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I have learnt that only chiral or unsymmetrical molecules can rotate the plane of linearly polarized light. But, why is it so?

And how can molecules rotate the plane or what does it actually mean by 'rotating'? Does it mean that the electric field vectors are tilted or turned left or right depending on the type of isomer?

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See also: How do Optically Active Compounds Rotate Plane Polarized Light?

This is because optical rotation is a chiral phenomenon.

Take a molecule, and draw arrows depicting the polarization of incoming and outgoing light on it. Even if the molecule is achiral, the molecule with the arrows is chiral.

Chirality can't spring out of nowhere, it can only arise from a chiral process.

Also, see my answer here. Since molecules will exist in all rotations in a given fluid, for an achiral molecule the mirror image molecules cancel each other out.

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ManishEarth's second link provides an absolutely excellent explanation for why chiral molecules in solution cannot simply be reoriented.

I would like to add, however, that technically, molecules of the D2d symmetry can rotate light **only if ** they are in a crystal. These are known as birefringent crystals, and they only show optical activity in the crystal form: light going in the x-axis is rotated one way, light going in the y-axis is rotated the other way, and the z-axis is averaged to zero rotation.

There is a paper I've read on this subject, but it's nowhere near basic (I don't even pretend to understand half of it).

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