Cause of Spherical Aberrations

What is the cause of spherical aberrations in lenses? I know that it's due to the differing width of the lens, but I don't understand/know the physics of why the lens width affects the focal distance of the light ray. I've seen a lot of optics before, but presently about all I know is that we posit that lenses obey $$\frac{1}{f} = \frac{1}{O} + \frac{1}{I}\tag{1}$$ where $f$ is the focal distance, $I$ is the image distance, and $O$ is the object distance.

So how do we see that the lens width should have an effect on the focal distance?