A 60 $\circ$ prism has a refractive index of 1.52.Calculate the angle of incidence for the initial light ray that is then refracted inside the prism and just undergoes total internal reflection at the opposite face of the prism.
A)41.1 $\circ$
B)18.9 $\circ$
C)29.4 $\circ$
D)30.6 $\circ$
E)60.6 $\circ$

Question

A 60 $\circ$ prism has a refractive index of 1.52.Calculate the angle of incidence for the initial light ray that is then refracted inside the prism and just undergoes total internal reflection at the opposite face of the prism.
A)41.1 $\circ$ 
B)18.9 $\circ$ 
C)29.4 $\circ$ 
D)30.6 $\circ$ 
E)60.6 $\circ$

Quizplus · Accepted Answer

For total internal reflection to occur at the opposite face, the angle of incidence inside the prism at that face must equal the critical angle. The critical angle can be found using Snell's law, $n_1 \sin(\theta_c) = n_2 \sin(90^\circ)$, where $n_1$ is the refractive index of the prism (1.52), $n_2$ is the refractive index of air (approximately 1), and $\theta_c$ is the critical angle. Solving for $\theta_c$ gives a value that, when applied to the geometry of the prism and using Snell's law again for the entrance face, results in an initial angle of incidence that allows the light to just undergo total internal reflection at the opposite face, which corresponds to the scenario described.

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