In the double-slit experiment, for interference patterns to be observed, it is necessary to have a coherent source of light or particles. Coherence refers to the property of waves being in phase with each other, which allows for constructive and destructive interference to occur.
If the two lights passed through the double-slit are from a coherent source, such as a laser or a well-designed setup with a single light source split into two beams, they can interfere with each other and create fringes on the screen or detector. In this case, the interference pattern will be visible as alternating bright and dark fringes.
The interference arises because the two coherent light waves coming from the two slits overlap and interact with each other. When the crests of one wave align with the crests of the other wave, they interfere constructively, resulting in brighter regions (constructive interference). Conversely, when the crests of one wave align with the troughs of the other wave, they interfere destructively, leading to darker regions (destructive interference). This interference pattern is what produces the characteristic fringes.
It's worth noting that if the two lights passing through the slits are not coherent or if the phase relationship between them is not maintained, the interference pattern will not be observed, and the resulting pattern on the screen will resemble a simple superposition of the two independent light sources.