Molecular chirality and optical rotation
since for every orientation of the molecule, we can reverse the orientation such that the light appears to be falling on the molecule from a direction other than the one for our original molecule.


This is false.

Let's take 2-butanol. For this stereoisomer, light is turning clockwise when viewed from the right side (I'm not sure of this, but we can assume).



Here, the disks are there to clarify the direction from which we are viewing the entire setup. Here, the "face" of the disks is to the right so we are viewing it from the right.

By the principle of reversibility of light, if light enters from the other side, we get the reverse path:



Rotate this diagram (by $180^\circ$ around an axis perpendicular to your screen):



Note that the disks are being viewed from the other side (the left) now. But we can flip them:



Take a close look at this. This is the same molecule as the first, just oriented backwards. And looking from the right, it still gives a clockwise twist to the angle.

So while rays of light incident on different orientations of a molecule may differ in the exact value of the angle of rotation, rays of light incident on a reversed (not stereoisomeric, just spatially rotated) molecule have the same direction and value of the angle of rotation and do not cancel.

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