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

by fantasizeme
Tags: bulbs, incoherent, light, separate, waves
 P: 1 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
 PF Patron Sci Advisor Emeritus P: 6,203 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.
 P: 133 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 coherence length, 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.
Mentor
P: 21,652

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

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.
PF Patron
Emeritus
P: 6,203
 Quote by 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.
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 coherence length, 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.