Total Internal Reflection

Total internal reflection, discussed in NCERT, happens when light in a denser medium meets the boundary with a rarer medium at an angle exceeding the critical angle, defined by $\sin {\theta }_c=\frac{n_{rarer}}{n_{denser}}$. For diamond to air, $n_{denser}=2.42$ and $n_{rarer}=1$, so $\sin {\theta }_c=\frac{1}{2.42}=0.413$. Taking the inverse sine yields ${\theta }_c={\sin }^{-1}(0.413)\approx 24.4^{\circ }$. The unusually small critical angle explains why diamonds sparkle: light striking most internal facets exceeds this angle and is trapped, bouncing repeatedly before exiting. The value $41.8^{\circ }$ is wrong because it corresponds to water ($n=1.5$ region) not diamond, using a lower index. The value $48.6^{\circ }$ is wrong as it belongs to glass of index 1.33-type distractors, again the wrong medium. The value $65.6^{\circ }$ inverts the ratio and takes the arcsine of 2.42, which is impossible since sine cannot exceed 1. As stated in NCERT Class 12, Chapter 9, a higher refractive index produces a smaller critical angle. A magnitude check confirms the very high index of diamond gives a strikingly small critical angle, consistent with its brilliant appearance.