Dielectric boundary I am trying to determine why electric field may be confined to a certain region if there is a large difference in the permitivity for example if electric field flows through water and then reaches a water air boundary. 
I have also been reading about EM waves, is it possible to model electric field as a wave because if so then the transmission T and reflection R coefficients given below in terms of n which is $\propto \epsilon_{r}^{1/2} $ and so if $\epsilon_{1}>>\epsilon_{2}$ then $n_{1}>>n_{2}$ ;
$\displaystyle R$    $\textstyle =$    $\displaystyle \left(\frac{n_1-n_2}{n_1+n_2}\right)^2, \rightarrow 1$
$\displaystyle T$    $\textstyle =$    $\displaystyle \frac{n_2}{n_1}\left(\frac{2 n_1}{n_1+n_2}\right)^2 \rightarrow 0.$
and so it is clear that the wave is reflected at the boundary, is this approach valid ?
http://farside.ph.utexas.edu/teaching/em/lectures/node103.html
 A: One way to understand what append at the boundary of two dielectrics is to use the Fresnel formula when you know about the indices of your media.
Then, you have to solve the wave equation (d'Alembert equation) with the boundaries condition given by thoses Fresnel coefficient.
The confinement is due to the boundaries conditions betwen the two dielectrics. To explain it, you don't need the microscopic approach give by your link.
A: What you're saying is mostly correct, but your language is a bit imprecise, which makes me think your understanding is a bit incorrect.
To be clear: there are both static electric fields, as well as time varying electric fields, which occur together with magnetic fields electromagnetic (EM) waves. The equations you're using describe reflection and transmission of an EM wave at a boundary between two different media (e.g. air and water), but only at normal incidence; if the wave hits the interface at an angle, these formula fail. Based on these equations, some of the energy will transmit, while some will reflect. A larger different in index of refraction will result in greater reflection at the interface.
If you're trying to describe static fields, then these formula are completely irrelevant. You can't model static fields as waves.
A: The answer to the second part of your question is yes your approach is OK. I have gone through the link you have posted and want to say that the inferences drawn from formulae written above are for non collisional   case i.e. dielectric constant $\epsilon$ is real. However if $\epsilon$ is complex you can not draw the same conclusion from above formulae. 
For the first part of your question when you deal with static fields there is no reflection because the fields are not propagating. 
High dielectric constant (para-electric medium) enhance the electric field inside the medium via alignment of molecular dipoles. If the dielectric constant of one medium is much higher than that of other most of the electric field strength will appear to be trapped inside that medium. In reality the field inside the medium is enhanced via its para-electric properties.
I hope it will help
