The brilliance of a diamond is due to the phenomenon of total internal reflection of light. Total internal reflection occurs when light traveling through a denser medium, such as diamond, reaches the boundary with a less dense medium, like air, at a specific angle called the critical angle. At this critical angle, the light is reflected back into the denser medium instead of refracting out.

In the case of diamonds, the high refractive index of the diamond causes a large critical angle. As a result, when light enters the diamond, it undergoes multiple internal reflections before finally exiting the diamond. These internal reflections keep the light trapped inside the diamond for a longer period, enhancing its brilliance.

Interference of light (option 1) is not the reason for the brilliance of diamonds. Diffraction of light (option 2) and polarization of light (option 3) are also not responsible for the diamond`s brilliance.

Hence, the correct answer is option 4, total internal reflection of light.