How is the refractive index of a medium related to the speed of light ? Obtain an expression for refractive index of a medium with respect to another in terms of speed of light in these two media ?

Explanation

The refractive index of the medium is defined as the ratio of speed of light in vacuum to the speed of light in the medium. It is expressed as
Refractive index, `mu=("speed of light in vacuum, c")/("speed of light in medium, v")`
`mu_(1)=` refractive index of first medium
`mu_(2)=` refractive index of second medium
` v_(1)=` velocity in first medium
`v_(2)=` velocity in second medium
For medium 1, we have `mu_(1)=(c)/(v_(1))`
For medium 2, we have ` mu_(2)=(c)/(v_(2))`
`:. " " mu_(21)=(mu_(2))/(mu_(1))=((c)/(v_(2)))/((c)/(v_(1)))=(v_(1))/(v_(2))`