Question

An isosceles prism has one of the refracting surfaces silvered. A ray of light is incident normally on the refracting face AB. After two reflections, the ray emerges from the base of the prism perpendicular to it. Find the angle of the prism.

Answer 1

Consider an isosceles prism with one refractive silvered surface. A ray of light is incident normally on the refractive face $AB$

consider the diagram incident ray and normal at $Q$ are parallel,

Therefore,

$\alpha =2A$

$2\alpha +A={180}^{\circ }$

Solve the above equations,

$2\left(2A\right)+A={180}^{\circ }$

$5A={180}^{\circ }$

$A={36}^{\circ }$

$\alpha ={180}^{\circ }-{36}^{\circ }={72}^{\circ }$