If `epsi_(0)` and `mu_(0)` are respectively, the electric permittivity and the magnetic permeability of free space, `epsi` and `mu` the corresponding quantities in a medium, the refractive index of the medium is

Options

A. `sqrt((epsilon)/(epsilon_(0)))`
B. `sqrt((epsilon_(0)mu)/(epsilon mu_(0)))`
C. `sqrt((epsilon_(0)mu_(0))/(epsilon mu))`
D. `sqrt((epsilon mu)/(epsilon_(0)mu_(0)))`

Answer

D

Explanation

We know that velocity of electromagnetic wave in vacuum `(v_(0))=(1)/(sqrt(mu_(0)epsilon_(0)))` and velocity of electromagnetic wave in medium is `(v)=(1)/(sqrt(mu epsilon)).`
Therefore refractive index of the medium
`(mu)=("vel.of E.M. wave in vacuum "(v_(0)))/("vel. of E.M. wave in medium (v)")=(1//sqrt(mu_(0)epsilon_(0)))/(1//sqrt(mu epsilon))`
`=sqrt((mu epsilon)/(mu_(0)epsilon_(0)))`