Solve Image Charge Problem with Method of Images

[aaaa202]

I suppose you are all familiar with the standard image charge problem of calculating the electric potential for a point charge above a grounded conducting plane at y=0. In this case you solve the problem using the method of images.
I have a slightly problem. Rather than having an infinitely thin conducting plane, mine occupies a region 0<y<a, i.e. it must now hold that V(x,y)=0 for 0<y<a.
Is it still possible to solve this using the image method?

 

[Dazed&Confused]

For the area y&gt; a you can use the same image charge at the appropriate point below y = a. For the area y &lt; a you know can add an image charge -q at the same spot as the original charge to cancel out the charge. Thus V = 0 at all the points y \leq a. This is a round about way of saying that the solution is to Laplace's equation is unique and since V=0 at the boundaries we know that V=0 is the unique solution for the entire area y \leq a.