Question

If ${\epsilon }_0$ and ${\mu }_0$ are the electric pemittivity and magnetic permeability in vacuum, $\epsilon$ and $\mu$ are corresponding quantities in medium, then refractive index of the medium is

• A. $\sqrt{\frac{\epsilon }{{\epsilon }_0}}$
• B. $\sqrt{\frac{{\epsilon }_0\mu }{\epsilon {\mu }_0}}$
• C. $\sqrt{\frac{{\epsilon }_0{\mu }_0}{\epsilon \mu }}$
• D. $\sqrt{\frac{\epsilon \mu }{{\epsilon }_0{\mu }_0}}$

Answer 1

The correct option is D $\sqrt{\frac{\epsilon \mu }{{\epsilon }_0{\mu }_0}}$

We know that velocity of electromagnetic wave in vacuum $\left(v_0\right)=\frac{1}{\sqrt{{\mu }_0{\epsilon }_0}}$ and velocity of electromagnetic wave in medium is $\left(v\right)=\frac{1}{\sqrt{\mu \epsilon }}$
Therefore refractive index of the medium
$\left(\mu \right)=\frac{velocityofelectromagneticwaveinvacuum\left(v_0\right)}{velocityofelectromagneticwaveinmedium\left(v\right)}$
$=\frac{\frac{1}{\sqrt{{\mu }_0{\epsilon }_0}}}{\frac{1}{\sqrt{\mu \epsilon }}}=\sqrt{\frac{\mu \epsilon }{{\mu }_0{\epsilon }_0}}$