Write two definitions and equations of relative refractive index.

(N/A) Definition $1$: The relative refractive index of medium $2$ with respect to medium $1$ is defined as the ratio of the speed of light in medium $1$ $(v_{1})$ to the speed of light in medium $2$ $(v_{2})$.
Equation: $n_{21} = \frac{v_{1}}{v_{2}} = \frac{n_{2}}{n_{1}}$
Definition $2$: According to Snell's law, the relative refractive index of medium $2$ with respect to medium $1$ is defined as the ratio of the sine of the angle of incidence $(i)$ in medium $1$ to the sine of the angle of refraction $(r)$ in medium $2$.
Equation: $n_{21} = \frac{\sin i}{\sin r}$
Relationship: If $n_{21}$ is the refractive index of medium $2$ with respect to medium $1$ and $n_{12}$ is the refractive index of medium $1$ with respect to medium $2$, then $n_{12} = \frac{1}{n_{21}}$, which implies $n_{21} \times n_{12} = 1$.