Case based

The British physicist Thomas used an ingenious technique to lock the phases of the waves emanating from two coherent sources $S_1$ and $S_2$. As these sources were derived from same source symmetrically placed wrt $S_1$ and $S_2$, the phases of waves were same. If any abrupt change happens in original sources, will manifest exactly similar phase changes in the light coming out of two sources $S_1$ to $S_2$. Due to constructive interference and destructive interference at different points in space and screen alternate dark and bright fringes of equal width were obtained. This pattern was called as interference pattern. The width of each band was equal with central fringe as bright fringe.

If two sources of intensifies $I_0$ each have a randomly varying phase difference $\phi$, the resultant intensity at centre of screen will be:

$2 I_0$

The correct answer is Option (3) → $2 I_0$