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

The formula to calculate the intensity of the interference pattern in Young's double slit experiment can be written as

$I = 4{I}_{0}\cos^{2}\left(\dfrac{ϕ}{2}\right) . . . \left(1\right)$

Hence, the ratio of the required intensities can be calculated as follows-

$\begin{cases}\dfrac{{I}_{1}}{{I}_{2}} & = & \dfrac{4{I}_{0}\cos^{2}\left(\dfrac{\pi}{6}\right)}{4{I}_{0}\cos^{2}\left(\dfrac{\pi}{4}\right)} \\ & = & \dfrac{\dfrac{3}{4}}{\dfrac{1}{2}} \\ & = & \dfrac{3}{2}\end{cases}$