I am a high school student trying to learn spherical mirrors, and I’ve been told that the focal point is the equidistant point between the center and the surface of the sphere. I played around with the system geometrically and it seems like this information is a bit off. Tried to explain it better with a sketch.

Am I missing something or is this some kind of an approximation that works with very big spheres where the discrepancy of the surface and the tangential line would be smaller?

I am a high school student trying to learn spherical mirrors, and I’ve been told that the focal point is the equidistant point between the center and the surface of the sphere. I played around with the system geometrically and it seems like this information is a bit off. Tried to explain it better with a sketch.

Text in the Image: The focal point seems to be closer to the mirror's surface rather than it's centre.

Am I missing something or is this some kind of an approximation that works with very big spheres where the discrepancy of the surface and the tangential line would be smaller?