Q. The principal section of a glass prism is an isosceles triangle $ABC$ with $AB = AC.$ The face $AC$ is silvered. A ray of light is incident normally on the face $AB$ and after tworeflections, it emerges from the base $BC$ perpendicular to the base. Angle $BAC$ of the prism is
A) $30{^\circ}$
B) $36{^\circ}$
C) $60{^\circ}$
D) $72{^\circ}$
Explanation
(b) From the figure
[image:9_image107.jpeg]
$i_{1} = 90{^\circ} - (90{^\circ} - A) = A$
$and\ \propto \ = 90{^\circ} - 2i_{1} = 90{^\circ} - 2A$
$\therefore\ i_{2} = 90{^\circ} - \alpha = 90{^\circ} - (90{^\circ} - 2A) = 2A$
$\therefore\ \beta = 90{^\circ} - i_{2} = 90{^\circ} - 2A$
From the geometry of the figure
$A + 2A + 2A = 180{^\circ}$
$\therefore\ A = 36{^\circ}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.