Explanation

The speed of electromagnetic waves in a medium is given by

$$ v = \frac{1}{\sqrt{\mu \epsilon}} $$

For vacuum,

$$ v_0 = \frac{1}{\sqrt{\mu_0 \epsilon_0}} $$

For the given medium, dielectric constant $k = \dfrac{\epsilon}{\epsilon_0} = 3$ and permeability $\mu = 2\mu_0$.

Hence speed in the medium is

$$ v = \frac{1}{\sqrt{(2\mu_0)(3\epsilon_0)}} = \frac{1}{\sqrt{6\mu_0\epsilon_0}} $$

Now the ratio of speeds in vacuum and the medium is

$$ \frac{v_0}{v} = \sqrt{6} $$

Therefore,

$$ v_0 : v = \sqrt{6} : 1 $$

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