Confusion about Fraunhofer Diffraction

Zarquon

I'm looking at the explanation for single slit Fraunhofer diffraction, in particular the location of the intensity minima. a is the slit width, lambda is the wavelength and theta is the angle. By dividing the slit into two parts and viewing the wavefront as a sum of many small sources i can see that everything cancels out when a*sin(theta)/2=lambda/2. I also see why the same happens for a*sin(theta)=2*lambda, by dividing the slit into four regions. However: If we let a*sin(theta)=2*lambda, and instead divide the slit into two regions as before, it looks to me like we get full constructive interference by using the same logic as in the case of the first minima. I know I'm making som basic mistake here, just can't figure it out. Hope somebody can make sense of this. [It's a little hard for me to explain the problem, but i hope someone who is familiar with the explanation i am talking about (from University Physics by Young and Friedman btw) might understand the question.]

dlgoff

Have you looked at a graphical approach to the problem?



http://hyperphysics.phy-astr.gsu.edu...pt/sinint.html

Zarquon

Thanks! I see now why my reasoning is wrong.