A linearly polarized electromagnetic wave given as E→=E0cos(kz−wt)i^ is incident normally on a perfectly reflecting infinite wall at z=a. Assuming that the material of the wall is optically inactive, the reflected wave will be given as

When a wave is reflected  from denser medium the reflected wave is without change in type of wave but with a change in phase by 1800 or π radian. Therefore, additional phase of π in the incident wave is introduced. Also, the direction is reversed hence,  for the reflected wave we will replace   z by−z (in the phase) and i^ by −i^ . The incident electromagnetic wave is,E→=Eocos(kz−wt)i^ The reflected electromagnetic wave isEr→=E0cos[k(−z)−wt+π](-i^)  = −E0cos[−(kz+wt)+π]i^ =E0cos[(kz+wt)] i^                 [cos(−θ+π)=-cos(θ)]