The dimensional formula of sqrt{mu_{r} vareps | vedclass

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(D) The refractive index $n$ of a medium is given by the ratio of the speed of light in vacuum $c$ to the speed of light in the medium $v$,i.e.,$n = \

Vedclass · Accepted Answer

None of these.

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(D) The refractive index $n$ of a medium is given by the ratio of the speed of light in vacuum $c$ to the speed of light in the medium $v$,i.e.,$n = \frac{c}{v}$.We know that $c = \frac{1}{\sqrt{\mu_{0} \varepsilon_{0}}}$ and $v = \frac{1}{\sqrt{\mu \varepsilon}} = \frac{1}{\sqrt{\mu_{0} \mu_{r} \varepsilon_{0} \varepsilon_{r}}}$.Substituting these values,we get $n = \frac{1/\sqrt{\mu_{0} \varepsilon_{0}}}{1/\sqrt{\mu_{0} \mu_{r} \varepsilon_{0} \varepsilon_{r}}} = \sqrt{\mu_{r} \varepsilon_{r}}$.Since the refractive index $n$ is a ratio of two speeds,it is a dimensionless quantity.Therefore,the dimensional formula is $M^{0} L^{0} T^{0} A^{0}$,which is not listed in the options.Thus,the correct option is $D$.

The dimensional formula of $\sqrt{\mu_{r} \varepsilon_{r}}$ is . . . . . . .

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