The refractive index is a measure of how much light slows down when it passes through a medium. It is defined as the ratio of the speed of light in vacuum to the speed of light in the medium. In this question, the refractive index of fused artz is given as 1.46 and that of sapphire is given as 1.77.

To determine the correct relation between the speeds of light in the two mediums, we need to compare their refractive indices. If the refractive index of a medium is greater, it means that the speed of light in that medium is slower compared to the speed of light in the other medium.

Given that the refractive index of sapphire (1.77) is greater than the refractive index of fused artz (1.46), we can conclude that the speed of light in sapphire (vs) is slower than the speed of light in fused artz (v).

Therefore, the correct relation is option 1: v > vs. It means that the speed of light in fused artz is greater than the speed of light in sapphire.