Explain the intensity of the point of superposition of the waves emanating from it by explaining the coherent and incoherent sources.

Explanation

If light sources having constant initial phase difference or their phase difference does not change with time, then this sources is called coherent sources.
In the interference pattern intensity at any point does not change with time. This type of interference is known as stationary interference.
There should be two coherent sources for stationary interference and the amplitude should also be the same.
The position of the maximum and minimum in the stationary interference will not change with time.
When the phase difference between the two vibrating sources changes very rapidly over time then this sources is known as incoherent source.
The light intensities is added into each other due to superposition of the waves emanating from incoherently sources hence two different light sources illuminate the wall.
When the path difference of the two sources is not constant, the interference pattern also changes with time. If the path difference changes very rapidly with time, the position of maximum and minimum will also change rapidly with time and we will see the average distribution of intensity with time.
This average intensity is given by,
`ltIgt==4I_(0)ltcos^(2)((phi)/(2))gt`
where `ltcos^(2)((phi)/(2))gt` represent time averaging term.
If `phi(t)` varies randomly with time, the time averaged quantity `ltcos^(2)((phi)/(2))gt` will be `(1)/(2)` and the resulting intensity at all point,
`I=4I_(0)ltcos((phi)/(2))gt`
`=4I_(0)xx(1)/(2)`
`:.I=2I_(0)` at all points.