Question

If $ {{\varepsilon }_{0}} $ and $ {{\mu }_{0}} $ are respectively the electric permittivity and magnetic permeability of free space, $ \varepsilon $ and $ \mu $ are the corresponding quantities in a medium, the index of refraction of the medium is :

• A. $ \sqrt{\frac{{{\varepsilon }_{0}}{{\mu }_{0}}}{\varepsilon \mu }} $
• B. $ \sqrt{\frac{\varepsilon \mu }{{{\varepsilon }_{0}}{{\mu }_{0}}}} $
• C. $ \sqrt{\frac{{{\varepsilon }_{0}}\mu }{\varepsilon {{\mu }_{0}}}} $
• D. $ \sqrt{\frac{\varepsilon }{{{\varepsilon }_{0}}}} $

Answer 1

Answer: (B)

Refractive index of medium is given by $ n=\sqrt{{{\mu }_{r}}{{\varepsilon }_{r}}} $ Here, $ \mu ={{\mu }_{0}}\,{{\mu }_{r}} $ $ \Rightarrow $ $ {{\mu }_{r}}=\frac{\mu }{{{\mu }_{0}}} $ and $ \varepsilon ={{\varepsilon }_{0}}\,\,{{\varepsilon }_{r}} $ $ \Rightarrow $ $ {{\varepsilon }_{r}}=\frac{\varepsilon }{{{\varepsilon }_{0}}} $ $ \therefore $ $ n=\sqrt{\frac{\mu }{{{\mu }_{0}}}.\frac{\varepsilon }{{{\varepsilon }_{0}}}}\sqrt{\frac{\varepsilon \mu }{{{\varepsilon }_{0}}{{\mu }_{0}}}} $ NOTE: The above expression can be written as $ n=\sqrt{\frac{\varepsilon \mu }{{{\varepsilon }_{0}}{{\mu }_{0}}}}=\frac{{{C}_{vacuum}}}{{{C}_{medium}}} $ as $ {{c}_{v}}=\frac{1}{\sqrt{{{\varepsilon }_{0}}{{\mu }_{0}}}} $ = speed of light in vacuum $ {{c}_{m}}=\frac{1}{\sqrt{\varepsilon \mu }} $ = speed of light in medium