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The principal section of a glass prism is an isosceles triangle $A B C$ with $A B=A C$. The face $A C$ is silvered. A ray of light is incident normally on the face $A B$ and after two reflections, it emerges from the base $B C$ perpendicular to the base. Angle $B A C$ of the prism is
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Verified Answer
The correct answer is:
$36^{\circ}$
$$
\begin{array}{llrl}
& i_1 =90^{\circ}-\left(90^{\circ}-A\right)=A \\
\text { and } \alpha & =90^{\circ}-21_1=90^{\circ}-2 A \\
\therefore & i_2 =90^{\circ}-\alpha=90^{\circ}-\left(90^{\circ}-2 A\right)=2 A \\
\therefore & \beta =90^{\circ}-i_2=90^{\circ}-2 A
\end{array}
$$
From the geometry of the figure
$$
\begin{aligned}
& A+2 A+2 A=180^{\circ} \\
& \therefore \quad A=36^{\circ}
\end{aligned}
$$
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