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 $\frac{1}{2}(\hat{i}-\sqrt{3}\hat{j})$. What is the angle of incidence?

• A. ${30}^o$
• B. ${45}^o$
• C. ${60}^o$
• D. ${75}^o$

Answer 1

The correct option is A ${30}^o$

$\cos (180°-2\alpha )=\frac{(\frac{i}{2}+\frac{\sqrt{3}}{2}\hat{j}).(\widehat{\frac{i}{2}}-\frac{\sqrt{3}}{2}\hat{j})}{\sqrt{{\left(\frac{1}{2}\right)}^2+{\left(\frac{\sqrt{3}}{2}\right)}^2}\sqrt{{\left(\frac{1}{2}\right)}^2+{\left(\frac{\sqrt{3}}{2}\right)}^2}}\cos (180°-2\alpha )=-\frac{1}{2}180°-2\alpha =120°\alpha =30°$