## Coherence :

A wave which appears to be a pure sine wave for an infinitely large period of time or in an infinitly extended space be said to be a perfectly coherent wave. In such a wave there is a definite relationship between phase of wave and a given time and at a certain time later for at a point and at a certain distance away.

Coherence describes all properties of the correlation between physical quantities of a single wave or between several waves or wave packets.

No actual light source however emits a perfect coherent wave. Light waves which are pure sine waves only for a limited period of time or in a limited space, are partially coherent waves.

### i) Temporal Coherence :

**Example of temporal coherence:**

However, no light source produces perfect temporal coherence. This is because, “when an excited atom returns to the initial state, it emits light pulse of short duration such as of the order of 10^-10 s, after which pulse abruptly changes. Hence the field due to actual light is shown as :

The average time interval for which the field remains sinosodial is known as coherence time or temporal coherence of light wave. It os denoted by τ.

^{-10}s.

### iii) Spatial Coherence :

The spatial coherence is the cross-correlation between two points in a wave for all times if a wave has only 1 value of amplitude over an infinite length it is perfectly spatially coherent.

Let A and B depends on the distance AB and the temporal coherence.

If AB << L ( Coherence length) there will be a definite phase relationship between A and B i.e. high coherence between A and B. On the other hand if AB >> L, there will be no coherence between A and B.

Let us now consider points A and C which are equidistant from S. If the source S is a true point source, then the waves shall reach the points A & C in exactly the same phase, i.e., the two points will have perfect (spatial) coherence.

The beams emerging from S1 and S2, having been derived from the same original beam, maintains a constant phase difference at all point on the screen. Hence a stationary interference pattern is observed on the screen.

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