Question

If \(\vec{n}_1\), \(\vec{n}_2\), and \(\vec{i}\) represent unit vectors along the incident ray, reflected ray, and normal to the surface, respectively, then:

• A. \(\vec{n}_2 = \vec{n}_1 - 2(\vec{n}_1 \cdot \hat{t})\hat{t}\)
• B. \(\vec{n}_2 = \vec{n}_1 + 2(\vec{n}_1 \cdot \hat{t})\hat{t}\)
• C. \(\vec{n}_2 = -\vec{n}_1\)
• D. \(\vec{n}_2 = 2\vec{n}_1 - (\vec{n}_1 \times \hat{t})\)

Hint:

The law of reflection states that the angle of incidence equals the angle of reflection. In vector form, this can be represented using the normal vector andthe dot product for the direction of the reflected ray.

Answer 1

The Correct Option is B

1. Step 1: Reflection follows these rules: the incident ray, reflected ray, and surface normal are in the same plane, and the incidence angle equals the reflection angle.
2. Step 2: Using vectors for reflection, we find: \[ \vec{n}_2 = \vec{n}_1 + 2(\vec{n}_1 \cdot \hat{t})\hat{t} \]
This equation accurately represents the reflected ray's direction based on the law of reflection.