Physics - Geometrical Optics Question with Solution | TestHub

$\alpha$= angle between vectors
$\text{cos}\alpha =\frac{\frac{1}{2}\left(\widehat{\text{ i}}+\sqrt{3}\widehat{\text{ j}}\right)·\frac{1}{2}\left(\widehat{\text{ i}}-\sqrt{3}\widehat{\text{ j}}\right)}{\left|\hat{\text{i}}+\sqrt{3}\widehat{\text{ j}}\right|\left|\hat{\text{i}}-\sqrt{3}\widehat{\text{ j}}\right|}$
$=\frac{1}{4}\frac{\left(1-3\right)}{1\times 1}=\frac{-2}{4}=-\frac{1}{2}$
$\alpha =120°=\frac{2\pi }{3}$
$\therefore \pi -\alpha =2\theta$
$\pi =\frac{2\pi }{3}=2\theta$
$\theta =\frac{\pi }{3\times 2}=\frac{\pi }{6}=30°$