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) \[\sqrt{\frac{\varepsilon }{{{\varepsilon }_{0}}}}\]
Correct Answer: B
Solution :
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
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