Refraction And Snell's Law

Snell's law, introduced in NCERT, states that when light passes from one medium to another the ratio of the sine of the incidence angle to the sine of the refraction angle equals the ratio of refractive indices, $n_1\sin {\theta }_1=n_2\sin {\theta }_2$. Here light moves from air ($n_1=1$) into glass ($n_2=1.5$) with ${\theta }_1=30^{\circ }$, so $\sin {\theta }_2=\frac{n_1\sin {\theta }_1}{n_2}=\frac{1\times 0.5}{1.5}=0.333$. Taking the inverse sine gives ${\theta }_2={\sin }^{-1}(0.333)\approx 19.5^{\circ }$. Because the ray enters a denser medium it bends toward the normal, so the refracted angle must be smaller than $30^{\circ }$, which matches. The value $30^{\circ }$ is wrong because that would mean no bending, which only happens between identical media. The value $48.6^{\circ }$ is wrong because it multiplies by the index instead of dividing, sending the ray the wrong way. The value $45^{\circ }$ is a distractor with no derivation supporting it. As stated in NCERT Class 12, Chapter 9, denser media slow light and bend rays toward the normal. A direction check confirms bending toward the normal upon entering glass, so an angle below the incidence value is physically correct.