(Rayleigh scattering / Random
polarizations / Lateral scattering)
In this
section, Feynman briefly discusses Rayleigh scattering, random polarizations, and lateral scattering. In the Audio
Recordings* [14
min: 05 sec], Feynman says something like: “If there is a beam of light like the Sun shining on the
air, it will have an electric field say this way or in this way, it will change
if it is unpolarized. If we stand down over here, we see that when I am doing
the time that it is polarized in this direction, the wave will be generated
this way (scattered wave) by the motion of charge in the air. On the other hand, when the light is polarised
this way during the time that it is doing that during the unpolarised
(averaging in space) because the current is in the line of sight, so there is
no field generated in the eye, when it is this way, all the field would be
generated in the eye is polarised up and down.” This
section is heavily edited, but there could be some diagrams to explain the polarization of
scattered light. It could also be titled “Polarization by scattering of light”
because the next section is about “Polarization by absorption.”
*The Feynman Lectures
Audio Collection: https://www.feynmanlectures.caltech.edu/flptapes.html
1. Rayleigh Scattering:
“The first example of the polarization effect that we
have already discussed is the scattering of light. Consider a
beam of light, for example from the sun, shining on the air. The electric field will produce oscillations of charges in
the air, and motion of these charges will radiate light with its maximum
intensity in a plane normal to the direction of vibration of the charges
(Feynman et al., 1963, p. 33-3).”
The term scattering refers to Rayleigh
scattering, i.e., the absorption of light by a particle and the emission of
light due to the particle’s oscillation. In other words, the electric field of
the incoming light oscillates the electrons, and the oscillated electrons will
emit scattered light (or secondary waves) in different directions. However, some may not be able to visualize the plane, normal to the direction of vibration of the charges, that has maximum intensity.
Specifically, the radiation pattern due to the scattering of a single molecule has
a doughnut (or donut) shape (see Fig. 1) and the intensity is zero along the
direction of the oscillation of the charge. Strictly speaking, the intensity
would not be zero because of multiple scattering and the air molecules are randomly oriented.
 |
| Fig. 1 |
We can deduce the radiation
pattern of an oscillating charge to be doughnut-shaped using the third term of the Feynman-Heaviside
expression of accelerated charge (equation 28.3). This helps to explain why
Feynman says: “motion of these charges will radiate light with its maximum intensity in a plane normal to the direction of vibration of the charges.”
To be precise, maximum intensity occurs at a horizontal plane if the charge is
oscillating vertically. This radiation pattern is an idealization because the
oscillation of the charge is not always along the same axis. In the real world,
we may imagine the radiation pattern to be a rotatable doughnut about the
direction of propagation of light (z-axis) and it is dependent on the
linear polarization of light in the x-axis or y-axis.
2. Random polarizations:
The beam from the sun is unpolarized, so the
direction of polarization changes constantly, and the direction of
vibration of the charges in the air changes constantly (Feynman et al.,
1963, p. 33-3).
Instead of saying “the beam
from the Sun is unpolarized,” we may clarify that the wave packets
emitted by the Sun are randomly polarized. Firstly, the term wave packet
means a short oscillatory directional pulse that is emitted within a duration
on the order of 10-8 s to 10-9 s. This corresponds to a state
of atomic excitation (or a short-lived resonance phenomenon) whereby the excited
atom spontaneously relaxes back to a lower state and loses the excitation
energy. On the other hand, the Sun consists of a very large number of randomly
oriented atomic emitters and the wave packets from the Sun are randomly polarized. Thus, the direction of
polarization changes randomly and the direction of vibration of the
charges in the air changes randomly (instead of changing constantly).
Perhaps Feynman could have mentioned there was a crisis in optics over
the challenge to develop a general formula of randomly and partially polarized
light. In 1852, Sir George Gabriel Stokes, Rayleigh’s
optics teacher, proposed that any polarization state can be completely
described by four measurable quantities or parameters. The four Stokes parameters are not
dependent on a coordinate system, but they can be easily calculated or
measured. For example, we can investigate the pulsar in the Crab Nebula using Stokes parameters and measuring its optical
and radio-frequency radiation. (Feynman discusses the radiation emitted by the
Crab Nebula in the next chapter.) However, some may argue whether linearly and
circularly polarized light are special cases of elliptically polarized light from
the perspective of Stokes parameters.
3. Lateral scattering:
“If we consider light scattered at 90o, the vibration of the charged
particles radiates to the observer only when the vibration is perpendicular to
the observer’s line of sight, and then light will be polarized along the
direction of vibration (Feynman et al., 1963, p. 33-3).”
 |
| Fig. 2 (Source: https://byjus.com/physics/polarisation-by-scattering/) |
It may not be clear why “Feynman” says the light will be polarized along the direction of vibration if it is scattered at 90o and the vibration is perpendicular to the observer’s line of sight. This could be illustrated using a diagram (see Fig. 2): Firstly, the scattered light rays that are parallel to the incoming light are completely unpolarised. Secondly, the light rays scattered at 90o are completely polarized because there is no polarized light that oscillates in the direction of the incoming light. (Based on the definition of polarized light, the electric field of incoming light and scattered light “cannot oscillate longitudinally” in the direction of propagation of light.) Thirdly, the scattered light rays in all other directions (between 0o and 90o) are partially polarized. To be precise, the light scattered at 90o is maximally polarized (instead of completely polarized) because of multiple and random scattering.
Fig. 3
The “light scattered at 90o” (lateral scattering) can
occur at an infinite number of possible angles (Fig. 3). In general, the lateral scattering of light by a single molecule could be elaborated from the
perspective of horizontally (x-direction) and vertically (y-direction) polarized light (Fig. 4). If
the incoming light is moving in the z-direction and horizontally
polarized, the light scattered in the y-direction (upward or downward) should
remain as horizontally polarized. If the incoming light is moving in the
z-direction and vertically polarized, the light scattered in the x-direction
(toward or away from the observer) should remain vertically polarized. Although
we can assume polarized light to have no longitudinal component, but this assumption
is violated in a glass fiber (Junge et al., 2013).
Fig. 4
Review Questions:
1. How would you explain the oscillation of charges in the air radiates
light with its maximum intensity in a plane normal to the direction of
vibration of the charges?
2.
Does the direction of vibration
of the charges in the air change constantly
(or randomly?) if the sunlight is unpolarized?
3. How would you explain the light is maximally polarized
if it is scattered at 90o?
The moral of the lesson: Light rays are horizontally polarized along the entire
horizon when the sun is high up in the sky at noon, but they are maximally
polarized along the meridian that passes through the zenith during sunset (See
Fig. 5).
Fig. 5
Note: In Chapter 36, Feynman
elaborates: “The bee can tell, because the bee is quite
sensitive to the polarization of light, and the scattered light of the
sky is polarized.” In 1949, Karl von Frisch established
that bees, through their perception of polarized light, are able to remember polarization
patterns presented by the sky at different times of the day when the Sun is not
visible. Karl von Frisch is awarded the Nobel Prize in Physiology or Medicine 1973
for explaining the waggle dance used by bees to communicate the location of
food sources.
References:
1. Feynman, R. P. (1985). QED: The strange theory of light and matter.
Princeton: Princeton University Press.
2. 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.
3. Junge, C., O’shea, D., Volz, J., & Rauschenbeutel, A. (2013). Strong coupling between single atoms and nontransversal photons. Physical review letters, 110(21), 213604.
