Question

If $\mu_{0}, \varepsilon_{0}$ are the absolute permeability and permitivity respectively, of space, $\mu_{r}, \varepsilon_{r}$ are the relative permeability and permittivity respectively of mediums and $\mu, \varepsilon$ are the absolute permeability and permittivity of medium respectively, then the refractive index of the medium is

• A. $\sqrt{\frac{\mu \varepsilon}{\mu_{0} \varepsilon_{0}}}$
• B. $\sqrt{\frac{\mu_{r} \varepsilon_{r}}{\mu_{0} \varepsilon_{0}}}$
• C. $\sqrt{\mu_{r} \varepsilon_{r}}$
• D. $\sqrt{\frac{\mu \varepsilon}{\mu_{0} \varepsilon_{r}}}$

Answer 1

Answer: (A), (C)

As, $\mu=\frac{c}{v}=\frac{1 / \sqrt{\mu_0 \varepsilon_ 0}}{\sqrt{\mu \varepsilon}}$
$=\sqrt{\frac{\mu \varepsilon}{\mu_{0} \varepsilon_{0}}}=\sqrt{\frac{\mu_r \mu_0 \varepsilon_0 \varepsilon_r}{\mu_{0} \varepsilon_{0}}}$
$=\sqrt{\mu_{r} \varepsilon_{r}}$