180°), as the Fresnel reflection coefficient acquires a non-zero imaginary part. We shall now explain this effect for electromagnetic waves in the case of linear, homogeneous, isotropic, non-magnetic media. The phase shift turns out to be an advance, which grows as the incidence angle increases beyond the critical angle, but which depends on the polarization of the incident wave. In equations (), (), (), (), and (), we advance the phase by the angle ϕ if we replace by (that is, if we replace by ), with the result that the (complex) field is multiplied by . So a phase advance is equivalent to multiplication by a complex constant with a negative argument. This becomes more obvious when (e.g.) the field () is factored as where the last factor contains the time-dependence. To represent the polarization of the incident, reflected, or transmitted wave, the electric field adjacent to an interface can be resolved into two perpendicular components, known as the s and p components, which are parallel to the surface and the plane of incidence, respectively; in other words, the s and p components are respectively square and parallel to the plane of incidence. For each component of polarization, the incident, reflected, or transmitted electric field in Eq.() has a certain direction, and can be represented by its (complex) scalar component in that direction. The reflection or transmission coefficient can then be defined as a ratio of complex components at the same point, or at infinitesimally separated points on opposite sides of the interface. But, in order to fix the signs of the coefficients, we must choose positive senses for the "directions". For the s components, the obvious choice is to say that the positive directions of the incident, reflected, and transmitted fields are all the same (e.g., the direction in Fig.11). For the p components, this article adopts the convention that the positive directions of the incident, reflected, and transmitted fields are inclined towards the same medium (that is, towards the same side of the interface, e.g. like the red arrows in Fig.11). But the reader should be warned that some books use a different convention for the p components, causing a different sign in the resulting formula for the reflection coefficient. For the s polarization, let the reflection and transmission coefficients be and respectively. For the p polarization, let the corresponding coefficients be and . Then, for linear,