Tools to synthesize the learning of thin films

After a review of textbooks written for undergraduate courses in physics, we have found that discussions on thin films are mostly incomplete. They consider the reflected and not the transmitted light for two instead of the four types of thin films. In this work, we complement the discussion in elementary textbooks, by analysing the phase differences required to match the conditions for constructive and destructive interference, in the reflected and transmitted light in four types of thin films. We consider thin films with varied sequences in the refractive index, which we identify as barriers, wells and stairs (up and down). Also, we use the conservation of energy in order to understand the complementary colour fringes observed in the reflected and transmitted light through thin films. We analyse systematically the phase changes by introducing a phase table and we synthesize the results in a circular diagram matching 16 physical situations of interference and their corresponding conditions on the film thickness. The phase table and the circular diagram are a pair of tools easily assimilated by students, and useful to organize, analyse and activate the knowledge about thin films.