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.