Interference

On being permanently in or out of step

You have seen that two beams meeting can cause instructions from two sources to arrive at a single point – two lots of do like me, later. These usually cause transient effects because the two sets of vibrations come into and out of step rather often.

Might careful arrangements of the sources slow these transients right down, so that you can see the effects?

One way to slow the changing patterns right down is to ensure that the contributions from the different waves don't go into and out of step all the time. That ensures that the mountains and pits don't wander about all over the place. As we arrange things so that the two contributions remain in step for longer and longer, so the resultants become less transient and more stationary. If the two contributions are kept in step then they are said to be in phase. You can imagine that this is very hard to do unless they are also of the same frequency.

To get two vibrations arriving at the same detector in step usually means fixed trip times for both radiations delivering the vibrations and selecting the sources rather carefully as well: a couple of car headlamp bulbs won't do – and this is rather fortunate because the lighting patterns might be interesting where they overlap. You'll see why shortly.

Sources that are of the same frequency and in phase are called coherent. Beams produced by them are also described as coherent. As a reasonably intense beam consists of a random hail of many photons, it is hard to arrange two independent sources to be coherent, and a more common arrangement is to take a single source and then split it in two, often by reflecting a part of the beam.

Stationary patterns: moving vibrations

Interference is a stationary pattern of varying intensities as a result of two or more colliding beams. These beams must be coherent, and there are a few simple ways of taking one vibrating source and producing two beams. One vibration can be used to drive two sources, as when a single electrical signal drives two loudspeakers. A single beam of photons can be split by a prism, or by reflection. This is rather harder to do for sound, because it does not travel in such well defined beams. Look out for the account of diffraction in this episode to see why that is so.

These intensities can vary from the sum of the intensities of the contributing beams to their difference. So two beams of light illuminating one detector can apparently produce a lower intensity than either one by itself, if the detector is placed so that the contributions are always exactly out of step, and so the resultant amplitude is, at all times, the difference in amplitudes.

A particularly interesting case arises when the amplitudes of the contributing beams are equal. Then the two beams produce, in some places, total darkness. This can only be explained if light does some vibrating, and it was crucial, historically, in persuading people that light could not be fully explained by a simple particle model. It's hard to see how two particles passing by a single point act as if there are no particles passing, and then, once past that point, act as if there are two independent particles again.

All radiations exhibit this phenomenon of interference: from very high-frequency photons, such as gamma radiation, to low-frequency photons, such as radio waves; through water waves, to very low-frequency sound waves. So it's a real fingerprint of a travelling vibration. If you suspect you'd like to use a wave description of a phenomenon, try to show interference from the appropriate source.