He had the right formulas. He knew Maxwell’s equations by heart. But every time he tried to match the boundary conditions, his answer dissolved into nonsense. He felt like he was standing in a thick fog, hearing the distant horn of a ship (the correct answer) but unable to see the path to it.
He tried problem 4.17 again. He struggled. He got stuck at the boundary condition at z=0. Instead of giving up, he opened the manual just for that step . He saw that he had forgotten that the tangential E-field must be continuous, but the normal D-field jumps by the surface charge. Electromagnetic Fields And Waves Iskander Solutions Manual
"Aha!" he shouted.