Question

Two vertical plane mirrors are inclined at an angle of ${60}^0$ with each other. A ray of light travelling horizontally is reflected first from one mirror and then from the other. The resultant deviation is

• A. ${60}^0$
• B. ${100}^0$
• C. ${180}^0$
• D. ${240}^0$

Answer 1

Answer: (D)

${240}^0$

$\begin{array}{c}Fromthefigure\\ a+b={90}^0\\ \Rightarrow b={90}^0-a\\ Now,\\ b+60+c=180\\ \Rightarrow c=180-60-b\\ =180-\left(90-a\right)\\ =30+a\\ Now,\\ d+c=90\\ d=90-c\\ =90-\left(30+a\right)\\ =60-a\\ Thus,intrianglePQR\\ \angle Q=2a\\ \angle R=2d=2\left(60-a\right)=120-2a\\ so,angle\angle QPTis=\angle Q+\angle R=120\\ Now,\\ angleofdeviation=reflex\angle QPT\\ =360-120\\ ={240}^{\circ }\\ Hence,theoptionDisthecorrectanswer.\end{array}$