Superposition Of Waves With Different Polarization: Interference

Superposition of waves with different polarization: So far, we have discussed the case, when the electric field vectors two light waves point in the same direction. Let us now consider a more general case. Once again we assume that the two waves are propagating in the z direction. The electric field vectors of these waves must lie in the x-y plane . We have seen in the earlier section, that the amplitude of the resultant wave, depends on the phase difference between the two waves and not on the phases of individual waves. Let, at a given point z, one of these waves has phase zero and other is having a phase . The two waves are now given as

               ---------------------- (1)

        ---------------------- (2)

The resultant wave is given by

         ---------------------- (3)

The resultant of these two waves will propagate along z direction; let us express the resultant wave as

                                           -----------------------(4)

Where is the amplitude of wave and is the phase (or the phase difference between ) . Applying the knowledge of vector additions we have

                 -        ----------------------- (5)

And the phase of resultant wave as

               ---------------------------- (6)

Fig. A : phase diagram showing resultant of two waves ( & ) with different polarisation and having phase difference .

The energy of the resultant wave is therefore given as :     ------------------ (7)

Where are the intensities of individual waves.

Eqn (7) is similar to equation

,

however, we see that resultant intensity depends not only on the relative phase difference between the two waves, but also on the relative orientation (polarization) of two waves.