Understanding Newton's Rings and Coherence in Interference Patterns

[becko]

I'm trying to understand Newton's rings. So we have a plano-convex lens supported in a plane (please, see image here http://scienceworld.wolfram.com/physics/NewtonsRings.html). The incident light is divided into the light that is reflected at the convex surface and the light that is reflected at the supporting plane. These two waves interfere, at least close to the support point.

Now what I want to understand is why we ignore part that is reflected at the plane surface of the lens. I think it has something to do with coherence. But I can't figure it out.

If someone could explain this to me in clear terms, I would very much appreciate it. Thanks.

 

[JDługosz]

(please, see image here http://scienceworld.wolfram.com/phys...tonsRings.html ).

Your href is munged. The ellipses are present in the link itself, not just in the visible text.

 

[cesiumfrog]

If I understand the question, it has to do with "coherence length" (in particular, that the exact frequency of the light wave randomly fluctuates a bit from one period to the next). There's only a few wavelengths difference in whether the light reflects from the plane or from the far side of the lens (in the region where interference rings are visible). But there's a huge difference (on the scale of the wavelength) between either or those and the near side of the lens (so the cumulative effect is no precise phase-relationship, hence any interference would not be stable through time).

Note that Newton's rings are only visible very close to the contact point. If you lift the lens a few mm, or even just look for rings much further from the contact point, you'll see any interference has washed out.

 

[Andy Resnick]

<snip>

Now what I want to understand is why we ignore part that is reflected at the plane surface of the lens. I think it has something to do with coherence. But I can't figure it out.

If someone could explain this to me in clear terms, I would very much appreciate it. Thanks.

You don't *have* to ignore it. But, two things to consider:

1) where are the interference fringes localized?
2) if you are illuminating the lens with a plane wave, what is the effect of the flat surface?

 

[becko]

Your href is munged. The ellipses are present in the link itself, not just in the visible text.

fixed

 

[becko]

If I understand the question, it has to do with "coherence length" (in particular, that the exact frequency of the light wave randomly fluctuates a bit from one period to the next). There's only a few wavelengths difference in whether the light reflects from the plane or from the far side of the lens (in the region where interference rings are visible). But there's a huge difference (on the scale of the wavelength) between either or those and the near side of the lens (so the cumulative effect is no precise phase-relationship, hence any interference would not be stable through time).

Note that Newton's rings are only visible very close to the contact point. If you lift the lens a few mm, or even just look for rings much further from the contact point, you'll see any interference has washed out.

Ok. So I think I'm starting to get the idea. Problem is I don't have a clear idea of what "coherence length" is. I was hoping to improve my understanding with this particular example of Newton Rings. What I need is an explanation of what is happening without using the word coherence (since I don't know what it means exactly). From this I think I can work out the meaning of coherence.

Thanks.

 

[becko]

You don't *have* to ignore it. But, two things to consider:

It's not that I have to ignore it. It's that it can be ignored, because it doesn't interfere with the other waves. But I don't understand why.

1) where are the interference fringes localized?

I guess they are located at the top, where I put a plane to visualize the light patterns.

2) if you are illuminating the lens with a plane wave, what is the effect of the flat surface?

Light is divided in two waves, one reflected and one transmitted. The incidence is normal, so there is no deviation.

 

[Andy Resnick]

It's not that I have to ignore it. It's that it can be ignored, because it doesn't interfere with the other waves. But I don't understand why.

Well, there is a reflection off the air-glass top surface, and it does interfere with the light reflected off the mirror (and there's also interference with any light reflected from the glass-air (curved) surface, but the intensity is very low.

I guess they are located at the top, where I put a plane to visualize the light patterns.

What if I said the fringes were created at the curved surface?

Light is divided in two waves, one reflected and one transmitted. The incidence is normal, so there is no deviation.

Yes, but what is the spatial variation of the phase of the incident light at the top (flat) surface? Hint- there isn't any.

But to your point about coherence, in order for these fringes to appear, you need light that has a coherence length about the size of the gap, or in terms of the coherence time: the light has a narrow spectral distribution.

 

[JDługosz]

I'm trying to understand Newton's rings. So we have a plano-convex lens supported in a plane (please, see image here http://scienceworld.wolfram.com/physics/NewtonsRings.html). The incident light is divided into the light that is reflected at the convex surface and the light that is reflected at the supporting plane. These two waves interfere, at least close to the support point.

Now what I want to understand is why we ignore part that is reflected at the plane surface of the lens. I think it has something to do with coherence. But I can't figure it out.

If someone could explain this to me in clear terms, I would very much appreciate it. Thanks.

See http://www.citycollegiate.com/Newtons_rings.htm" for a better illustration that includes the rays. The reflection of the incident off the top of the first glass surface is not shown, but you can see it would be at a higher angle and if your eye were positioned to see the rings, would not matter. If there is some overlap, the intensity is very low so it would only detract from the pattern a little bit.

(The following post describes looking at it such that the specular reflection was out of the way. That reflection is the ray you are wondering about!)

 

[cesiumfrog]

Well, there is a reflection off the air-glass top surface, and it does interfere with the light reflected off the mirror (and there's also interference with any light reflected from the glass-air (curved) surface, but the intensity is very low.

Right, isn't the OP asking why it is low? It isn't as if the top reflection occurs with low amplitude.

What if I said the fringes were created at the curved surface?

Why do you think there is any significance in ascribing a "creation location" to the fringes? (What if I said they were created just in front of my retina?)

Yes, but what is the spatial variation of the phase of the incident light at the top (flat) surface? Hint- there isn't any.

Why not? I've only observed Newton's rings under uncollimated illumination from a sodium-vapour lamp, with the illumination directed from a large angle (to prevent observations from directly above being saturated by the specular reflection of the lamp). I think that would produce extreme spatial variation of the incident light phase.

But to your point about coherence, in order for these fringes to appear, you need light that has a coherence length about the size of the gap

Problem is I don't have a clear idea of what "coherence length" is. [..] What I need is an explanation of what is happening without using the word coherence (since I don't know what it means exactly).

becko,
Imagine your light source produces some waves a little bit randomly, so that about half of the peak-to-peak lengths are 9 units, and the rest of the cycles have peak-to-peak length of 11. This means that any two points that are 10 units apart (regardless of whether you start measuring from a peak, node, or trough) will have a small phase difference (neglecting the whole cycle) of plus or minus 1 (which is about a tenth of the average wavelength), and if you add the amplitude at those two points it will certainly almost double (the intensity almost quadruples). If you look at two points that are 25 units apart, the phase difference (neglecting the two complete cycles) could be 2.5-7.5 (i.e., half a wavelength on average), so if one of those points is a peak then the other will be close to a trough (but not exactly: you could have up to about a quarter of a wavelength of misalignment), so the interference between any points with this separation will certainly be destructive but not perfectly complete (the intensity will go low but not quite zero). Lastly, if you consider two points with 1000 separation, there could be anywhere between about 90 and 110 cycles between the points, that is, the possible phase difference is (even ignoring the 100 whole wavelengths) is still plus or minus about 10 entire wavelengths. This means, even if the first point is exactly on a peak, the second point isn't necessarily near a peak or a trough, it could randomly be on any part of a wave-cycle whatsoever, and so when we add these two parts of the wave, we'll need to do statistics to examine how likely the amplitudes are to increase or decrease (in fact we'll find that the intensities will add simply, there is no kind of consistent interference between pairs of points separated this far along the wave, and it makes absolutely no noticeable difference whether the distance was really 1000 units or 1005). So the "coherence-length" is somewhere greater than 10 but less than 1000 units. Does that help at all?

 

[becko]

Yes it does help! I think the best way to understand something is to take a simple example and find a simple explanation to it. Thanks for your help!