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There are plenty of questions related to this topic on this site but no proper answer.

Can anyone please explain to me how plane polarized light is rotated by chiral compounds, and why it cannot be rotated by achiral compounds?

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    $\begingroup$ Good question. Anyone willing to answer should also share the "why" part of optical rotation. The standard explanation of slowing down of one component of the electromagnetic radiation by a chiral molecule is rampant everywhere. $\endgroup$ – M. Farooq Jul 13 at 3:15
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    $\begingroup$ This can be helpful.en.wikibooks.org/wiki/Organic_Chemistry/Chirality/… $\endgroup$ – Osal Thuduwage Jul 13 at 4:22
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    $\begingroup$ @SafdarFaisal, I mean someone should explain in-depth. I don't know the in-depth answer. The links you and others have provided explain superficially. As I wrote in the above comment, textbooks have a surface treatment of the subject. A good answer may explain why do we only consider the electric field? What happens to the magnetic field-most textbooks are silent about it! How does the electric field interact with the chiral molecule and so on and how does the electric field "know" that it is in a chiral environment. $\endgroup$ – M. Farooq Jul 13 at 4:56
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    $\begingroup$ Of course,@M.Farooq has oriented this question to a proper path. $\endgroup$ – Osal Thuduwage Jul 13 at 5:00
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    $\begingroup$ I agree with @M.Farooq, these points should be in the question itself, to make it complete. $\endgroup$ – Rahul Verma Jul 13 at 5:04
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Circularly polarized light is like a helix that twists through space. The two components are mirror images of each other.

Now, every molecule interacts with both the left-handed twisting light and the right handed twisting light. The interactions differ. Every molecule, in different orientations, interact differently with the left-handed and the right-handed circularly polarized light. enter image description here

Animation Reference: https://en.wikipedia.org/wiki/Circular_polarization

Now, if the molecules in solution have any mirror symmetry themselves, then if averaged over all the molecule interactions the left-handed and right-handed circularly polarized light interact in the same way, and so the polarization does not change.

But this does not hold for chiral molecules: for a particular interaction between a molecule in a certain orientation and the left-handed circularly polarized light there is no corresponding identical interaction with the right-handed circularly polarized light. There is no such molecule of that mirrored shape around.

This results in a net difference in interactions of the molecules with the left-handed and right-handed circularly polarized light, which can be described as a difference in refractive index for the two light waves. And this difference in refractive index can be detected as a change in the direction of the polarization for the sum of the two light waves.

enter image description here

Now, if we want to consider this using the concept of the speed of light varying in media, light goes slower in matter than in vacuum. This slowing down of light in matter is measured using the refractive index n. A higher refractive index means that the light goes slower and so keeps the light longer in the medium. Now if the medium is chiral, it gives the light two different speeds, one for the light that rotates its polarization clockwise and the other one for rotating polarization counter-clockwise. Any polarized light has only two parts (clockwise and counter-clockwise).

The two parts are combined and so the light shows a direction of polarization. When these two parts of light pass through chiral matter, one goes faster and the other slower. The result is that the polarization of light is rotated.


Response to @ Michael Seifert comment;

The way of splitting the light really depends on the matter, rather not decided by the light itself. . If matter has two directions (like a calcite crystal), light is split linearly (parallel and perpendicular). If matter is chiral, (like a solution of bio-substance) light is split circularly (clockwise and counter-clockwise). If matter is both, then all four polarizations are possible, which makes the out-going light hard to nail down.


References:

https://en.wikibooks.org/wiki/Organic_Chemistry/Chirality/Optical_activity#Why_Polarized_Light_Is_Affected

https://en.wikipedia.org/wiki/Optical_rotation

https://www.quora.com/How-do-chiral-molecules-rotate-the-plane-of-polarised-light

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    $\begingroup$ Good answer (& +1), but it might be helpful to explain the relationship between circularly polarized light and linearly polarized light in a bit more detail. $\endgroup$ – Michael Seifert Jul 13 at 15:35
  • $\begingroup$ @Michael Seifert: Thanks for the opinion and glad to hear your kind words. I have edited my answer response to your comment. If you want more details I like to suggest you to follow intelsat.com/wp-content/uploads/2013/02/Polarization.pdf $\endgroup$ – Osal Thuduwage Jul 13 at 18:22
  • $\begingroup$ What is an example of a substance that is both chiral and birefringent? $\endgroup$ – Ruslan Jul 13 at 18:33
  • $\begingroup$ @Ruslan Birefringence is a property of macroscopically anisotropic matter, optical activity of microscopic chirality of e.g. molecules. I assume that a single crystal of basically any pure enantiomer would also be birefringent. $\endgroup$ – Karl Jul 13 at 19:52

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