Section 33–5 Optical activity

 (Optical rotation / Optical rotatory power / Optical rotatory dispersion)

 

In this section, Feynman demonstrates the concept of optical activity using a transmission cell containing corn syrup and two polaroid sheets. This demonstration could be analyzed from the perspective of optical rotation, optical rotatory power, and optical rotatory dispersion.

 

1. Optical rotation:

“Such a substance may show an interesting effect called optical activity, whereby as linearly polarized light passes through the substance, the direction of polarization rotates about the beam axis (Feynman et al., 1963, p. 33–6).”

 

Feynman defines optical activity as an interesting effect whereby the direction of polarization rotates about the beam axis if linearly polarized light passes through a substance. This definition is imprecise because optical activity is also known as the ability of a substance that can cause optical rotation, circular dichroism*, and rotatory dispersion. However, we can define optical rotation in terms of three perspectives: (1) polarization: the rotation of the plane of polarization of light through a substance; (2) asymmetrical molecules: the presence of chiral molecules (or optical isomer) that do not have a plane of symmetry, i.e., the molecule is not the same as its mirror image; (3) interaction: the two opposite circularly polarized light in the substance would be out of phase after interacting with the molecules’ electrons.

 

*Optical rotation and circular dichroism can be formulated using the real and imaginary parts of the refractive index of an optically active substance, with optical rotation being related to the real part and circular dichroism being related to the imaginary part.

“Suppose all of the molecules in the substance are the same, i.e., none is a mirror image of any other. Such a substance may show an interesting effect called optical activity…… (Feynman et al., 1963, p. 33–6).”

 

Note that the optical rotation phenomenon is not necessarily observed unless all of the molecules in the substance are the same, e.g., either all molecules are right-handed or left-handed. That is, it depends on the optical purity (or enantiomeric excess) of a mixture of asymmetric molecules. For example, a 50:50 mixture of left and right-handed isomers cannot rotate the plane of polarization because the opposite effects of right-handed or left-handed molecules cancel each other out. On the other hand, an optical purity of 50% means that it is a 75:25 mixture of left and right-handed isomers. In general, the observed optical rotation of the mixture of asymmetric molecules is dependent on the nature of the molecules or its optical rotatory power.

 

2. Optical rotatory power:

“… the existence of optical activity and the sign of the rotation are independent of the orientation of the molecules (Feynman et al., 1963, p. 33–6).”

 

Feynman did not specifically say the sign of the rotation is independent of the orientation of the molecules. Some may interpret the statement as right and left-handedness of the molecules result in the same optical rotation. Historically, Pasteur recognized the phenomenon of dissymmetry, i.e., the handedness of the molecules determines their optical rotatory power. Although the amount of optical rotation is dependent on the angular orientation of the molecules, the sign will remain the same if they have the same handedness. Thus, the above sentence highlighted in yellow pertaining to the molecules’ orientation could be changed to “the sign of the rotation does not depend on the angular orientation of the molecules (without changing the left-right orientation).”

“When a light beam linearly polarized along the y-direction falls on this molecule, the electric field will drive charges up and down the helix, thereby generating a current in the y-direction and radiating an electric field E_y polarized in the y-direction (Feynman et al., 1963, p. 33–6).”

Feynman’s discussion of optical rotation may not be the better way to understand how the plane of polarization is rotated when a linearly polarized light propagates along an optically active substance. Alternatively, Fresnel (1822) explains that a linearly polarized light entering the substance is split into left and right circularly polarized light (or a superposition of R- and L-states). In essence, two opposite circularly polarized lights can move with different velocities such that there is a relative phase difference between them depending on the distance moved. Then, the two circularly polarized lights form a plane polarized light whose plane of polarization has been rotated when they emerge from the substance. Fresnel’s explanation is based on the assumption that a simple harmonic motion can be considered as a resultant of two opposite circular motions of the same frequency.

“However, if we consider the x-components of the electric field arriving at z = z₂, we see that the field radiated by the current at z = z₁+A and the field radiated from z = z₁ arrive at z₂ separated in time by the amount A/c, and thus separated in phase by π+ωA/c. Since the phase difference is not exactly π, the two fields do not cancel exactly, and we are left with a small x-component in the electric field...  (Feynman et al., 1963, p. 33–6).”

 

Feynman’s explanation using the phase difference of π+ωA/c (=π+ωt) is a simplification that does not include the generation of a magnetic field and it may seem to lead to nowhere. This is because Feynman elaborates that “j_ye^-iwa/c - j_ye^iwa/c @ (i2wa/c)j_y,” (Fig 1) but it is omitted in the text during the editing. However, the optically active substance may be a mix of left- or right-handed molecules and we can idealize a linearly polarized light as a superposition of two orthogonal states of circular polarization. Therefore, we can deduce the optical rotatory power of the substance using the phase difference formula: (n_L – n_R)pd/l. It can be shown that a small difference between the two refractive indices can result in a large optical rotation.

Fig 1 (Source: https://www.feynmanlectures.caltech.edu/Photos1_toc.html)

 

3. Optical rotatory dispersion:

“Corn syrup is a common substance which possesses optical activity. The phenomenon is easily demonstrated with a polaroid sheet to produce a linearly polarized beam, a transmission cell containing corn syrup, and a second polaroid sheet to detect the rotation of the direction of polarization as the light passes through the corn syrup (Feynman et al., 1963, p. 33–7).”

 

It is unclear why the above sentences on the demonstration involving the corn syrup are shifted to the end of the section. Feynman describes this demonstration before explaining the concept of optical activity. In the Audio Recordings** [34 min: 10 sec] of this lecture, Feynman says: “here we have the stuff which consists of Karo corn syrup mixed with water… Then I think you can see in here for those who are at least here at right angle to the thing: interesting spiral colors. Now the reason for this is really a combination of two phenomena at the same time, three in fact.” The observation of spiral colors may be termed optical rotatory dispersion which refers to the variation of optical rotation of a substance with respect to the wavelength of light. The three phenomena may include optical rotation (circular birefringence), circular dichroism, and rotatory dispersion.

**The Feynman Lectures Audio Collection: https://www.feynmanlectures.caltech.edu/flptapes.html

 

In the Audio recordings [35:55], Feynman elaborates: “also, of course, the colors which come out from the other end is polarized if we turn the polarizer we should get different colors…… The effect is different for a different color. So the blue and red and so on have their spirals (each is chromatic)…...” In essence, shorter wavelengths (e.g., violet) are rotated more than longer wavelengths (e.g., red) per unit of distance. Mathematically, the rotatory dispersion may be modeled using Drude’s formula a = A/(l² - l₀²) where A is the rotation constant, l₀ is the dispersion constant and l is the wavelength of light (Nixon, & Hughes, 2017). An experimental setup for optical rotation and optical rotatory dispersion involving corn syrup is shown below (Fig 2). Perhaps Feynman could have ended the section by concluding similar experiments have important implications in Biology, Chemistry, and Pharmacy.

 

Fig 2 An experimental setup (Nixon, & Hughes, 2017)

Review Questions:

1. How would you define an optically active substance?

2. Would you adopt Feynman’s mathematical explanation of optical rotation or Fresnel’s concept of circularly polarized light?

3. Does Feynman’s demonstration involve the phenomena of circular birefringence, circular dichroism, and rotatory dispersion (or interference, polarization, and dispersion)?

 

The moral of the lesson: optical activity is a phenomenon in which a substance rotates the plane of polarization of light, and this rotation can be characterized by its optical rotatory power and its variation with respect to the wavelength of light, which is known as optical rotatory dispersion.

 

References:

1. Feynman, R. P., Leighton, R. B., & Sands, M. (1963). The Feynman Lectures on Physics, Vol I: Mainly mechanics, radiation, and heat. Reading, MA: Addison-Wesley.

2. Fresnel, A. (1822). Mémoire sur la double réfraction que les rayons lumineux éprouvent en traversant les aiguilles de cristal de roche suivant des directions parallèles à l’axe. Oeuvres, 1, 731-751.

3. Nixon, M., & Hughes, I. G. (2017). A visual understanding of optical rotation using corn syrup. European Journal of Physics, 38(4), 045302.