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Old Jan 14th 2015, 02:55 AM   #1
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4 slit interference with unequal spacing

Hi all

I'm currently working on something and need a little help. I have very limited knowledge in this area, so please bare with me, but if anyone can provide some pointers then please do.

Basically, I need to derive some kind of equation to simulate a 4 slit interference pattern, where the slits are spaced at unequal intervals (that I can set). I'm aware that this may result in one, or a series of, long and complicated formula, but I'll be running it through excel (or something), so that doesn't really matter.

There are loads of derivations of equally spaced slits, but I don't really know how to manipulate this to cater for the unequal spacings. I have found a derivation using 'phasors' of two slit interference, giving;

I = I_0 * (cos(del/2))^2
where
del = (2 * pi/wavelength) * a * sin(theta)
as is covered elsewhere on the net.

This phasor derivation makes sense to me, but expanding it seems to over-simplify it; I don't think I'm doing it correctly. I guess I just need to add to this the effect of another slit, and then again, but I'm not sure how to go about it.

Does anyone have any pointers?

Thanks
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Old Jan 14th 2015, 07:54 AM   #2
MBW
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I would think that you should be able to treat each pair of slits independently, then superimpose (add) the results.

Note that for 4 slits you have 6 different ways to combine these into pairs.
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Old Jan 14th 2015, 08:16 AM   #3
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Originally Posted by MBW View Post
I would think that you should be able to treat each pair of slits independently, then superimpose (add) the results.

Note that for 4 slits you have 6 different ways to combine these into pairs.
Thanks for the reply

I'm looking into this; I need to plot the intensity as a function of the angle from 'straight ahead' if that makes sense. That makes this slightly more problematic, although I guess I could make that conversion later on in the process.
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