We discuss common features in mechanical, electromagnetic and quantum systems, supporting identical results for the transmission and reflection coefficients of waves arriving perpendicularly at a plane interface. Also, we briefly discuss the origin of special notions such as refractive index in quantum mechanics, massive photons in wave guides and an elementary connection of results for a plane interface to experiments in graphene where the Klein paradox could be tested. The paper is intended for undergraduate level, and a basic knowledge of waves, relativity and quantum physics is required. Its educational purpose is to provide an integrated discussion of waves in order to fit the teaching to the requirement of a shorter sequence of university physics courses.