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The origin of linear birefringence in crystal can be easily explained by the symmetry of the crystal. However, it seems it is hard to be applied in circular birefringence (i.e. optical activity), since there is no macroscopic symmetry in sugar solutions.

So I wonder how we explain the levorotatory and the dextrorotatory in atom level POV?

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So I wonder how do we explain the levorotatory and the dextrorotatory in atom level POV?

It is not easy to predict whether solution of given molecule will be levorotatory or dextrorotatory; this will depend in a complicated way on the structure of the molecule and also on the frequency of light in question. There are models to calculate indices of refraction and absorption for left and right-polarized light for given frequency and molecular structure, but they are quite involved to explain here. The important idea in these is the observation that most often optically active molecules have three-dimensional structure of nuclei that is not congruent with its mirror image (we cannot take molecule and by rotating and translating it superimpose it on its mirror image). Optically active molecules have more spatially separated parts (at least 4 different atoms to allow for this mirror asymmetry) and an important role in the calculations of indices of refraction has the way these parts interact.

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  • $\begingroup$ Thanks for the reply. I know it comes from the chiral of the molecular, but the molecular in the solution isn't aligned well. I can't imagine it if these molecular are randomly aligned but always give the same effect on circular polarized light. I guess the detailed explanation maybe something like Zeeman effect? The energy level will be split under magnetic field. Thus the frequency of radiated light will differ which causes the optical activity? $\endgroup$
    – Tom
    Commented Dec 25, 2013 at 4:38
  • $\begingroup$ No, it is not the same as effects due to magnetic field. In the Faraday effect, the asymmetry is due to magnetic field that is the same all over many molecules. In ordinary optical activity, the asymmetry is just molecular. Although the molecules are oriented randomly, their chirality will manifest in their interaction with light. $\endgroup$
    – Ján Lalinský
    Commented Dec 25, 2013 at 20:02
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Check the Wikipedia page: basically, an asymmetry of one type or another leads to a phase delay in one axis relative to the other, which causes the output to be circularly polarized. Change the sign of the asymmetry and you change the sign of the rotation (of the polarization).

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