Question

Identify the incorrect statement regarding the reflection of light from a plane mirror when a light ray is incident obliquely. $\overrightarrow{R},\overrightarrow{I}$ and $\overrightarrow{N}$ represents the vectors along the reflected ray, incident ray and normal direction.

• A. $\overrightarrow{R}.(\overrightarrow{I}\times \overrightarrow{N})=0$
• B. $\overrightarrow{N}.(\overrightarrow{I}\times \overrightarrow{R})=0$
• C. $\overrightarrow{I}.(\overrightarrow{N}\times \overrightarrow{R})=0$
• D. $\overrightarrow{N}\times \overrightarrow{I}=0$

Answer 1

The correct option is D $\overrightarrow{N}\times \overrightarrow{I}=0$

Reflection of light from a plane mirror is shown in the figure.

We know that incident ray, reflected ray and normal all will lie in the same plane.
Therefore, $\overrightarrow{I}\times \overrightarrow{N}$ will be $\perp$ $\overrightarrow{R}$. Thus,
$\overrightarrow{R}.(\overrightarrow{I}\times \overrightarrow{N})=0$
Similarly, $\overrightarrow{N}.(\overrightarrow{I}\times \overrightarrow{R})=0$ and $\overrightarrow{I}.(\overrightarrow{N}\times \overrightarrow{R})=0$
As ray has been incident obliquely, therefore, $0^{\circ }<\theta \le {90}^{\circ }$.
So, $\overrightarrow{N}\times \overrightarrow{I}\ne 0$
Hence, option $\left(d\right)$ is correct.