Why does the sum of incoherent light sources result in non-zero intensity?

In summary, the conversation discusses the behavior of monochromatic light sources, specifically in a sodium lamp. The electric field of each source is independent and has a random phase, resulting in a total electric field close to zero due to interference. However, this does not align with the observed intensity of the light. The mistake was made in calculating the intensity, as it is related to the average square of the amplitude rather than the average amplitude itself. This leads to the conclusion that the intensity is the sum of the individual intensities of the light sources.
  • #1
fantispug
105
0
I was thinking about a collection of monochromatic light sources with a randomly oriented phase - for example in a sodium lamp the atoms will radiate almost independently, so they should act as such a collection of incoherent light sources.

Assume for simplicity each light source is classical and has the same electric field magnitude [tex]E_0[/tex]. The electric field of each of them at a point in space would be [tex]E_0e^{(i\varphi)}[/tex] (for some [tex]\varphi[/tex] dependent on the individual light source and the position in space) and the total electric field would be the sum over all of these electric fields at that point.

Given that the phases of the sources are unrelated it should be expected that any value of [tex]\varphi[/tex] could occur with equal probability, that is the phasor (complex vector) corresponding to the electric field could be oriented in any direction with equal probability. The sum over a large number of these sources should thus give something close to zero.

However this would imply zero intensity and since we can observe the light from a sodium lamp this doesn't make sense.
What am I doing wrong here?
 
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  • #2
Isn't the intensity related to the average square of the amplitude, rather than the average amplitude?
 
  • #3
Yeah, you're completely right. I don't know why I was thinking the square of the average, rather than the average of the square (since the electric field at a point can tell you nothing about the power passing through that point). So the cross-terms from the square - the interference terms - will average to zero, and the intensity will just be the sum of the individual intensities!
Thank you so much, that makes much more sense
 
  • #4
Pleased to help :smile:
 

What are incoherent light sources?

Incoherent light sources are light sources that emit light waves that are not aligned in phase. This means that the light waves do not have a consistent relationship with each other, resulting in a random pattern of light.

What are some examples of incoherent light sources?

Some examples of incoherent light sources include incandescent light bulbs, fluorescent lights, and LEDs. These sources emit light waves that are not aligned, resulting in a diffuse and scattered light pattern.

What is the difference between incoherent and coherent light sources?

The main difference between incoherent and coherent light sources is the alignment of the light waves. In coherent sources, such as lasers, the light waves are in phase and have a consistent relationship with each other. In incoherent sources, the light waves are not aligned and have a random pattern.

What are the applications of incoherent light sources?

Incoherent light sources have a wide range of applications, including general lighting, photography, and medical imaging. They are also used in scientific research, such as in spectroscopy and microscopy.

How are incoherent light sources created?

Incoherent light sources are created by using a source of energy, such as electricity or heat, to excite atoms or molecules in a material. As the excited atoms or molecules return to their ground state, they release energy in the form of light waves. The resulting light waves are incoherent and emit in all directions.

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