Question

A ray of light is reflected by a plane mirror. $\widehat{e_0},\hat{e}\hat{n}$ 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. $\widehat{e_0}+2\left(\widehat{e_0}\hat{n}\right)\hat{n}$
• B. $\widehat{e_0}-2\left(\widehat{e_0}\hat{n}\right)\hat{n}$
• C. $\widehat{e_0}-\left(\widehat{e_0\hat{n}}\right)\hat{n}$
• D. $\widehat{e_0}+\left(\widehat{e_0\hat{n}}\right)\hat{n}$

Answer 1

Answer: (B)

$\widehat{e_0}\hat{n}=1\times 1.cos\left(180-\theta \right)$
$\widehat{e_0}\hat{n}=cos\theta .............\left(i\right)$
$\widehat{e.}\hat{n}=1\times 1\times cos\theta .............\left(ii\right)$
$\widehat{e.}\hat{n}-\widehat{e_0}\hat{n}=2cos\theta$
$\left(\hat{e}-{\hat{e}}_0\right).\hat{n}=2\left[-\widehat{e_0}\hat{n}\right]$
$\left(\hat{e}-\widehat{e_0}\right)\widehat{n.\hat{n}}=-2\left(\widehat{e_0}\hat{n}\right)\hat{n}$
$\hat{e}=\widehat{e_0}-2\left(\widehat{e_0}\hat{n}\right)\hat{n}$