Why does a spherical lens/mirror have spherical aberration.

[wyosteve]

I know that a spherical lens does indeed have spherical aberration, and I know that this is caused by the marginal and axel rays of light converging at different points. My question is why? What is it about the lens that makes the rays incedent on the edges of the lens focus at a closer point? Just curious.
Thanks!

 

[vela]

There's really no good answer for that other than it's because of the shape of the lens/mirror. If you carefully work out the path of various rays, you'll find they don't converge to a single point. They come relatively close, so to a good approximation, you can consider the rays to be intersecting at a single point. When this approximation isn't good — in other words, when you can tell they don't meet at a single point — the effect you see is spherical aberration.

For a spherical mirror, for instance, rays from infinity intersect the axis as a distance $l=\frac{r}{2}\cos\theta$ from the center of the sphere, where r is the radius of the sphere and θ is the angle of incidence to the mirror surface. Then θ is small, you can approximate cos θ to be equal to 1. This implies then that the rays focus at a distance r/2 in front of the mirror. The rays for which the approximation cos θ≈1 isn't good result in spherical aberration.

 

[wyosteve]

Ok, that makes sense. Thank you