The ratio of intensities at two points P and Q on the screen in a...

Intensity at a point in Young's double slit experiment is given by
$\mathrm{I}=$\mathrm{I}$_1+$\mathrm{I}_2+2 \sqrt{\mathrm{I}$_1$\mathrm{I}_2} \cos \phi
Here $\mathrm{I}_1=$\mathrm{I}$_2=$\mathrm{I}$_0$ (say)
At $P$
$\therefore$\mathrm{I}$_{\mathrm{p}}=$\mathrm{I}$_0+$\mathrm{I}$_0+2$\mathrm{I}$_0 \cos \frac{\pi}{3}=2$\mathrm{I}$_0+2$\mathrm{I}$_0 \times \frac{1}{2}=3$\mathrm{I}$_0$
At $Q$
$\mathrm{I}_{\mathrm{Q}}=$\mathrm{I}$_0+$\mathrm{I}$_0+2$\mathrm{I}$_0 \cos 90^{{}^{\circ}}=2$\mathrm{I}$_0$
\frac{\mathrm{I}_{\mathrm{P}}}{\mathrm{I}_{\mathrm{Q}}}=\frac{3}{2}