Relative Refractive Index

In Snell's law, the ratio $n_2/n_1$ is called the refractive index of the second medium relative to the first, written $n_{21}=n_2/n_1$. Two useful relations follow directly from this and from the principle of reversibility: the inverse rule, $n_{12}=1/n_{21}$ (swapping which medium is 'first' inverts the ratio); and the chain rule, $n_{32}=n_{31}\times n_{13}=n_{31}/n_{12}$ (the refractive index of medium 3 relative to medium 2 can be built up from indices relative to a common third, intermediate medium). These rules let an unknown relative refractive index be computed across a chain of media -- for instance, working out the refractive index of oil given the refractive index of glass relativ …