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

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Physics

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Question

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

45º

60º

30º

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$cosθ = \frac{\vec{a} . \vec{b}}{ab}$

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

$∴ θ$ = 120°

$∴ α$ = 30°

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