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help wanted regarding normal map

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Hi! I have an image, that has a black background and normal map of a sphere at the center. This image is wrapped as the texture on a rectangle parallel to x,y axes and lying on z = 0 plane. Now, I'm sending a light position vec4(sin(theta), 0, cos(theta), 1) as a parameter to the shader. This theta is incremented by some delta value in each frame. I mean, I'm sending a point, that moves on the perimeter of the circle x^2 + z^2 = 1. In the pixel shader... 1) I'm converting the 0 to 1 normals into -1 to 1 normalized normals 2) performing a dot product with my light position. 3) and setting the output color as (dotproduct, dotproduct, dotproduct) NOW, the problem I'm facing is... when ever the z value in vec4 becomes negative, the black background is being considered as (-1/root3,-1/root3,-1/root3) normal values and since the light's z < 0, all the pixels for the background are yeilding white pixels. Should I change my code or should I make changes to my normal map? Can someone help me please...

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