Question:
The incident ray, reflected ray and the outward drawn normal are denoted by the unit vectors $\bar{a}, \vec{b}$ and $\vec{c}$ respectively. Then choose the correct relation for these vectors.
Correct Option: , 4
Solution:
We see from the diagram that because of the law of reflection, the component of the unit vector $\vec{a}$ along $\vec{b}$ changes sign on reflection while the component parallel to the mirror remain unchanges, $\vec{a}=\overrightarrow{a_{11}}+\overrightarrow{a_{1}}$
and $\overrightarrow{a_{\perp}}=\vec{c}(\vec{a} \cdot \vec{c})$
we see that the reflected unit vector is $\vec{b}=\overrightarrow{a_{11}}-\overrightarrow{a_{\perp}} \Rightarrow \vec{a}-2(\vec{a} \cdot \vec{c}) \vec{c}$