If an optical medium possesses a relative permeability of \(\frac{10}{\pi}\) and relative permittivity of \(\frac{1}{0.0885}\), then the velocity of light is greater in vacuum than that in this medium by ________ times.
\(\left(\mu_0=4 \pi \times 10^{-7} \mathrm{H} / \mathrm{m}, \epsilon_0=8.85 \times 10^{-12} \mathrm{~F} / \mathrm{m}\right.\)
\(\left.\mathrm{c}=3 \times 10^8 \mathrm{~m} / \mathrm{s}\right)\)

Since velocity of light in terms of \(\mu \& E\) is
\(\begin{aligned}
& V=\frac{1}{\sqrt{\mu \epsilon}}=\frac{1}{\sqrt{\mu_0 \mu_r}} \times \frac{1}{\sqrt{\epsilon_0 \epsilon_r}} \\
& =\frac{1}{\sqrt{\mu_{\mathrm{r}} \epsilon_{\mathrm{r}}}} \times \frac{1}{\sqrt{\mu_0 \epsilon_0}} \\
& =\frac{C}{\sqrt{\mu_{\mathrm{r}} \epsilon_{\mathrm{r}}}}=\frac{C}{\sqrt{\frac{10}{\pi} \times \frac{1}{0.0885}}} \\
& =\frac{C}{\sqrt{36}}=\frac{C}{6}
\end{aligned}\)
\(\begin{aligned}
\mathrm{V} & =\frac{\mathrm{C}}{6} \\
\mathrm{C} & =6 \mathrm{~V}
\end{aligned}\)
Velocity of light in vacuum is greater by 6 times the velocity of light in medium
Answer is 6