Question

Two plane mirrors are inclined at ${70}^{\circ }.$ A ray incident on one mirror at incidence angle $\theta$ , after reflection falls on the second mirror and is reflected from there parallel to the first mirror. The value of $\theta$ is

• A. ${50}^{\circ }$
• B. ${45}^{\circ }$
• C. ${30}^{\circ }$
• D. ${25}^{\circ }$

Answer 1

The correct option is A ${50}^{\circ }$

$i=r=\theta \text{according to snell's law}$

$\begin{array}{c}\text{Applying geometry at}A\\ {180}^{\circ }=2\theta +k+x-\left(i\right)\end{array}$

$\begin{array}{cc}\text{Now in}△ABC& \\ 1{80}^{\circ }& =70+K+\alpha \\ {180}^{\circ }& =70+k+70\\ K& ={40}^{\circ }\end{array}$

$\begin{array}{cc}r=\theta & =90-40\text{from}\\ \text{figure}& \\ & ={50}^{\circ }\end{array}$

$\text{Now putting in (i)}$

$\begin{array}{cc}{180}^{\circ }& =2\theta +40+40\\ \theta & ={50}^{\circ }\\ & \end{array}$