A Perfect mirror,a Sphere, and a gate

> Imagine this sphere has a gate and when a photon comes towards the sphere it lets it in and instantly shuts so the photon cannot escape.

What will happen is, as you start getting more photons inside your sphere, you'll have more and more probability of the photons already inside your sphere escaping when you open the gate to allow a new one in. In other words, you'll approach a steady-state.

No matter how short a period of time the gate is open, there still is a probability of photons inside escaping.