What is the difference between simply epsilon and epsilon_0?
and
V = 1/sqrt(epsilon.mu) = 1/sqrt(epsilon_0.epsilon_r.mu_0.mu_r)
If you look at your formula carefully it says "epsilon_0" (\$\epsilon_0\$) and "epsilon_r" (\$\epsilon_r\$).
- \$\epsilon_0\$ is the absolute permittivity of free space in farads per metre. Also known as vacuum permittivity
- \$\epsilon_r\$ is the relative permittivity of a material with \$\epsilon_0\$ as the reference.
Hence, \$\epsilon_0 \epsilon_r\$ is the absolute permittivity of the material in farads per metre.
Likewise with mu and mu_0?
"mu" is the magnetic permeability (in henries per metre) so, it's the same principle as above but substituting \$\mu\$ for \$\epsilon\$.
So, speed of light in a medium is: -
$$c = \dfrac{1}{\sqrt{\epsilon_0 \epsilon_r \mu_0\mu_r}}$$