why does a cut diamond shine more than a glass piece of same shape

Diamond has more refractive index than glass and also the variation of the refractive index is more wrt wavelength for diamond as compared to glass, so it spreads more.

If we compare a diamond with a Glass cut into same shape; diamond Will obviously reflect more light than glass .This is simply because of the higher refractive index of diamond .Since diamond has higher refractive index it will disperse more light hence causing more sparkling effect .Actually diamond don`t shine they reflect .Due to this phenomenon diamond would shine more than the Glass

Critical angle is inversely proportional to refractive index.The refractive index of glass is 1.5And refractive index of diamond is 2.4So critical angle of diamond is less than the same for glass.Moreover, the diamond is cut in such a way that light is incident on it at an angle greater than the critical angle.So, Total Internal Reflection takes place and hence diamond appears to be bright