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My physics textbook shows two separate diagrams of light being reflected off of a spherical concave mirror. In the first, it labels a focus where all the rays pass through. In the second, it shows spherical aberration where the rays do not converge to a single point (as opposed to certain parabolic mirrors).

What's the confusion, and what am I not understanding?

Diagram 1 Diagram 2

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The first figure is showing the first-order behavior of light. It ignores other confounding issues. First-order optics is useful for figuring out simple properties like image location and size, but doesn't tell you how good your image will look.

In the real world, when a parallel bundle of rays are incident on a concave mirror and if the mirror is perfectly spherical, you get something called spherical aberration. This is displayed by the second figure. Rays at different heights from the optical axis will focus at difference distances. In order to fix this you have to use a mirror in the shape of a parabola.

You can think of spherical aberration as a variation in focal length with aperture (or pupil) radius.

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  • $\begingroup$ Your statement in the first sentence needs to be re-thought. Even a perfect spherical mirror will have spherical aberration. The first figure shows the paraxial approximation behavior, not perfect behavior. It is a first-order approximation. $\endgroup$ – Bill N Feb 4 '17 at 4:43

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