Yes, there is a deterministic theory that can explain partial reflection, known as classical electromagnetic theory or classical electrodynamics. In classical electrodynamics, reflection of electromagnetic waves is described using Maxwell's equations, which are a set of partial differential equations that govern the behavior of electric and magnetic fields.
When an electromagnetic wave encounters an interface between two media with different refractive indices, part of the wave is typically reflected back while the rest is transmitted into the second medium. The behavior of reflection and transmission at the interface can be determined using the boundary conditions of the electromagnetic fields.
The Fresnel equations, derived from Maxwell's equations, provide a mathematical description of the reflection and transmission coefficients for electromagnetic waves at an interface. These equations allow for the calculation of the amplitude and intensity of the reflected and transmitted waves based on the incident angle, polarization, and the refractive indices of the media involved.
The Fresnel equations are deterministic in the sense that, given the appropriate boundary conditions and input parameters, they can be used to precisely calculate the reflection and transmission coefficients for a given electromagnetic wave. This deterministic approach does not involve probabilistic considerations as in quantum electrodynamics (QED), where probabilities are used to describe the behavior of particle interactions.
It's important to note that classical electrodynamics provides an excellent approximation for many macroscopic phenomena and is widely used in engineering and everyday applications. However, at the microscopic level, where quantum effects become significant, the probabilistic nature of quantum electrodynamics, as described by Feynman's approach, is required to fully explain and predict the behavior of particles and their interactions with electromagnetic fields.