Yep, that's exactly what the problem is from the looks of it, you need to find and turn up the ray recursion limit. Looks like its on the "Transparency" panel, and the default appears to be "2" which means once a ray passes thru 2 layers of transparency it "runs out of energy" and just returns the constant value, which in your case is white. If you set that value higher, it should solve the problem, you don't want to set it too high tho, as it will likely increase your render time slightly. 

 

Also, keep in mind, a similar issue, tho often less noticeable can happen when you have multiple refelctive surfaces on the scene together. There's a depth limit on the "Mirror" properties panel as well, you might want to increase that if you notice reflections are "running out" as well.

 

Where on earth did you get a monitor which a resolution of 2800x1800 pixels by the way???

 

 

EDIT: Whoops, looks like we crossed up while i was poking around blender for the right buttons to push.

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