question_answer

If \[{{\varepsilon }_{0}}\] and \[{{\mu }_{0}}\] are the permittivity and permeability of free space and \[\varepsilon \] and \[\mu \]  are corresponding quantities for a medium, then show that the refractive index of the medium is \[\sqrt{\frac{\mu \varepsilon }{\mu {{\varepsilon }_{0}}}}\].

Answer:

                Velocity of light in vacuum \[=c=\frac{1}{\sqrt{{{\mu }_{0}}{{\varepsilon }_{0}}}}\] Velocity of light in medium \[=\upsilon =\frac{1}{\sqrt{\mu \varepsilon }}\] \[\therefore \]Refractive index of the medium, \[\mu =\frac{c}{\upsilon }=\sqrt{\frac{\mu \varepsilon }{{{\mu }_{0}}{{\varepsilon }_{0}}}}\]