Double slit displaying anti-fringes?

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Discussion Overview

The discussion revolves around the possibility of creating a double slit experiment that produces anti-fringes, where the intensity maxima and minima are inverted compared to the conventional interference pattern. Participants explore theoretical and experimental arrangements to achieve this effect, including the use of phase shifts and retarding plates.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant suggests that a phase difference of 90° between the two slit-beams could lead to an anti-fringe pattern, but notes that using a 90° retarding plate results in a mixed diffraction pattern.
  • Another participant questions why a phase quadrature setup would lead to a 'mixed and blurred' diffraction pattern, seeking clarification on this point.
  • A different perspective proposes that using two pieces of glass with one piece λ/4 thicker could achieve the desired phase shift without blurring, emphasizing that cancellation and enhancement occur at the same rate near the axis.
  • One participant asserts that rotating a plate to place one slit half a wavelength in front of the other is a straightforward method, although they acknowledge the practical challenges of achieving precise setups.
  • Another participant agrees that rotating the plate is a simple method but clarifies that the resulting pattern would not be blurred, instead describing how maxima and minima would behave in relation to the Gaussian envelope.
  • There is a discussion about the role of half-wave plates in polarization experiments and whether they can be used to achieve the necessary path length change for the anti-fringe effect.
  • One participant introduces the idea of increasing the number of slits to create a phased array, suggesting potential applications in radar and ultrasound, while also discussing the implications of path differences in multi-element setups.
  • A question is raised about the visibility of anti-fringes and whether they can be observed independently of other patterns.

Areas of Agreement / Disagreement

Participants express various hypotheses and approaches regarding the creation of anti-fringes, but there is no consensus on a definitive method or understanding of the phenomenon. Multiple competing views and uncertainties remain throughout the discussion.

Contextual Notes

Participants acknowledge practical limitations in achieving precise experimental setups, which may affect the outcomes. There are also unresolved questions regarding the visibility and nature of anti-fringes in relation to conventional interference patterns.

Marco Masi
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The conventional Young double slit experiment displays the interference fringes with the first intensity maxima at the center of the detection screen ('center' means aligned with the center between two slits of equal aperture). These are simply called 'fringes'. However, I'm wondering if and how one can construct a similar double slit experiment with anti-fringes appearing? Anti-fringes have the maxima where the fringes have minima, and vice-versa. That should be the case when the phase difference between the two slit-beams is of 90°. However, putting in front of one of the slits a 90° retarding plate won't result in an anti-fringe pattern alone but is mixed and blurred up with the diffraction envelope (the usual normal distribution Gaussian Bell-shaped function). If one places two retarding plates of 45° on each slit one won't get the anti-fringe pattern either, one gets again only the diffraction pattern (as the sum of the fring+anti-fringe). So, I'm wondering if there is a simple experimental arrangement that displays only the anti-fringes?
 
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Marco Masi said:
. So, I'm wondering if there is a simple experimental arrangement that displays only the anti-fringes?

Hmmm.. my initial guess was to try as you suggest- putting one slit in phase quadrature with the other. Why do you say that results in a 'mixed and blurred' diffraction pattern?
 
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Andy Resnick said:
one slit in phase quadrature
Two pieces of glass, with one piece λ/4 thicker. As you say, "why blurred?" The cancellation and enhancement will still occur at the same rate (near the axis). Blurring would only occur if there were other sources of light. Filling in of the nulls would occur if the amplitudes of the two sources were unequal.
The best mental picture for all these questions is surely to use two radio frequency antennae, fed from the same source and with amplitude / phase knobs. (But then I may be biassed here.)
 
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The simplest method must be to rotate the plate so that one slit is half a wavelength in front of the other.
As we do not routinely set up this experiment with micron precision, it shows that we are never sure anyway what we are actually looking at, and it makes almost no difference. The whole pattern is just shifted by half a fringe spacing.
 
Yes, I realize now the image would not be blurred, it is just one beam phase shifted, no blurring. But also the fringes are not shifted. The maxima decrease to zero while the minima grow up to maxima. In between they sum up to the Gaussian. Indeed, rotating the plate in front of one slit is the simplest method to illustrate it. As I understand it it must be a half-wavelength plate, which causes for half rotation a 360° shift?
 
tech99 said:
The simplest method must be to rotate the plate so that one slit is half a wavelength in front of the other.
As we do not routinely set up this experiment with micron precision, it shows that we are never sure anyway what we are actually looking at, and it makes almost no difference. The whole pattern is just shifted by half a fringe spacing.
it may be more convincing to leave the slits and screen in the same orientation and move the source to one side (doing the geometry right) so that the waves arrive at the back of the slits in the relative phase you wanted.
Marco Masi said:
As I understand it it must be a half-wavelength plate, which causes for half rotation a 360° shift?
I'm not sure what you mean here and in this context. Isn't a half wave plate a component in polarisation experiments? You need a path length change of a half wave in one path.
 
Increasing the number of slits effectively produces a phased array, and a stearable beam. A concept that has real world applications in radar and ultrasound.
 
Is an anti-fringe, where there is destructive interference and so decreased visibility? Is it visible by itself?
 
Julian Phillips said:
Increasing the number of slits effectively produces a phased array, and a stearable beam. A concept that has real world applications in radar and ultrasound.
You would need to change the thickness if you wanted to 'steer' the beam. It would be more of a 'tilted' beam. This is nothing unusual.
But we are missing the fact that there is a path from 3 to 1, as well as a path from 1 to 3. In terms of multiple element antenna arrays, it would be the equivalent to weighting the outside elements (Amplitude and phase) differently. That could broaden or narrow the beam marginally.
I guess what's special about this effect is that it operates between alternate slits; there is no one way path from 1 to 2 or 3 to 3.
 

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