Question

The angle between an incident ray and the plane mirror is ${30}^o$. The total angle between the incident ray and reflected ray will be:

• A. ${30}^o$
• B. ${60}^o$
• C. ${90}^o$
• D. ${120}^o$

Answer 1

The correct option is B ${60}^o$

$\begin{array}{c}\text{incident angle is i}\\ \text{angle of reflechon}=r\\ \angle AOx+i={90}^{\circ }\\ 30+i=90\\ i={60}^{\circ }\end{array}$

$\begin{array}{c}\text{We know that}\\ i=r\\ \therefore r={60}^{\circ }\end{array}$

$\angle AO{x}^{\prime }+i+\gamma +\angle BOX=180$ (angle in st.line)

$\Rightarrow 30+60+60+\angle BO\times =180$

$\Rightarrow \angle BOX={30}^{\circ }$

$\angle AO{X}^{\prime }=\angle A^{\prime }O\times \left(VOR\right)$

$\begin{array}{cc}& \begin{array}{cc}\text{Now, angle blw incident}& \\ \Rightarrow \angle BO{R}^{\prime }=& \angle BOX+\angle A^{\prime }OX\\ =& 30+30\\ =& 60\end{array}\\ & \therefore \text{(B)}{60}^{\circ }\text{is correct option.}\end{array}$