The principal section of a glass prism is an isosceles triangle $A B C$ with $A B=A C$. The face $A C$ is…

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
  1. $30^{\circ}$
  2. $36^{\circ}$
  3. $60^{\circ}$
  4. $72^{\circ}$

Solution


$ \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} $

Asked in: AP EAMCET 2004

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