For a transparent medium, relative permeability and permittivity, μr and ϵr are 1.0 and 1.44 respectively. The velocity of light in this medium would be,

CONCEPT:

The velocity of the light in the medium is written as;

\(v = \frac{1}{\sqrt{\mu \epsilon}}\)

Here we have \(\mu\) is the permeability and \(\epsilon\) is permittivity.

CALCULATION:

Given: Relative permeability, μ_r = 1.0

and relative permittivity, ϵ_r = 1.44

The velocity of light in the medium is written as;

\(v = \frac{1}{\sqrt{\mu \epsilon}}\) ----(1)

\(\mu = \mu_r \mu_o\) and \(\epsilon = \epsilon_r \epsilon_o\)

Now, using equation (1) we have;

\(v = \frac{1}{\sqrt{\mu_r\mu_o \epsilon_r \epsilon_o}}\) ----(2)

As we know that \(\epsilon_o = 8.854 \times 10^{-12}\)  F/m and

\(\mu_o = 4\pi \times 10^{-7}\) H/m

Now, by putting the given values we have;

\(v = \frac{1}{\sqrt{1.44 \times 4 \pi \times 10^{-7} \times 1 \times 8.854 \times 10^{-12} }}\)

\(\Rightarrow v = \frac{1}{\sqrt{1.44 \times 4 \times 3.14 \times 10^{-7} \times 1 \times 8.854 \times 10^{-12} }}\)

\(\Rightarrow v = \frac{1}{\sqrt{160.21\times 10^{-19} }}\)

\(\Rightarrow v = 2.49 \times 10^8\) m/s

Hence, option 3) is the correct answer.