The extraordinary sparkling of an appropriately cut diamond is due to

The correct answer is Option (4) → Total internal reflection

Diamond has a very high refractive index (about 2.42), so its critical angle is small, about \( 24.4^\circ \). A diamond is cut so that light entering it strikes the inner faces at angles larger than this and undergoes total internal reflection many times before leaving through the top. This trapping and return of light makes it sparkle.

Option (1) dispersion — Incorrect. Dispersion splits white light into colours inside the diamond, but the brilliance comes from the repeated total internal reflections.

Option (2) polarisation — Incorrect. Polarisation concerns the direction of vibration of the light and plays no part here.

Option (3) low refractive index — Incorrect. Diamond has a high, not a low, refractive index; a high index gives the small critical angle needed.

Option (4) Total internal reflection — Correct. The small critical angle makes light undergo multiple total internal reflections inside the cut stone.

NCERT (2026-27):
Summary – “… 2. The critical angle of incidence i_c for a ray incident from a denser to rarer medium, is that angle for which the angle of refraction is 90°. For i > i_c, total internal reflection occurs. Multiple internal reflections in diamond (i_c ≅ 24.4°), totally reflecting prisms and mirage, are some examples of total internal reflection.”