Refraction Through A Prism

At minimum deviation the ray passes symmetrically through the prism, so the internal angles are equal and the path is parallel to the base. Under this condition the refractive index relates to the prism angle $A$ and minimum deviation $D_m$ by $n=\frac{\sin \left(\frac{A+D_m}{2}\right)}{\sin \left(\frac{A}{2}\right)}$. With $A=60°$, $\sin \left(\frac{A}{2}\right)=\sin 30°=0.5$, so $\sin \left(\frac{A+D_m}{2}\right)=n\times 0.5=1.5\times 0.5=0.75$. Thus $\frac{A+D_m}{2}={\sin }^{-1}(0.75)\approx 48.59°$, giving $A+D_m\approx 97.18°$ and $D_m\approx 37.2°$. The symmetry condition is physically meaningful: as the angle of incidence is varied, the total deviation first decreases, reaches a single minimum where the ray inside the prism runs parallel to the base, and then increases again, so $D_m$ is the unique stationary value of the deviation. At this point the angle of incidence equals the angle of emergence, which is why a spectrometer is set to minimum deviation to measure refractive index accurately. The value 30° is wrong because it equals $A/2$ and ignores the deviation entirely. The value 48.6° is wrong as it is the half-angle $\frac{A+D_m}{2}$, not the deviation itself. The value 60° is wrong because it merely repeats the prism angle. This is the classic NCERT prism formula used in spectrometer experiments. A plausibility check confirms $D_m$ is positive and less than $A$, which is typical for a moderate-index prism.