Point charge at a boundary between dielectrics

[quenderin]

Homework Statement

A point charge Q is at the boundary plane of two infinite, homogeneous dielectrics
with dielectric constants \epsilon_1 and \epsilon_2. Calculate the electric potential, the electric field and the displacement vector at any point in space.

Homework Equations

The Attempt at a Solution

Okay. I don't have a real clue of where to begin analytically, but I can guess a solution, namely Phi = 2/(\epsilon_1 + \epsilon_2) Q/r. If I work this out, then D normal to the plane is continuous, and so is E parallel to the plane, and applying Gauss' law on the charge gives the right answer. Does this make sense?

 

[graphene]

this is simple.
the field at a point depends on the dielectric constant at that point only.
so divide the space into two regions & work on each of them individually.