Q44 / 60 · JEE Advanced 2013 (Paper 1) · Physics

A ray of light, travelling in the direction $\frac{1}{2} (\hat{i} + \sqrt{3} \hat{j})$ , is incident on a plane mirror. After reflection, it travels along the direction $\frac{1}{2} (\hat{i} - \sqrt{3} \hat{j})$ . The angle of incidence is

Correct answer
A
$30 °$
B
$45 °$
C
$60 °$
D
$75 °$

Solution

α

= angle between vectors

cos α = \frac{\frac{1}{2} (\hat{i} + \sqrt{3} \hat{j}) \cdot \frac{1}{2} (\hat{i} - \sqrt{3} \hat{j})}{|\hat{i} + \sqrt{3} \hat{j}| |\hat{i} - \sqrt{3} \hat{j}|}

= \frac{1}{4} \frac{(1 - 3)}{1 \times 1} = \frac{- 2}{4} = - \frac{1}{2}

α = 120 ° = \frac{2 π}{3}

∴ π - α = 2 θ

π = \frac{2 π}{3} = 2 θ

θ = \frac{π}{3 \times 2} = \frac{π}{6} = 30 °

Hence, the correct answer is option: 'A'.

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