WAEC Physics 2011 Paper

Concept:For a prism, the refractive index is calculated using the angle of the prism $A$ and the angle of minimum deviation $D_m$.Explanation:The prism is equilateral, so each angle of the prism is $A = 60^\circ$.The angle of minimum deviation is given as $D_m = 40^\circ$.The refractive index $n$ of the prism is given by the formula:$$n = \frac{\sin\left(\frac{A + D_m}{2}\right)}{\sin\left(\frac{A}{2}\right)}$$Substitute $A = 60^\circ$ and $D_m = 40^\circ$:$$n = \frac{\sin\left(\frac{60^\circ + 40^\circ}{2}\right)}{\sin\left(\frac{60^\circ}{2}\right)}$$$$n = \frac{\sin 50^\circ}{\sin 30^\circ}$$$$n = \frac{0.7660}{0.5} = 1.532$$This value is approximately $1.53$.Answer:$n = 1.53$Correct option: C. $1.53$