Conditions For Interference

Conditions for Interference: It is not always necessary that two superimposing light waves always interfere and result in redistribution of energy (fringes). Only when these superimposing waves satisfy certain conditions the fringe pattern is observed on screen. These conditions are as follows.

• The phase difference between the two waves should not change with time. If the phase difference between the waves, changes with time, the intensity at a given point will be a function of time and fringe pattern will not be clean. The phase difference between the waves can be maintained if the sources of these two light waves are coherent this could be achieved if the waves are derived from one single source.
• The two waves must have same state of polarization i.e. their electric field vectors must point in the same direction. For, if the electric field vectors of two waves point in orthogonal direction term in eq. will be zero and the resultant intensity will not depend upon the phase difference . Further if the electric field vectors of these waves are not completely orthogonal, the components which are parallel (anti parallel) to each other will interfere. However, in this case the difference between maximum and minimum intensity will not be as large as in the case when two waves are in the same state of polarization (fringe visibility will be poor).
• The two interfering waves should have same wavelength. If the wavelengths are very different, the interference cannot take place. In the case when there is slight variation in wavelength, the resultant wave (intensity) behaves like a group of waves and result in beat formation.

Coherent and Non coherent Sources:

A light source emits photons, when the atoms undergo transition from one state to another. This process is highly chaotic, as the photons emission process from a collection of atoms is independent of each other. The light wave coming from the source, is therefore, superposition of many waves with random phases, and resembles a sinusoidal wave for about 10ns or so (the typical time interval in an emission process). Since the phase of the resultant wave from the source is not constant with time, such a source is called a non coherent source. Now if the two super imposing waves are coming from different sources, their phases will change randomly and their phase difference will not be constant with time and the waves will not interfere.

If the phase difference between two waves, coming from different sources is not a function of time, these sources are said to be coherent sources. Such sources are obtained by dividing from a single light source, since in this case both the sources (waves) will have the same phase at the point of division. A constant phase difference between them can be introduced by introducing some, path difference. The waves derived from single source thus have constant phase difference and interfere.