JEE PYQ: Ray Optics Question 11
Question 11 - 2021 (26 Feb Shift 2)
The incident ray, reflected ray and the outward drawn normal are denoted by the unit vectors $\hat{a}$, $\hat{b}$ and $\hat{c}$ respectively. Then choose the correct relation for these vectors.
(1) $\hat{b} = 2\hat{a} + \hat{c}$
(2) $\hat{b} = \hat{a} - \hat{c}$
(3) $\hat{b} = \hat{a} + 2\hat{c}$
(4) $\hat{b} = \hat{a} - 2(\hat{a} \cdot \hat{c})\hat{c}$
Show Answer
Answer: (4)
Solution
We see from the diagram that because of the law of reflection, the component of the unit vector $\hat{a}$ along $\hat{b}$ changes sign on reflection while the component parallel to the mirror remains unchanged. $\hat{a} = \hat{a}{\parallel} + \hat{a}{\perp}$ and $\hat{a}{\perp} = \hat{c}(\hat{a} \cdot \hat{c})$ we see that the reflected unit vector is $\hat{b} = \hat{a}{\parallel} - \hat{a}_{\perp} \Rightarrow \hat{a} - 2(\hat{a} \cdot \hat{c})\hat{c}$
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