In "QED: The Strange Theory of Light and Matter," Richard Feynman introduces the concept of partial reflection using a stopwatch analogy to provide an intuitive understanding of the phenomenon. While the stopwatch analogy is a helpful visualization, to calculate the percentage of reflected light more rigorously, one would typically employ the principles of quantum electrodynamics (QED) and mathematical formalism.
In QED, the reflection and transmission of light at a boundary between two materials can be described using scattering amplitudes and probabilities. The probability amplitudes for reflection and transmission are calculated based on the properties of the materials and the incident light.
To determine the percentage of reflected light, one typically starts by specifying the boundary conditions and the properties of the materials involved, such as refractive indices and the angle of incidence. These parameters are used to calculate the scattering amplitudes for reflection and transmission.
The reflection coefficient, denoted by the symbol 'R,' represents the probability amplitude for reflection. It is related to the intensity of the reflected light. The squared magnitude of the reflection coefficient, |R|^2, gives the fraction of incident light that is reflected.
The exact calculation of the reflection coefficient and the subsequent determination of the percentage of reflected light can be mathematically involved, especially for complex systems. The specific equations and techniques used depend on the details of the system under consideration and the mathematical framework being employed, such as wave optics or the quantum mechanical formalism of QED.
In practice, various mathematical tools and approximations may be utilized to simplify the calculations. These can include solving Maxwell's equations for the electromagnetic fields, applying boundary conditions, employing perturbation theory, or using numerical methods.
While Feynman's stopwatch analogy provides a qualitative understanding of partial reflection, to obtain precise quantitative results, one typically relies on the mathematical formalism of QED and associated techniques to calculate the reflection coefficient and determine the percentage of reflected light.