Critical angle of quartz (R.I. ${fallingdotseq}$ 1.553) and diamond (R.I. = 2.417) are $40.09^{circ}$ and $24.26^{circ}$ that calculated by $sin{ heta}=r_2/r_1$ (r = refractive index, $r_1$ > $r_2$). Brilliance of quartz and diamond are 20.33% and 55.07%. The brilliance data are result of study on the incident light internal round brilliant cut quartz and diamond by the critical angle. Cause of bow-tie phenomenon can be studied by application of critical angle theory and light path inside fancy shape brilliant cut. When refractormetry with typical gem refractometer, critical angle of quartz and corundum are $59.1^{circ}$ and $77.9^{circ}$.