In the arrangement shown $L_1$, $L_2$ are slits and $S_1$, $S_2$ two independent sources on the screen, interference fringes

$$\begin{gathered} \text{ On the screen, we have four amplitudes pair wise coherent. } \\ \left({\mathrm{A}}_1+{\mathrm{A}}_2\right)+\left({\mathrm{A}}_3+{\mathrm{A}}_4\right)\equiv {\mathrm{A}}_{12}+{\mathrm{A}}_{34} \\ \text{ However, if }{\mathrm{A}}_{12}\text{ and }{\mathrm{A}}_{34}\text{ have equal magnitude because of random } \\ \text{ phase of }{\mathrm{A}}_{12}\text{ and }{\mathrm{A}}_{34},\text{ no fringes will be seen. } \end{gathered}$$