AL PHY Wave interference

Q: what is coherent length?

Simply speaking, "coherence length" is the distance over which the waves can maintain a relatively constant phase.

For examples, light from a filament bulb (white light) is of coherence length about 600 nm only. But the coherence length for laser can be as long as hundreds of metres.

That is to say, white light that we normally observed appears as incoherent, because of its short coherence length, whereas light from a laser is coherent.

Q: For interference , why does the path difference should be smaller than the coherent length?

The crucial point in producing a steady interference pattern from waves emitted by two sources is that the waves must be coherent. If not, an intereference pattern cannot be observed.

It is thus apparaent that if the path difference between the two waves is smaller than the coherence length of the waves, it is for sure that the condition for a constant phase difference between the two waves can be met. A steady interference pattern can therefore be produced. On the other hand, if the phase difference varies with time, a steady interference pattern would not be observed.