Write two definitions and equations of relative refractive index.

Explanation

If the velocity of light in medium (1) is `v_1`, and in medium (2) it is `v_2` then ratio of `v_1/v_2` is called refractive index.
`therefore n_(21)=v_1/v_2`
but `n_(21)=n_2/n_1`
`therefore n_2/n_1=v_1/v_2`
For the two given media if `i_1`, is the angle of incidence and `ir_2`, is the angle of refraction, then the ratio `(sin" "i)/(sin" "r)` is a constant.
This ratio is called the refractive index of medium (2) with respect to medium (1), `n_(21)`
If i is incidence angle and r is refraction angle, then
`therefore` Relative refractive index `n_(21)=(sin" "i)/(sin" "r)` (Snell.s law)
If `n_(21)`=refractive index of medium-2 w.r.t. medium-1 and `n_(12)` refractive index of medium -1 w.r.t. medium -2 , then
`n_(12)=(1)/(n_(21))`
Hence, `n_(21)xxn_(12)=1`