Question

A ray of light is reflected by a plane mirror. $\hat{e_{0}}, \hat{e} \hat{n}$ be the unit vectors along the incident ray, reflected ray and the normal to the reflecting surface respectively. Which of the following gives an expression for $\hat{e}$ ?

• A. $\hat{e_{0}} +2 \left(\hat{e_{0 }}\hat{n}\right)\hat{n}$
• B. $\hat{e_{0}} -2\left(\hat{e_{0}} \hat{n}\right)\hat{n}$
• C. $\hat{e_{0}} -\left(\hat{e_{0} \hat{n}}\right)\hat{n}$
• D. $\hat{e_{0}} +\left(\hat{e_{0} \hat{n}}\right)\hat{n}$

Answer 1

Answer: (B)

$\hat{e_{0}} \hat{n} =1\times1.cos \left(180-\theta\right)$
$\hat{e_{0} }\hat{n} =cos\theta.............\left(i\right)$
$\hat{e.}\hat{n}=1\times1\times cos\theta.............\left(ii\right)$
$\hat{e.}\hat{n}-\hat{e_{0}}\hat{n} =2cos\theta$
$\left(\hat{e}-\hat{e}_{0}\right).\hat{n}=2\left[-\hat{e_{0 }}\hat{n}\right]$
$\left(\hat{e} -\hat{e_{0}}\right)\hat{n.\hat{n}} =-2\left(\hat{e_{0}}\hat{n}\right)\hat{n}$
$\hat{e} =\hat{e_{0}} -2\left(\hat{e_{0}} \hat{n}\right)\hat{n}$