What is the model for wave reflection? in this animation from the Fresnel equation wiki we can see a wave bouncing back in the "negative" compared to the "positive" incoming wave.
What physics model govern such behavior in transverse waves?
 A: You would like a conceptual answer, so here it is.  Imagine that, at the surface of the medium, the incident light wave stimulates movement of electrons in response to the changing E field in the incident wave.  The movement produces an electromagnetic wave that propagates symmetrically in both directions but which has opposite phase to the incident wave: it moves both in the same direction as the incident wave (forward) and in the opposite direction to the incident wave (backward).
If the stimulated wave is equal in magnitude and opposite in phase to the incident wave, then the transmitted wave will be perfectly cancelled by the portion of the stimulated wave moving in the "forward" direction.  The backward moving portion of the stimulated wave is the reflected wave.  
In the case of partial reflection illustrated by the animation you referenced, the stimulated wave has a reduced amplitude with respect to the incident wave.  Accordingly, the transmitted incident wave is reduced, but not to zero.  The reflected wave (the backward portion of the stimulated wave) is also reduced because it is the stimulated wave, which is lower amplitude than the incident wave.
A: The physics model governing electromagnetic waves is of course, Maxwell's equations. A plane incident on an interface between two dielectric material is governed by Maxwell's equations in linear media:
Gauss's Law replaces the electric field, $\vec E$, with the displacement field, $\vec D$, which with no free charges, becomes:
$$ \nabla\cdot\vec D = 0 $$
where:
$$ \vec D = \epsilon \vec E $$
Ampere's Circuital law (with no free currents) becomes:
$$ \nabla \times \vec H = \frac 1 c \frac{\partial \vec D}{\partial t} $$
where:
$$ \vec H = \frac 1 {\mu} \vec B $$
The other (source-free) equation remain the same
$$ \nabla \cdot \vec B = 0$$
$$ \nabla \times \vec E  = -\frac 1 c \frac{\partial \vec B}{\partial t}$$
When applying these equations to a plane wave at an interface between 2 media,
you need to distinguish 2 polarization states. Now all polarization is
perpendicular to the direction of travel, but that space is spanned by two orthogonal directions. In one formalism, they are called S and P , where P has the electric field vector(s) coplanar with all the directions of propagation and S has it orthogonal to all directions of propagation.
So: applying the linear-media equations to the plane waves at the interface, the following conditions determine the scattering:
(1) The tangential component of $\vec E$ is continuous.
(2) The normal component of $\vec D$ is continuous.
(3) The normal component of $\vec B$ is continuous.
(4) The tangential component of $\vec H$ is continuous.
Now in the situation you described (normal incidence), the normal components of all the fields are zero, so you just apply the tangential conditions.
