Question $1$: What should be the separation distance, $d,$ between the two slits such that the path difference between the two light waves emanated from both slits is one$-$third of its wavelength?

Question $2$: The figure below shows an experimental setup for a double$-$slit experiment. The interference fringes are formed on the screen OP$.$ The path difference of the coherent light wave is given by $S{S}_2-S{S}_1=\frac{}{},$ where $$ is the wavelength of the light and $in\{1,2,3,$dots,$\}.$ Find the condition for the constructive and destructive interference at any point $P$ on the screen, in terms of $=S_{2}P-S_{1}P.$

Question $3$: The figure below shows the experimental setup for a double$-$slit experiment. Identify whether there is a change in the interference pattern if the light source $S$ is shifted to a new position $S^{\text{'}}.$ Justify your answer. Note: The source positions, $S$ and $S^{\text{'}},$ is far from the double$-$slit.