Question:

If $ \mu_{0}$ be the permeability and $\varepsilon_{0} $ be the permittivity of a medium, then its refractive index is given by

Updated On: Jul 2, 2022
  • $ \frac{1}{\sqrt{\mu_{0}\varepsilon_{0}}} $
  • $\frac{1}{ \mu_{0}\varepsilon_{0} }$
  • $ \sqrt{\mu_{0}\varepsilon_{0}} $
  • $ \mu_{0}\varepsilon_{0} $
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The Correct Option is C

Solution and Explanation

Refractive index of medium is $= \frac{c}{v}$ where $c = \frac{1}{\sqrt{\mu_{0}\varepsilon_{0}}}$ and $v = \frac{1}{\sqrt{\mu _{0}\varepsilon _{0}\mu_{r}\varepsilon_{r}}}$ $\therefore\quad\mu = \frac{1 /\sqrt{\mu _{0}\varepsilon _{0}}}{1 / \sqrt{\mu _{0}\varepsilon _{0}\mu _{r}\varepsilon _{r}}} = \sqrt{\mu _{r}\varepsilon _{r}}$ Given $\mu_{r} = \mu_{0}$ and $\varepsilon_{r} = \varepsilon_{0}$ then $\mu = \sqrt{\mu _{0}\varepsilon _{0}}$
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