Question

the refractive index of the Diamond is much greater than ordinary glass how does a diamond cutter use this fact​

Answer 1

Diamond is an alotrope of carbon

it is naturaly harder

Answer 2

The critical angle for diamond is less than that for glass. A diamond cutter uses a large angle of incidence to ensure that the light entering the diamond is totally reflected from its faces. This is the reason for the sparkling effect of a diamond.