If there is a field described by the vectors A^→ and B^{→ .} These are related by B^→ =kA^→ where k is a constant. The two vectors are found to satisfy the differential equations
1) ∇^→.A^→=0
2) ∇^→*B^→=0

questions:
1. Using these relations derive the boundary conditions that relate the values of the components of the vectors A^→ and B^→ on the two sides of a boundary between materials 1 and 2, where the constant k has two different values k1 and k2 in materials 1 and 2 respectively. So please give your answer in terms of k1 and k2 .

2. Now suppose that the boundary occupies the x-y plane (z=0). In medium 1 vector A^→ has components A^→ = B^→ =Ao(x^+z^) and k1=1. In medium 2, k2 =2. Find the components of A^→ and B^→f  in medium 2.

Please explain the steps as you go. I want to be able to understand how this problem was solved and what is happening.