Question

The ${\epsilon }_0$ and ${\mu }_0$ are the electric pemittivity and magnetic permeability in a free space. If $\epsilon$ and ${\mu }^{}$ are the corresponding quantities in medium, the refractive index of the medium is

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

Answer 1

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

$c=\frac{1}{\sqrt{{\mu }_0{\epsilon }_0}}\left(freespace\right)v=\frac{1}{\sqrt{\mu \epsilon }}\left(medium\right)\therefore n=\frac{c}{v}=\sqrt{\frac{\mu \epsilon }{{\mu }_0{\epsilon }_0}}$