Incoherence of Light Sources: Phase Difference & Intensity

[person_random_normal]

Why will it happen so that-two light sources such that the
''phase difference between the two vibrating sources changes
rapidly with time, we say that the two sources are incoherent and when
this happens the intensities just add up ''

assuming that the wave characteristics of light are significant

 

[blue_leaf77]

The intensity of the superposition of two waves are in general
$$
|E(t)|^2 = |E_1(t)|^2 + |E_2(t)|^2 + 2|E_1(t)||E_2(t)|\cos \Delta\phi(t)
$$
The intensity is perceived by a classical detector as an integrated signal over a certain time interval. If the phase difference $\Delta \phi(t)$ varies very rapidly within this recording interval, then the 3rd term above will be very small as compared to the first two terms. In this case
$$
I_{total} \approx I_1+I_2
$$
where $I_i \propto \int_0^T |E_i(t)|^2 dt$ with $T$ the measurement interval and $i=1,2$.

 

[tech99]

Why will it happen so that-two light sources such that the
''phase difference between the two vibrating sources changes
rapidly with time, we say that the two sources are incoherent and when
this happens the intensities just add up ''

assuming that the wave characteristics of light are significant

In day-to-day engineering terms we might loosely say that incoherent sources add on a power basis and coherent ones on a voltage basis. Actually, I am not sure about your definition of "incoherent", because it allows for the phase shift to be changing in a predictable manner. I would expect the term to refer to the case when the phase difference is randomly changing.

 

[person_random_normal]

Thank you !