In the double slit experiment with light, we assume that the two waves have exactly the same phase when exiting the slits - but this seems unrealistic. Why don't random phase shifts at the slits wipe out the interference pattern?
The light waves which come out from the slits will have a constant phase difference which could be zero.
The phase difference depends on the angle the incoming light makes with the plane containing the slits.
If the incoming light was at right angles to the plane containing the slits then the light emerging from each of the slits would be in phase.
All a constant phase difference between the light which comes out of each of the slits will do is to shift the position of the interference pattern.