative permittivity of the medium.

The Refractive index of medium is given by:

$n=\frac{c}{v}$

or $v=\frac{c}{n}$

$\Rightarrow \frac{3\times {10}^8}{1.5}=2\times {10}^{8}m/s$

Here, $\mu =5\times {10}^{-7}H{m}^{-1}$
We know that, $v=\frac{1}{\sqrt{\mu \epsilon }}=\frac{1}{\sqrt{\mu {\epsilon }_0{\epsilon }_r}}$

${\epsilon }_r=\frac{1}{v^2\mu {\epsilon }_0}$

$=\frac{1}{(2\times {10}^8{)}^2\times (5\times {10}^{-7})\times (8.85\times {10}^{-12})}$

$\Rightarrow 5.65\simeq 6$

Option $\left(D\right)$ is correct