I know that the field inside a dielectric is changed and is $\epsilon$ times less the original field (some books use $K$ for this constant).

This is because the induced field inside the dielectric is in opposite direction to the original field.

But what happens to the field after it passes the dielectric?

For example:

Assume a point charge $q$ is somewhere on the $z$ axis, above the $x-y$ plane, and that the $x-y$ plane is made out of a dielectric material with $\epsilon>1$, does the field below the $x-y$ plane is still given by $E=\frac{q}{r^{3}}\vec{r}$?