Section 26–1 Light

 (Geometrical optics / Wave theory / Quantum theory)

 

In this section, Feynman discusses the properties of light that are from the perspectives of geometrical optics, wave theory, and quantum theory.

 

1. Geometrical optics:

“… a condition exists in which the wavelengths involved are very small compared with the dimensions of the equipment … we can make a rough first approximation by a method called geometrical optics (Feynman et al., 1963, section 26–1 Light).”

 

According to Feynman, we can apply geometrical optics if the wavelengths are very small compared with the dimensions of an equipment and the photon energies are small compared with the energy sensitivity of the equipment. That is, light is idealized as a stream of particles (or rays) in which the wavelength l ® 0 and one may clarify that the equipment could be a curved mirror or a lens. In Chapter 27, Feynman mentions that “[t]he most advanced and abstract theory of geometrical optics was worked out by Hamilton … (Feynman et al., 1963, section 27–1 Introduction).” In short, Hamilton intended to show that all problems of geometric optics can be solved by only one method. In a sense, Hamilton has also contributed to wave optics and quantum optics because Schrödinger applied the Hamiltonian principle by passing from geometrical optics to wave optics, and developed the Schrödinger’s equation.

 

Feynman says that he does not even bother to say what the light is, but just find out how it behaves on a large scale compared with the dimensions of interest. In general, one may describe light as a photon, electromagnetic waves, or quantum field. Perhaps Feynman could have stated the behavior of light using three empirical observations (or idealized rules): 1. Straight lines: Light rays travel in straight lines in free space. 2. Law of reflection: the angle of incidence is equal to the angle of reflection. 3. Law of refraction: the ratio of sine of angle of incidence to the sine of angle of refraction for two refractive media is a constant. 

 

2. Wave theory:

“… the wavelengths are comparable to the dimensions of the equipment, which is difficult to arrange with visible light but easier with radiowaves … This method is based on the classical theory of electromagnetic radiation (Feynman et al., 1963, section 26–1 Light).”

 

In the second example, Feynman says that the classical theory of electromagnetic radiation is used to study the wavelengths (e.g., radio waves) that are comparable to the dimensions of the equipment. In this case, he disregards quantum mechanics because the photon energies are negligibly small. As a suggestion, one should explain that the equipment may be a narrow slit that is shorter than the wavelengths of radio waves. Importantly, the diffraction of light through the narrow slit cannot be explained by geometrical optics. For relatively longer wavelengths, we can apply wave optics to study wave properties of light in phenomena such as diffraction, interference, and polarization of light for which the ray approximation is not valid. 

According to Feynman, the light goes from one place to another in straight lines are based on observations, and the rays do not seem to interfere with one another. In other words, light is crisscrossing in all directions, but the light that is passing across our line of vision does not affect the light that comes to us from some objects. Specifically, Huygens (1690) uses his wave theory of light to explain how it is possible for two persons mutually seeing one another’s eyes. He did not only use this argument to refute the corpuscular theory of light, but shows that the speed of light is slower in a denser medium. However, it is incorrect to say that the light does not interfere with each other because we can see 3D hologram that is due to the interference of light rays (or lasers).

 

3. Quantum theory:

“… furthermore, the photon energies, using the quantum theory, are small compared with the energy sensitivity of the equipment (Feynman et al., 1963, section 26–1 Light).”

In the third example, Feynman discusses very short wavelengths, where we can disregard the wave properties of photons. We can use the quantum theory when the photons have very high energy compared with the energy sensitivity of the equipment. This condition is unclear because he did not state a possible range of wavelengths and the equipment. Feynman could have specified the type of electromagnetic wave such as ultraviolet radiation or x-rays that has very short wavelengths as compared to the dimensions of the equipment. Furthermore, one may explain how the photon energies are higher as compared with the energy sensitivity of the equipment using the formula E = hc/l. It is related to Quantum Optics that uses quantum physics to study submicroscopic phenomena involving light.

 

Feynman did not elaborate on the nature of photons, but only gives a rough picture. During a lecture titled QED, Feynman (1985) says that “[t]he first important feature about light is that it appears to be particles… (p. 36).” Currently, the word photon has different meanings, for example, Hentschel (2018) identifies six photon models: 1. the corpuscular model, 2. the singularity model, 3. the binary model of photons, 4. wave packet model, 5. the semiclassical model and, 6. QED model. According to QED, “photons are quantized states of the electromagnetic field whose energy generally belongs to the whole region of space occupied by the radiation field (Hentschel, 2018, p. 174).” Interestingly, Glauber (his Nobel prize is related to quantum optics) says that “I don’t know anything about photons, but I know one when I see one.”

 

Review Questions:

1. How would you explain the condition in which the wavelengths involved are very small compared with the dimensions of the equipment?

2. How would you explain the condition in which the wavelengths are comparable to the dimensions of the equipment and the photon energies are still negligibly small?

3. How would you explain the condition in which the wavelengths are very short and the photons have a very high energy compared with the sensitivity of the equipment?

 

The moral of the lesson: we may apply geometrical optics, waves optics, or quantum optics depending on the wavelengths of electromagnetic waves and their energy.

 

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. Hentschel, K. (2018). Photons: The History and Mental Models of Light Quanta. Cham: Springer.

4. Huygens, C. (1690). Traité de la Lumière. Leiden: Pieter van der Aa.