GRED Answer: Double slit with late divider

[RJN]

Guess the Result of the Experiment of the Day (GRED)

A classic double slit experiment is done with light (photons) that creates an interference pattern on the image screen. The experiment is repeated, except now a thin, black, opaque divider is placed from the slit screen, dividing the two slits, to the image screen. Here is an ASCII schematic:

Code: Select all

                                                            
                               |                             |
     s                         |-----------------------------|
                               |       opaque divider        |

    Photon                   Double                         Image
    Source                    Slit                          Screen
                             Screen

What pattern appears on the image screen?

The initial poll, where spoilers were not allowed, can be found here: http://asterisk.apod.com/vie ... 30&t=19609 . If you are new to this GRED and want to ponder this question without seeing spoilers, please go there now instead of scrolling down.

What I believe to be the answer to this GRED is now posted below and can be found here: http://asterisk.apod.com/vie ... 10#p122971 .

Comments and candidate answers are still invited below. Other GREDs can be found here: http://asterisk.apod.com/viewforum.php?f=30

- RJN

[alter-ego]

The opaque divider placed AFTER, and in between the slits, prevents interference between the slits, i.e it is identical to blocking one slit or the other. A two-slit interference is simply the convolution of the single-slit diffraction pattern (assuming the same slit widths) and a uniformly spaced modulation function determined by wavelength and slit separation (the larger the slit separation, the "higher" the modulation frequency of the intensity pattern on the screen). When either slit is blocked (or an opaque screen prevents the two sources from interfering) only the single-slit diffraction pattern will be visible, without modulation.

Unlike the case of the "early" divider, where both slits are still illuminated by the same source (as long as the divider is thin enough to not block the source) and therefore does not affect the interence pattern on the screen, the "late" divider clearly changes the intensity pattern on the screen.

Consider making the opaque divider shorter toward the slits. As it is shortened, and increasingly more light from each slit is allowed to interfere at the screen, one should see intereference beginning at the middle and progressing outward. Barring confusion from divider edge diffraction, as the interference becomes visible, the modulation frequency won't change and only the number of fringes increases.

[alter-ego]

By the numbers, this experiment is not trivial to do at home using visible light. Given the following setup:
1. Lambda = 0.633 microns (Red, Helium Neon laser)
2. a = Slit Width = 50 microns
3. d = Slit Separation = 0.65mm

A divider screen, L ~ 75mm long is needed to block ~2/3 of the fringes across the central diffraction lobe! Unfortunately, the remaining visible fringes occupy the central brightest region of the diffraction lobe, so the results might be muddied. To reduce the unblocked fringes to 10%, the divider needs to be ~250mm long, or the slit width needs to be ~15 microns. For the example above, the central diffraction lobe full-width is ~1.4 degrees (25mm at 1 meter), and the interference fringe separation is ~1mm at 1 meter. A generalized good estimate for the unblocked, visible fringe fraction = (a*d)/(2*L*Lambda). You want this ratio to be as small as possible and <1 to be physically meaningful, i.e. you can have at most 100% fringes visible. The angular separation between fringes ~Lambda/d, the diffraction lobe full-width ~2*Lambda/a, and the central unblocked interference full-width ~d/L.

Definitely a coherent (monochromatic) source (e.g. laser) is important to get good fringe visibility. Is it possible to use much larger slits and water as the wave medium? Maybe. Even larger scaling using sound waves generated in a room and open windows as slits?? Interesting... In any case, going to a longer wavelength and/or reducing the slit separation is key to better fringe resolution and effective blocking using the divider screen, while decreasing slit width, a, increases the total number of fringes that potentially can be visible. The downside of reducing the slit separation, d, is it's harder to place a screen between them. The downside of a narrower slit is the brightness reduction on the viewing screen. The experiment looks interesting and seems doable, you just need to optimize the parameters.

I think I kept my factors of 2 straight

[RJN]

The answer is, I believe, "No interference pattern." Once it is possible to know "which path" information for the photons striking the image screen, then an interference pattern cannot form. The late divider makes it possible to match up photons with which slit they went through, so there cannot be an interference pattern. Additionally, light from each slit would have to strike the same place in order for this light to interfere. The late divider prevents this. Alter-ego, below, also provides a good analysis. (Thanks AE!)

Alter-Ego also details one way to do this experiment in practice. Additionally, a Scientific American article published a few years ago here:
http://www.scientificamerican.com/artic ... xperiments
detailed how to do simple two-slit experiments using only a laser-pointer and a pin.