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.

$$\left(\mu_0=4 \pi \times 10^{-7} \mathrm{H} / \mathrm{m}, \epsilon_0=8.85 \times 10^{-12} \mathrm{~F} / \mathrm{m}, \mathrm{c}=3 \times 10^8 \mathrm{~m} / \mathrm{s}\right)$$

<p>$$\begin{aligned} &\text { Since velocity of light in terms of } \mu \& E \text { is }\\ &\begin{aligned} & V=\frac{1}{\sqrt{\mu \epsilon}}=\frac{1}{\sqrt{\mu_0 \mu_{\mathrm{r}}}} \times \frac{1}{\sqrt{\epsilon_0 \epsilon_{\mathrm{r}}}} \\ & =\frac{1}{\sqrt{\mu_{\mathrm{r}} \epsilon_{\mathrm{r}}}} \times \frac{1}{\sqrt{\mu_0 \epsilon_0}} \\ & =\frac{C}{\sqrt{\mu_{\mathrm{r}} \epsilon_{\mathrm{r}}}}=\frac{C}{\sqrt{\frac{10}{\pi} \times \frac{1}{0.0885}}} \\ & =\frac{C}{\sqrt{36}}=\frac{C}{6} \end{aligned} \end{aligned}$$</p> <p>$$\begin{aligned} V & =\frac{C}{6} \\ C & =6 V \end{aligned}$$</p> <p>Velocity of light in vacuum is greater by 6 times the velocity of light in medium Answer is 6</p>