JEE Main 2024 — 6 April, Shift 1 — Question 54

For ${{\delta }_{\text{min }\!\!~\!\!\text{ }}}$

\begin{array}{*{35}{r}}{} & \text{i}=\text{e} \\{} & {{\text{r}}_{1}}={{\text{r}}_{2}}=\frac{\text{A}}{2} \\{} & \frac{{{\delta }_{\text{min}}}}{\text{A}}=1 \\{} & \frac{2\text{i}-\text{A}}{\text{ }\!\!~\!\!\text{ A}}=1 \\{} & 2\text{i}=2\text{ }\!\!~\!\!\text{ A} \\{} & \text{i}=\text{A} \\\end{array}

Snell's law $1 \times \sin \mathrm{i}=\mu \sin \mathrm{r}$

$\sin i=\mu \sin \left(\frac{A}{2}\right)$

$\sin A=\mu \sin \left(\frac{A}{2}\right)$

$2 \sin \frac{\mathrm{~A}}{2} \cos \frac{\mathrm{~A}}{2}=\sqrt{3} \sin \left(\frac{\mathrm{~A}}{2}\right)$

$\cos \left(\frac{\mathrm{A}}{2}\right)=\frac{\sqrt{3}}{2}$

$\therefore \frac{\mathrm{A}}{2}=30^{\circ}$ $\therefore \mathrm{A}=60^{\circ}$