The distance of $n^{\mathrm{th}}$ bright fringe to the $(n+1{)}^{\text{th}}$ dark fringe in Young's experiment is equal to,

A parallel beam of light $\left(\lambda =5000\stackrel{°}{A}\right.)$ is incident at an angle $\alpha =30°$ with the normal to the slit plane in a young's double slit experiment. Assume that the intensity due to each slit at any point on the screen is $I_0.$ Point $O$ is equidistant from $S_1 \& S_2.$ The distance between slits is $1 \mathrm{mm}.$

In a double silt experiment, two identical point sources $S_1$ and $S_2$ are placed on a line perpendicular to the two slits $P$ and $Q$ as shown (the figure is not to scale). The screen is placed away compared to the distance between the slits.

When only $S_1$ is switched on, there is an interference pattern with a peak intensity $I_1$. When only $S_2$ is switched on, there is an interference pattern with peak intensity $I_2 \left(I_2<I_1\right)$. When both $S_1$ and $S_2$ are switched on,