Total Internal Reflection

Total internal reflection occurs when light moving from a denser to a rarer medium meets the boundary at an angle exceeding the critical angle, for which the refracted ray would graze along the surface at 90°. The critical angle satisfies $\sin {\theta }_c=\frac{1}{n}$ when the rarer medium is air, where $n$ is the refractive index of the denser medium. Here $n=1.5$, so $\sin {\theta }_c=\frac{1}{1.5}=0.667$, giving ${\theta }_c={\sin }^{-1}(0.667)\approx 41.8°$. For any incidence greater than this, no refracted ray exists and the light is wholly reflected back into the glass with negligible loss. This loss-free reflection is precisely what makes total internal reflection superior to ordinary metallic mirrors for guiding light, since metal coatings always absorb a small fraction. The phenomenon requires light to originate in the denser medium and meet the boundary beyond the threshold, conditions met inside optical fibres where repeated total internal reflection confines signals over kilometres. The value 48.6° corresponds mistakenly to $n=4/3$ (water), not glass. The value 30° is wrong because $\sin 30°=0.5$ would imply $n=2$. The value 60° is wrong as it exceeds the true critical angle and merely names a valid TIR incidence rather than the threshold. This is the NCERT basis for optical fibres and prisms. A check confirms a larger refractive index gives a smaller critical angle, as 1.5 sensibly yields about 42°.