by alter-ego » Wed Jun 02, 2010 5:57 am
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
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[u] and <1[/u] 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 :D