How are allowed and forbidden reflections calculated?

[ScareCrow271828]

Question:
Explain the rules of reflection for different cubic lattices (SC, BCC, FCC)
based on the Bragg ́s law. Help: If we have incident of X-rays, which planes have constructive/ distractive reflection? Why? Please calculate it for the following crystal planes. 001, 011, 111, 200, 210, 211

Equations:
2dsin(θ)=nγ
d=a/√(h^2+k^2+l^2)
γ=lambda (cant find the symbol sorry)
∴
sin²(θ)=(γ²/4a²)*(h²+l²+k²)Attempt At Solution:
I know the rules. SC=any h,k,l BCC=h+k+l=even. FCC=h,k,l= all odd or even. And that it has to do with the satisfaction of Bragg's law that leads to constructive interference which leads to normal reflection. Although, I'm having trouble understanding exactly what to calculate. Any help would be greatly appreciated, If I could be pointed in the right direction or given an example for just one calculation that would be great.

 

[kuruman]

Perhaps "calculate" is a bad choice of wording. I believe the question is asking you to state whether each of the given planes for each of the lattices exhibits constructive or destructive interference and explain your reasons. The explanation part will require some calculation involving h, k and l.