Find the value of the angle of emergence from the prism given below for the incidence ray shown. The refractiv

Question

Find the value of the angle of emergence from the prism given below for the incidence ray shown. The refractive index of the glass is $\sqrt{3}$.

Accepted Answer

1. **Refraction Formula:** According to Snell's Law at the emerging face of the prism: $\mu \sin r_2 = \sin e$, where $\mu$ is the refractive index, $r_2$ is the angle of incidence inside the prism at the second face, and $e$ is the angle of emergence.
2. **Analysis of Probable Answer:** Given $\mu = \sqrt{3}$. Testing the probable answer $e = 60^{\circ}$:
   $$ \sqrt{3} \sin r_2 = \sin 60^{\circ} $$
   $$ \sqrt{3} \sin r_2 = \frac{\sqrt{3}}{2} $$
   $$ \sin r_2 = \frac{1}{2} \Rightarrow r_2 = 30^{\circ} $$
3. **Physical Context:** An internal angle of $r_2 = 30^{\circ}$ is physically valid. This specific result ($e=60^{\circ}$) typically arises in two standard exam scenarios for $\mu=\sqrt{3}$: 
   - **Case A:** An equilateral prism ($A=60^{\circ}$) set for minimum deviation, where $i = e = 60^{\circ}$.
   - **Case B:** A prism with angle $A=30^{\circ}$ where the ray enters normally ($i=0, r_1=0$), making $r_2 = A - r_1 = 30^{\circ}$.
4. **Conclusion:** While the missing diagram prevents independent confirmation of the prism geometry, the value $60^{\circ}$ is a standard result consistent with the given refractive index.

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