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Note from mentor: This thread was originally posted in a non-homework forum, so it does not use the homework template.

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We have n slits, however suppose half of the middle ones are covered. How could you go about finding the angles at which the minima occur at in the Fraunhofer limit? I've been told using phasors is the best approach to do this.

All I can see is that the phase difference between adjacent slits will be kdsinθ with slit separation d, wavenumber k. However there is a jump in phase as we go from slit n/4 to 3n/4 of 0.5nkdsinθ. To obtain a minimum we need the remaining n/2 phasors to sum vectorially to give a closed loop. However converting this into some mathematical condition is proving very confusing.

A few things I have thought:

a) Consider the two groups of n/4 slits separately, and ask that their phasors alone form closed circles. This sets nkdsinθ/4=2mπ for integer m>0 and so θ≈4mλ/nd.

b) If we consider all n slits, for the cases where the n phasors form circles that double/quadruple/octuple etc up on themselves, we can remove the middle n/2 phasors and still get closed circles. This gives nkdsinθ=2mπ for integer m>0, and so θ≈mλ/nd. Note this makes a) redundant.

However these aren't right. Any help? Thanks.

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We have n slits, however suppose half of the middle ones are covered. How could you go about finding the angles at which the minima occur at in the Fraunhofer limit? I've been told using phasors is the best approach to do this.

All I can see is that the phase difference between adjacent slits will be kdsinθ with slit separation d, wavenumber k. However there is a jump in phase as we go from slit n/4 to 3n/4 of 0.5nkdsinθ. To obtain a minimum we need the remaining n/2 phasors to sum vectorially to give a closed loop. However converting this into some mathematical condition is proving very confusing.

A few things I have thought:

a) Consider the two groups of n/4 slits separately, and ask that their phasors alone form closed circles. This sets nkdsinθ/4=2mπ for integer m>0 and so θ≈4mλ/nd.

b) If we consider all n slits, for the cases where the n phasors form circles that double/quadruple/octuple etc up on themselves, we can remove the middle n/2 phasors and still get closed circles. This gives nkdsinθ=2mπ for integer m>0, and so θ≈mλ/nd. Note this makes a) redundant.

However these aren't right. Any help? Thanks.

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