Rankers Physics

Properties of EM Waves: Practice Problem & Solution

If $\epsilon_0$ and $\mu_0$ are the electric permittivity and magnetic permeability in a free space, $\epsilon$ and $\mu$ are the corresponding quantities in medium, the refractive index of the medium is: (1994)
$\sqrt{\frac{\epsilon_0\mu_0}{\epsilon\mu}}$
$\sqrt{\frac{\epsilon\mu}{\epsilon_0\mu_0}}$
$\sqrt{\frac{\epsilon_0\mu}{\epsilon\mu_0}}$
$\sqrt{\frac{\epsilon}{\epsilon_0}}$

Solution Explained:

To solve this problem, we apply the core principles of Properties of EM Waves. Understanding the underlying formula is key to arriving at the correct answer below:

The refractive index is defined as $n = \frac{c}{v}$ . We know $c = \frac{1}{\sqrt{\mu_0\epsilon_0}}$ and $v = \frac{1}{\sqrt{\mu\epsilon}}$ . Substituting these expressions, we get $n = \frac{1 / \sqrt{\mu_0\epsilon_0}}{1 / \sqrt{\mu\epsilon}} = \sqrt{\frac{\mu\epsilon}{\mu_0\epsilon_0}}$ .

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