A sphere with its back silvered can act as a retroreflector. When a fine beam of light is directed to the sphere as shown, it is refracted at the front surface, and focused on the rear interior surface. Then, it is reflected, and finally leaves the sphere in the incident direction. To achieve this, what is the approx. refractive index of the sphere?
I've tried thinking through this, but I don't quite understand why a precise refractive index is required since if a ray gets refracted into the sphere, if it gets reflected along the same ray as it exits. Regardless of refractive index, it should always leave with the same incident ray. Any thoughts?