question_answer

Two identical coherent waves, each of  intensity \[{{I}_{0}}\], are producing an interference pattern. Write the value of the resultant intensity at a point of (i) constructive interference and (ii) destructive interference.                          

Answer:

                (i) Resultant intensity at point of constructive  interference                 \[I={{I}_{0}}+{{I}_{0}}+2\sqrt{{{I}_{0}}{{I}_{0}}}\cos {{0}^{\circ }}=\mathbf{4}{{\mathbf{I}}_{\mathbf{0}}}\] (ii) Resultant intensity at a point of destructive interference \[I={{I}_{0}}+{{I}_{0}}+2\sqrt{{{I}_{0}}{{I}_{0}}}\cos {{180}^{\circ }}\] \[=2{{I}_{0}}-2{{I}_{0}}=\mathbf{0}.\]