Two plane mirrors are placed in such a way that they make an angle of ${60}^{\circ }$ as shown in figure. A ray of light falls on one mirror and it reflects off once from each mirror. For this situation mark the correct statement(s).

For two reflections only, the situation is shown in figure. Here it is assumed, that after $2^{nd}$ reflection the ray doesn't fall on 1st mirror.

For this situation, $\varphi <{60}^{\circ }$

$\begin{array}{l}\Rightarrow {60}^{\circ }+{90}^{\circ }-\theta +\varphi ={180}^{\circ }\\ \Rightarrow \varphi =30+\theta <{60}^{\circ }\Rightarrow \theta <{30}^{\circ }\end{array}$

For two reflections undergone the total devation produced would be,

$\begin{array}{l}\delta ={\delta }_1+{\delta }_2\\ {\delta }_1=\pi -2\theta \text{ in ACW }\\ {\delta }_2=\pi -2(\frac{\mathrm{\pi }}{2}-\varphi )\text{ in ACW }\\ \delta =\pi -2\theta +\pi -\pi +2\varphi \\ =\pi -2\theta +2(30+\theta )=\pi +{60}^{\circ }\end{array}$

$={240}^{\circ }\text{ in }\mathrm{ACW}$