What is the angle of incidence for an equilateral prism of refractive index $\sqrt{3}$ so that the r

Question

What is the angle of incidence for an equilateral prism of refractive index $\sqrt{3}$ so that the ray is parallel to the base inside the prism

Professor PC Thomas Classes · Answer

For an equilateral prism, the angle of the prism is $A=60^{\circ}$. When the refracted ray is parallel to the base inside the prism, it implies the condition of minimum deviation, where $r_1=r_2= \frac{A}{2}$.
1. Find the angle of refraction ( $r$ ):
$$
r=\frac{A}{2}=\frac{60^{\circ}}{2}=30^{\circ}
$$
2. Apply Snell's Law $\left(\mu=\frac{\sin i}{\sin r}ight)$ :
$$
\begin{gathered}
\sqrt{3}=\frac{\sin i}{\sin 30^{\circ}} \
\sin i=\sqrt{3} 	imes \frac{1}{2}=\frac{\sqrt{3}}{2} \
i=60^{\circ}
\end{gathered}
$$