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

Refractive index compares the speed of light in a particular medium with the speed of light in vacuum. It measures the optical density of a medium. It should not be confused with the mass density of the medium.
For turpentine oil, it.s mass density is less than water but optical density is more than that of water.
Refractive index (n) = `("c(speed of light in vacuum)")/("v(speed of light in any medium)")`
for vacuum, refractive ndex = 1
This relation is also used in Snell.s law.
Let the refractive index of `"medium"_(1)` be `n_1` ...and the speed of light in `"medium"_(1)` be `v_1`.
Therefore, `n_1 = (c)/(v_1)" "`...(i)
Similarly,
Let the refractive index of `"medium"_2` be `n_2` ...and the speed of light in `"medium"_2` be `v_2`.
Therefore, `n_2 = (c)/(v_2)" "`...(ii)
Now,
`implies n_1 sin i = n_2 sin r`
`implies (sin i)/(sin r)=(n_2)/(n_1)" "`(Using equation (i) and (ii))
`implies (sin i)/(sin r)=(c)/(v_2)xx(v_1)/(c)`
`implies (sin i)/(sin r)=(v_1)/(v_2)`