Shaders 3D Shader - Modify color of pixels below a plane

Heya! I've been playing around with some simple shaders and was hoping to tackle something a little more complex. However, I've been unable to find any resources that pertain to what I'm looking for. A 3D shader that modifies the color of pixels that are viewed through a 3D plane.
For example:

Here is a hole.

A plane exists within this hole.

The pixels that are viewed through this plane should have their colors modified.
(I constructed this image to demonstrate this example.)

Any advice or links to resources / tutorials covering relevant topics would be greatly appreciated!