When a photon interacts with a detecting apparatus or enters our eyes, it is typically treated as a discrete particle-like entity rather than an expanding wave-sphere. Each photon is considered a quantum of light, carrying a specific amount of energy and momentum.
As for whether both of your eyes can ever see the same photon, it depends on the specific circumstances. If a single photon is emitted in a specific direction and travels towards your eyes, it is possible for both eyes to detect the same photon if their optical paths intersect with the photon's trajectory. In such a case, the photon would be absorbed by a photoreceptor in one eye and then subsequently absorbed by a photoreceptor in the other eye, allowing both eyes to "see" the same photon.
However, it's important to note that photons are extremely tiny particles, and the chances of a single photon being detected by both eyes simultaneously are exceedingly rare in everyday situations. In normal lighting conditions, the light reaching each eye consists of a vast number of photons coming from various directions, making it highly unlikely for a single photon to be detected by both eyes simultaneously.
Regarding the wave-particle duality of photons, it is a fundamental aspect of quantum mechanics. Photons can exhibit both wave-like and particle-like behaviors depending on the experimental setup and the type of measurement being performed. The wave nature of photons is often described using mathematical concepts such as wavefunctions and interference patterns. However, when it comes to detection and measurement, individual photons are typically treated as discrete particles.