JAMB Physics 2017 Paper

Concept:The angle of minimum deviation is found using the prism formula that links refractive index, prism angle, and deviation.Explanation:The prism formula is $$n = \frac{\sin\frac{A + D}{2}}{\sin\frac{A}{2}}$$ where $n$ is the refractive index, $A$ is the prism angle, and $D$ is the minimum deviation.Given $n = 1.5$ and $A = 60^\circ$, substitute these values: $$1.5 = \frac{\sin\frac{60^\circ + D}{2}}{\sin 30^\circ}$$ Since $\sin 30^\circ = 0.5$, multiply both sides by $0.5$: $$\sin\frac{60^\circ + D}{2} = 1.5 \times 0.5 = 0.75$$ The question states $\sin^{-1}(0.75) = 49^\circ$, so: $$\frac{60^\circ + D}{2} = 49^\circ$$ Multiply through by $2$: $$60^\circ + D = 98^\circ$$ Therefore: $$D = 98^\circ - 60^\circ = 38^\circ$$Answer:The angle of minimum deviation is $38^\circ$, which corresponds to option A.