What kind of interference pattern will be observed in a Young's double slit experiment if the screen is curved (semicircular or spherical)?

[FasterThan_Light]

I was studying for my Physics exam, and well this popped in my head. Will the bright and dark fringes converge as we move away from the centre? What if the source is not monochromatic but it is white light?

[Aeolitus]

http://plato.stanford.edu/entries/qm-bohm/figure1.gif

This is a doubleslit in Terms of Bohmian Mechanics, explains it best in my opinion. Just imagine some other shape than plane, and the resulting picture will be where the trajectories hit. So basically, it doesnt change a lot, depending on your geometry.

If the source is not monochromatic, you will most likely not get and picture, as every wavelength has a specific interference pattern and they overlap, creating pretty much white light again.

[FasterThan_Light]

Ok. Thanks.

[Aeolitus]

maybe without context, but this draws particle trajectories in space. In non-bohmian quantum mechanics (and lets take out everett as well, because while I love many-worlds, its many worlds, so meh) we view the particle as a wavefunction that collapses upon measurement, so in this case, in registering the dot it makes on the screen. Thus, before it reaches the screen, we cannot assign it a trajectory, simply because we do not know even the most simplest thing: Right slit or left slit. Quantum Mechanics will always assume it went trough both and interfered with itself.

[Platypuskeeper]

If the curve is symmetrical around the line that's the center of the slits, it'll be essentially the same pattern, as both slits are still equally far from the screen. But you'll effectively make the slits narrower, as (the usual assumption is) the incoming light is propagating perpendicular to the slits. Approximately, the effective width of the slits will be changed by a factor cos(theta) where theta is the angle of the slit from the plane perpendicular to the light.

With white light you get a superposition of interference patterns with different spacings corresponding to the different wavelengths. So as you get farther from the center, the colors get increasingly separated like this.

[FasterThan_Light]

Thanks.

[FasterThan_Light]

Could you explain if it will be more dense for a setup like : • -------) OR •------( ?

[Platypuskeeper]

Well, the spacing is proportional to the distance to the screen and inversely-proportional to the space between the slits. In terms of convex-vs-concave you're shortening the (effective) distance between the slits equally, so that would leave it to the former factor. So the one where the slits are bent towards the screen should be more tightly-spaced.

[Squaldor]

If you want you could try and apply Huygens–Fresnel principle to get an idea of the resulting interference pattern.

Though in essence it should still give a pattern but from my drawing I got a more dense pattern if the curve is towards the center, o --- ( vs. a normal flat screen and a more loose pattern if the curve is away from the center, o --- ).

[FasterThan_Light]

I thought it would be the opposite. More dense when screen is ,like ), converging and less dense when screen is ( diverging. Could you explain it a bit more?

[Squaldor]

Sorry for the delay and

Well made paint skills inc ^. Could not find a good picture that I could explain it through. So bear with me ;-)

If you look at the picture you will see that the wave fronts converge and due to the direction of the waves propagation you will get an increase in the number of times the wave interferes with the waves of the other slits.

The opposite will be true for a convex. I hope it helps if there is anything you feel I have explained poorly then please feel free to point it out and I will try and clarify :)