Problem with Dot product among normal and camera


I am trying to assign a different material depending on the sign of the dot product of the vectors Normal and Camera View. As you can see in the edit window, the normals in the internal part of the sphere are counter to the camera view so their dot product should be negative. But the result is the same, so or I am not using correctly the node Less Than, or this is a bug in the Dot product node.

Can you please help me?

Thank you in advance.


why not use the ‘Geometry’ node>>Front/Back???