Question:
The incident ray, reflected ray and the outward drawn normal are denoted by the unit vectors \(\vec{a}\), \(\vec{b}\) and \(\vec{c}\) respectively. Then choose the correct relation for these vectors.
The incident ray, reflected ray and the outward drawn normal are denoted by the unit vectors \(\vec{a}\), \(\vec{b}\) and \(\vec{c}\) respectively. Then choose the correct relation for these vectors.
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On reflection the component of \(\vec{a}\) along the normal reverses while the tangential component is unchanged.
Updated On: Nov 4, 2026
- \(\vec{b} = \vec{a} + 2\vec{c}\)
- \(\vec{b} = \vec{a} - 2(\vec{a}\cdot\vec{c})\vec{c}\)
- \(\vec{b} = 2\vec{a} + \vec{c}\)
- \(\vec{b} = \vec{a} - \vec{c}\)
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The Correct Option is B
Solution and Explanation
Resolve the incident direction: \(\vec{a} = (\vec{a}\cdot\vec{c})\vec{c} + \vec{a}_{\parallel}\), where \(\vec{a}_{\parallel}\) is the part along the surface.
Reflection reverses the normal component and keeps the tangential one: \(\vec{b} = -(\vec{a}\cdot\vec{c})\vec{c} + \vec{a}_{\parallel}\).
Substituting \(\vec{a}_{\parallel} = \vec{a} - (\vec{a}\cdot\vec{c})\vec{c}\): \(\vec{b} = \vec{a} - 2(\vec{a}\cdot\vec{c})\vec{c}\).
Option (4) is wrong because \(\vec{a} - \vec{c}\) is not a unit vector in general.
Answer: (2) \(\vec{b} = \vec{a} - 2(\vec{a}\cdot\vec{c})\vec{c}\)
Reflection reverses the normal component and keeps the tangential one: \(\vec{b} = -(\vec{a}\cdot\vec{c})\vec{c} + \vec{a}_{\parallel}\).
Substituting \(\vec{a}_{\parallel} = \vec{a} - (\vec{a}\cdot\vec{c})\vec{c}\): \(\vec{b} = \vec{a} - 2(\vec{a}\cdot\vec{c})\vec{c}\).
Option (4) is wrong because \(\vec{a} - \vec{c}\) is not a unit vector in general.
Answer: (2) \(\vec{b} = \vec{a} - 2(\vec{a}\cdot\vec{c})\vec{c}\)
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