# Why are light waves from 2 separate light bulbs incoherent?

#### fantasizeme

My notes says that this is due to how the wave patterns of both sets of light waves vary with time since the amplitudes vary due to electrons losing energy. But I dont get how this affects the coherence of both sets of light waves since they have the same frequency

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#### vanesch

Staff Emeritus
Gold Member
They don't have the same frequencies. Light from a light bulb has a whole spectrum of frequencies and you only need tiny differences in frequencies to have a 180 degree phase difference after a tiny time.

#### the_house

It's not just a question of frequency. It's the phase information that is important for the concept of coherence. No real light source--even a laser--consists of a perfect sine wave that goes on forever. Even if you take light from a single source and split it and recombine it, making the length difference between the two legs more than the http://en.wikipedia.org/wiki/Coherence_length" [Broken], there is no definite relationship between the phase of the two beams and this washes out the interference pattern. In other words, even for a monochromatic laser, there is a finite coherence time beyond which the phases at two different times are completely uncorrelated. Similarly when you have two separate light bulbs as in the original question, there is no definite phase relationship between the light from each source and they are therefore incoherent.

You can actually get an interference pattern from white light coming out of a single light bulb (although the coherence length is very short), so it's not really the presence of many frequencies that is the main issue here.

I'm not sure what is the meaning of the statement that varying amplitudes are the reason for incoherence. I'm not an expert on this, but I'm pretty sure amplitudes are completely irrelevant to coherence.

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#### russ_watters

Mentor
I'd explain it like this: a light bulb actually contains a huge number of little emitters of light, with nothing to make any of them in phase with each other.

#### vanesch

Staff Emeritus
Gold Member
It's not just a question of frequency. It's the phase information that is important for the concept of coherence. No real light source--even a laser--consists of a perfect sine wave that goes on forever.
It is maybe nitpicking, but from the moment that there is a phase incoherence, by definition you do not have a single frequency in your Fourier transform. The Fourier transform of a single frequency (a Dirac in frequency domain) is exactly a perfect sine wave that goes on for ever. From the phase coherence, you can derive a minimum width in the frequency domain. If that width is zero, that is, if the light is *perfectly* monochromatic, then it is by definition a single sine. The phase jitter corresponds to a tiny width in the frequency domain - although one might call this light still sloppily "monochromatic" because otherwise you never really have monochromatic light.

Even if you take light from a single source and split it and recombine it, making the length difference between the two legs more than the http://en.wikipedia.org/wiki/Coherence_length" [Broken], there is no definite relationship between the phase of the two beams and this washes out the interference pattern.
Exactly, and this is nothing else but a measurement of the width of the spectral "line". The "finite life time" of a "sine wave" is nothing else but the coherence time (which is the time equivalent of the coherence length), and gives you a measure of the width of the spectral line.

You can actually get an interference pattern from white light coming out of a single light bulb (although the coherence length is very short), so it's not really the presence of many frequencies that is the main issue here.
It is! And your example illustrates this. "white" light can be seen as a large "line width" and hence a very short coherence length.

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#### Cthugha

You can actually get an interference pattern from white light coming out of a single light bulb (although the coherence length is very short), so it's not really the presence of many frequencies that is the main issue here.
Temporal coherence is basically defined by taking the Fourier transform of the spectral power density and define the decay rate of the transform as the coherence time. Accordingly a small spread in frequencies assumes long temporal coherence and vice versa.

The reason why you can also get interference patterns from white light is spatial coherence. If you go far away from the light bulb you just take a small solid angle of the emission into account. This means that the path differences from the different points on the light source to your detector becomes smaller and therefore coherence is increased. This is why there is a pinhole in front of the double slit in the Young interference experiment. The pinhole mimics a point-like light source which offers full spatial coherence.

Accordingly you can make light from a light bulb as coherent as you like. Filter the light through an optical filter with narrow spectral width and go extremely far away from the source (or put a pinhole in front of it) and you can get arbitrarily high temporal and spatial coherence from a light bulb. However, this works for classical first order coherence only, but not for higher order coherences.

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