Physics

The relative refractive index is just the ratio of absolute refractive indices: $n_{12} = \frac{n_1}{n_2}$ and $n_{21} = \frac{n_2}{n_1}$. When you multiply these two fractions together, the numerators and denominators flip and cancel perfectly, leaving you with 1. This makes physical sense—if light bends a certain way going from medium 1 to 2, it must bend the opposite way returning, so these "relative" measures are reciprocals of each other.

The relative refractive index is just the ratio of absolute refractive indices: $n_{12} = \frac{n_1}{n_2}$ and $n_{21} = \frac{n_2}{n_1}$. When you multiply these two fractions together, the numerators and denominators flip and cancel perfectly, leaving you with 1. This makes physical sense—if light bends a certain way going from medium 1 to 2, it must bend the opposite way returning, so these "relative" measures are reciprocals of each other.