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Q.

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

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a

$45^{0}$

b

$60^{0}$

c

$75^{0}$

d

$30^{0}$

answer is A.

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Detailed Solution

$\cos (180^{0} - 2 α) = \frac{(\frac{\hat{i}}{2} + \frac{\sqrt{3}}{2} \hat{j}) . (\frac{\hat{i}}{2} - \frac{\sqrt{3}}{2} \hat{j})}{\sqrt{{(\frac{1}{2})}^{2} + {(\frac{\sqrt{3}}{2})}^{2}} \sqrt{(\frac{1}{2}) + {(- \frac{\sqrt{3}}{2})}^{2}}}$
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$∴ \cos (180^{0} - 2 α) = - \frac{1}{2}$
$∴ 180^{0} - 2 α = 120^{0}$
$∴ α = 30^{0}$

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A ray of light travelling in the direction 12(i^+3j^) is incident on a plane mirror. After reflection, it travels along the direction 12(i^−3j^). The angle of incidence is