What are phase constants in equation of electric field for deriving law of reflection at boundary of dielectric? I'm studying reflection of EM Waves at dielectric boundary from Optics by Eugene Hecht. But despite many attempts I am unable to understand
What is meant by statement "Here ϵr and ϵt are phase constant relative to EI and are introduced because position is not unique."?
Picture from book:

Thank You.
 A: $\epsilon_r$ and $\epsilon_t$ appear to be phase terms to shift the reference plane of the reflection. If the reference plane or origin was chosen to be the interface then $\epsilon_r$ , $\epsilon_t$ $=0$. However, if you chose a reference plane that was not at the interface then you would add a phase term $\epsilon_r$ , $\epsilon_t$ $\neq$ $0$.  These values should be proportional to the distance from the interface and the $\vec{k}$. Hope this helps.
A: Actually one can shift the expression along the interface. For instance, consider the transformation 
$$ \mathbf{r} \rightarrow \mathbf{r} + \mathbf{r}_0 $$
where $\mathbf{r}_0$ is a vector lying in the plane of the interface. Then the term in the argument would become
$$ \mathbf{k}_x\cdot\mathbf{r} \rightarrow \mathbf{k}_x\cdot\mathbf{r} + \mathbf{k}_x\cdot\mathbf{r}_0 , $$
where the subsript $x$ is either $r$ or $t$. Here $\mathbf{k}_x\cdot\mathbf{r}_0$ is a constant. Since one can do any such shift this constant represents an unspecified phase. Therefore , one should include these arbitrary phases.
