Explain why the amplification of a laser beam depends on multiple reflections of photons in the resonant cavity.
Given a resonant cavity with many excited atoms moving inside the cavity, we know that, every so often, unpredictably, some of these atoms will decay to a lower energy level and emit a photon. This process is called spontaneous emission, and it can help to see the process of stimulated emission.
This photon, once emitted, moves through the cavity, potentially colliding with other excited atoms. If it does, that atom will likely emit another photon identical to the one that collided with it, moving in the same direction at the same frequency in the same phase.
On the other hand, if the emitted photon does not collide with any excited atoms, it will reach the back end of the cavity. Both ends of the cavity have mirrors designed to reflect back any incident photons. This reflection sends photons back through the cavity for another pass, where they can again encounter excited atoms, leading to stimulated emission of photons. The more passes through the cavity a photon makes, the higher its probability of encountering an excited atom and stimulating the emission of another photon.
We can write then that having multiple reflections of photons in the resonant cavity increases the number of opportunities for collisions with atoms. And each collision with an excited atom can lead to the emission of another photon. This is why laser beam amplification depends on multiple reflections of photons in the resonant cavity.