1. The problem statement, all variables and given/known data The question is attached. 2. Relevant equations 3. The attempt at a solution I understand that the question would return to a typical conductor problem when ε2 >> ε1 so for the quadrant one, I placed image charges of q_1 at (d1 , 0 , -d2), -q1 at (-d1 , 0 , -d2) and another q1 at (-d1 , 0 , d2) with q1 = (ε1 - ε2)*q/(ε1 + ε2). When I applies the boundary conditions, I find that the image charges for quadrant two is q - q_1 at (d1 , 0 , d2), -q1 at (-d1 , 0 , -d2) and q1 at (-d1 , 0 , d2), for quadrant four is q - q_1 at (d1 , 0 , d2), -q1 at (-d1 , 0 , -d2) and another q1 at (-d1 , 0 , d2). The boundary conditions are well satisfies with these image charges. However, I failed to find image charges for quadrant three satisfying both the continuity of electric field and voltage at the boundaries connecting it with quadrant two and four. I have been working on this question for days and I am really frustrated. Is my attempt of approach is incorrect? Thank you for any help!