Question

If \( \vec{A}, \vec{B} \text{ and } \vec{C} \) are the unit vectors along the incident ray, reflected ray and outward normal to the reflecting surface, then:

• A. \( \vec{B} = \vec{A} - \vec{C} \)
• B. \( \vec{B} = \vec{A} + (\vec{A}\cdot\vec{C})\vec{C} \)
• C. \( \vec{B} = \vec{A} + \vec{C} \)
• D. \( \vec{B} = \vec{A} - 2(\vec{A}\cdot\vec{C})\vec{C} \)

Hint:

Reflection flips the component along normal while keeping parallel component unchanged.

Answer 1

The Correct Option is D

Concept: Reflection of vector: \[ \vec{B} = \vec{A} - 2(\vec{A}\cdot\hat{n})\hat{n} \]

Step 1: Interpretation.
\(\vec{C}\) is unit normal.

Step 2: Apply formula.
\[ \vec{B} = \vec{A} - 2(\vec{A}\cdot\vec{C})\vec{C} \]