Phase difference

1. The problem statement, all variables and given/known data
For single-slit diffraction, calculate the first three values of [tex]\phi[/tex] (the total phase difference betweenrays from each edge of the slit) that produce subsidiary maximu by

a) using the phasor model

b) setting [tex]\frac{dI}{d\phi} = 0[/tex], where I is given by [tex]I = I_0 \cdot (\frac{sin(\frac{1}{2} \cdot \phi)}{\frac{1}{2} \cdot \phi})^2[/tex]



2. Relevant equations

given


3. The attempt at a solution

I attempted to do part b first as I already knew the answers from part a (fairly straight forward) and was using them to check my answer.

I realized that even though I had used the exact described method, my answer was completely different as my values for phi ended up as:

1) [tex]\pi[/tex]
2) The first non-zero solution to [tex]tan(\frac{\phi}{2}) = \frac{\phi}{2}[/tex]
3) [tex]2 \cdot \pi[/tex]

 

Err. The equation for the intensity is given in the problem and d is not involved.