# I Coherence, Young's double slit experiments.

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1. Feb 13, 2019

### avicenna

In most textbook/internet explanation of light coherence, it gives two conditions
1) monochromatic light, same frequency.
2) light in phase or constant phase difference.

Only with the two conditions can light interference pattern be observed in the double slit experiment.

But this cannot be correct. Constructive and destructive interference can occur only if the both sources have the same polarization plane. Having the E-field plane differing by π would mean the original in phase waves to be out of phase by π.

Is it because the narrow slit of Young's experiment select light with polarization planes parallel to the slit. But this has never been mentioned.

2. Feb 13, 2019

### Staff: Mentor

I think you are exaggerating a bit here. The double slit experiment with polarisers has been mentioned many times here on PF.

I guess it is not often mentioned in textbooks because the experiment works with an unpolarised source. To remove the interference pattern requires adding two polarisers, one for each slit, which is not the same experiment.

3. Feb 13, 2019

### avicenna

I don't understand what you mean. Let's stick to the usual Young's experiment. A single source (random unpolarized) from the one slit falls onto the double slit and produced interference pattern.

What is the meaning of "in phase" ? Let's assume transverse EM waves. It means a propagation of an electric field oscillation(ignore B field); i.e. an E vector that oscillates at a frequency. We have to know the plane of oscillation. If the E-plane of the sources from the two slits are at π difference, in phase becomes out of phase by π - destructive superposition of E instead of constructive.

So talking of light source being "in phase" is meaningless without specific mention of what is the plane of oscillation of the E vector.

 Does it mean the light from the two slits would somehow be waves whose E-plane would be the same. If so, why?

Last edited: Feb 13, 2019
4. Feb 13, 2019

### sophiecentaur

From 1 to 2 is quite a big jump. 1 is the first stab at the topic and ignores the practicalities of and limitations of the basic Young's experiment. The light from a simple 'monochromatic source' will be unpolarised and will consist of a distribution of wavelength about a nominal centre. The emissions of a simple source will not consist of individual wave trains of any significant length (very low coherence). To improve the coherence, Young used a single narrow slot so that the relative path differences for all (most of) the short wave trains would be nearly the same. This would produce peaks and troughs which coincide well over a narrow angle. If the slits are not placed normal to the light path, the interference condition is worse and the pattern is less and less definite. The polarisation of wave trains will be random but the peaks and troughs will coincide.
If you use a polarised light source and rotate the polarisation of one of the paths, the co-polar components of the beams will produce an interference pattern but the cross polar components will not interfere and the overall pattern will be 'diluted'.

2 is rather badly put and doesn't include the fact that interference only happens for co-polar components of the two beams. You are right to say that this step tends to be ignored but we have jumped a long way in level of understanding and I guess it's taken for granted that 'the student' has already cottoned on to the consequences of polarisation. It's not something we can complain about - just something to take on board.

5. Feb 13, 2019

### avicenna

Please assume my physics is rudimentary. I still cannot understand what is meant by light coherence. The youtube experts give the two conditions of 1) monochromatic 2)in phase.

Wiki on Young's experment: "The experiment belongs to a general class of "double path" experiments, in which a wave is split into two separate waves that later combine into a single wave. Changes in the path lengths of both waves result in a phase shift, creating an interference pattern. ..."

Young's experiment was in 1801, way before our understanding of EM radiations. Young had a simplistic assumption about light waves; peak + peak enhances, peak + trough destructive. But then he might have an idea of peak/trough as in waves on water surface where the plane of oscillation is always in the vertical. So Young's explanation of in-phase or out-of-phase wave being the cause of interference is plausible.

But if we now assume transverse EM waves, then interference superposition can occur only if the two rays from the double slits have the same E-field oscillation plane.

So my question now is:
1) Do the two rays from the double slit have the same E-plane?
2) If so, why?

All textbook/internet explanation of light coherence never mention the questions 1) and 2).

6. Feb 13, 2019

### Andy Resnick

You are on the right track, but there is some missing information connecting points (1) and (2) above. Specifically, there is an important distinction between temporal coherence (single frequency) and spatial coherence (size of source).

http://electron6.phys.utk.edu/optics421/modules/m5/Coherence.htm

Young's double slit works for light that is highly spatially coherent- plane waves, spherical waves, etc. In fact, the condition for interference fringes in a Young interferometer is that there are not two independent sources (the slits), but instead the two slits form a single source by virtue of the fact that the field in each slit is highly correlated with the other.

And you are also correct that orthogonally-polarized fields do not interfere with each other.

Does that help?

7. Feb 13, 2019

### avicenna

OK. I think for the time being, I have to accept that the Young's experimental setup is able to produce two rays that are "coherent" (somehow) and therefore they could give the interference pattern. I'll have to read the link you give.

Thanks.

8. Feb 13, 2019

### sophiecentaur

The basic theoretical diagrams of the way interference works assumes that the two (or more) waves go on for ever and their phase relationship stays constant at their sources (for instance two idealised slits). In real life. In my last post I described real light, even monochromatic, can be thought of as consisting of many short wave trains. Each wave train will interfere 'with itself' when it is split between the two slits and meets on the other side. For off-axis paths, the length of a wave train can be shorter than the difference in the two paths so no interference can occur. That's why you need a laser to make holograms where the path lengths are much longer than the lengths of wave trains of conventional sources. The light from a laser has very long (virtually continuous) wave trains; it has a huge coherence length so you can form an interference (diffraction) pattern with its light shining on a large object. This is effectively what a hologram is.
Each wave train interferes with itself. The fact that they may all have different polarisations is irrelevant. You really don't need to get hung up on the polarisation thing - it all takes care of itself usually. But as I said previously. if you muck about with the polarisations of the two paths, interference may be reduced or even eliminated.

PS Re Polarisation. Are you aware that the Fields in a plane polarised beam can be resolved into two components at right angles and those components can be tinkered about with independently, producing a different resulting polarisation of what comes out the other end? It's just like resolving Forces and Velocities in Mechanics. A polariser is not like a plate with slots in that would let through only waves with E fields in one direction - it's only E fields at right angles to the polariser axis that are cut out entirely. Sorry if you already knew this but you did say your Physics is limited.

Last edited: Feb 14, 2019 at 3:46 AM
9. Feb 13, 2019

### Andy Resnick

No, that's not right- the slits don't produce coherent light. The source *behind* the slits produces spatially coherent light (or not). If you tried to use a double slit interferometer with a fluorescent bulb as the source, you'll never see interference. If you use a short-arc lamp as the source, you will see fringes (and rainbows, since the short-arc puts out polychromatic light).