question_answer

A region is illuminated by two sources of light. The intensity \[I\] at each point is found to be equal to \[{{I}_{1}}+{{I}_{2}}\], where \[{{I}_{1}}\] is the intensity of light at the point when source 2 is absent. \[{{I}_{1}}\] is similarly defined. Are the sources coherent or incoherent? Explain.    

Answer:

                When two waves of intensities \[{{I}_{1}}\] and \[{{I}_{2}}\] and having phase difference \[\phi \] meet at a point, the resultant intensity is \[I={{I}_{1}}+{{I}_{2}}+2\sqrt{{{I}_{1}}{{I}_{2}}}\cos \phi \] Given intensity, \[I={{I}_{1}}+{{I}_{2}}\] \[\therefore \]Interference term, \[2\sqrt{{{I}_{1}}{{I}_{2}}}\cos \phi =0\] or            \[\cos \phi =0\][\[{{I}_{1}}\] and \[{{I}_{2}}\] are not zero] That is, the phase difference \[\phi \] varies from 0 to \[2\pi \] in such a way that the average value of \[\cos \phi \] is zero over a cycle. Thus two sources have a phase difference which is not stable. Such sources are called incoherent sources.