3D Geometry
Reflection and Direction Cosines
Grade 12
Question:
<p>A mirror and a source of light are situated at the origin O and at a point on OX, respectively. A ray of light from the source strikes the mirror and is reflected. If the direction ratios of the normal to the plane are proportional to \(1, -1, 1\), then direction cosines of the reflected ray are</p>
<p>(a) \(\frac{1}{3}, \frac{2}{3}, \frac{2}{3}\)</p>
<p>(b) \(-\frac{1}{3}, \frac{2}{3}, \frac{2}{3}\)</p>
<p>(c) \(-\frac{1}{3}, -\frac{2}{3}, \frac{2}{3}\)</p>
<p>(d) \(\frac{1}{3}, -\frac{2}{3}, -\frac{2}{3}\)</p>
Step-by-Step Solution
Key Concept: The reflected ray direction is obtained using the law of reflection: the angle of incidence equals the angle of reflection with respect to the normal.
Solution incomplete in source material. This problem requires finding the reflected ray direction using the law of reflection and the given normal direction to the mirror plane.
Correct Answer: B