A ray of light travelling in the direction is incident on a plane mirror. After reflection, it travels along the direction The angle of incidence is [2013]

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 [2013]

Smart Achievers · Accepted Answer

(1)

From figure,

$\tan i = \frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}} = \frac{1}{\sqrt{3}}$

$∴$ $i = 30 °$

(Angle of incidence)

Solution

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 [2013]

1 $30 °$

2 $45 °$

3 $60 °$

4 $75 °$

Ans.
(1)

From figure,

$\tan i = \frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}} = \frac{1}{\sqrt{3}}$

$∴$ $i = 30 °$

(Angle of incidence)

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Solution

Q. 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 [2013]

1 30°

2 45°

3 60°

4 75°

Ans. (1) From figure, tani=1232=13 ∴ i=30° (Angle of incidence)