Single slit diffraction minima formula misunderstanding

[HuaYongLi]

Reading the derivation for the single slit diffraction minima formula from this site, I'm not convinced about its argument.
http://www.math.ubc.ca/~cass/courses/m309-03a/m309-projects/krzak/index.html"

What I'm having trouble understanding is the explanation of the formula for minima when m>1.
For example when dealing with m=2, the explanation is that the slit is split into four sections so there is a phase difference of pi for the paired up point sources and so destructive interference occurs. But if we used 2 sections for m=2 then the paired up point sources have a phase difference of 2pi and constructive interference occurs.
Also when m=3 (or an odd number), it seems we have to revert back to two sections to explain destructive interference which gives a phase difference of 3/2pi which is destructive interference.
Why does using 4 sections for m=2 give the 'right' answer of destructive interference and not 2 sections?

 

[Doc Al]

For example when dealing with m=2, the explanation is that the slit is split into four sections so there is a phase difference of pi for the paired up point sources and so destructive interference occurs. But if we used 2 sections for m=2 then the paired up point sources have a phase difference of 2pi and constructive interference occurs.

Just showing that paired points constructively interfere does not allow you to conclude anything interesting. Just because points A and A' and points B and B' constructively interfere does not mean that A and B do. A and B may still be out of phase.

On the other hand, if you can divide the slit in a way so you can show that each section is canceled by another, then that's that. That does allow you to conclude that all the light cancels and a dark fringe occurs.

 

[HuaYongLi]

Thank You, I see it now.
I failed to take into account that constructive interference isn't like destructive interference when dealing with this pairing up business.