http://local.eleceng.uct.ac.za/courses/EEE3055F/lecture_notes/2011_old/eee3055f_Ch4_2up.pdf [Broken] (Page 4.4 ) I am having a trouble with understanding why closed loop line integration is 0 at dielectric boundary. As far as I know, closed loop line integration is 0 because electric field is conservative. However, if we have a boundary condition, we'd have two electric vector fields where each has different permittivity epsilon_1, epsilon_2. and also directional components would be different due to refraction. If we break down the line integral into two parts of closed loop line integration, one for the top and the other for the bottom dielectric region, the middle boundary part will cancel out and the result Et1=Et2 makes sense. Also if we do the two closed loop line integration for top and bottom dielectric region, we can show that Et1 and Et2 are equal to the electric field at the boundary for any arbitrary closed loop. *However, it seems a little conunter intuitive to me because E1t and E2t would be diffrent due to refraction. How can I justify the result physically?