JAMB Physics 2018 Paper

Concept:The critical angle relates the refractive index of a transparent medium to air through Snell's law.Explanation:The critical angle $C$ is the angle of incidence inside the medium that gives an angle of refraction of $90^\circ$ in air.Applying Snell's law gives $n \sin C = 1 \times \sin 90^\circ$, since the refractive index of air is about $1$.Because $\sin 90^\circ = 1$, the equation simplifies to $n \sin C = 1$.Making the refractive index $n$ the subject of the formula yields $n = \frac{1}{\sin C}$.Substitute the given value $C = 34^\circ$: $n = \frac{1}{\sin 34^\circ}$.Using $\sin 34^\circ \approx 0.559$, we obtain $n = \frac{1}{0.559}$.Evaluating this division gives $n \approx 1.79$.Answer:The refractive index of the medium is $1.79$.Therefore, the correct option is C.