Distance of object and focal length/power of lens?

[virtuoso735]

A solution to a problem from BR physics says that "focusing on objects close up requires a small focal length and therefore, a more powerful lens than focusing on objects that are far away." I'm not understanding why this is. Don't the light rays get bent by the lens the same amount no matter the distance they travel? Why does the focal length matter?

Does it mean that for the image to be focused very close to the lens the focal point needs to be closer? I get that, but I don't understand why the focal length is smaller if the object is closer to the lens.

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[dranet]

You can understand this question by understanding our owneye. When objects are close two things happened. We converge our eyes and then we relax our ciliary muscles cusing the lens to become more roundish/convex this is accomodation. Take a look at what happens to someone when they look at something very close to their eyes, they go "cock-eyed", you can't see the lens changing shape but people who have cataracts eventually have trouble with focussing close up because despite what the ciliary muscles are doing their lens are particularly stiff. Any way, experimentally you'll find focusing at short distances to the eye shortens the focal length. If you measure Power using the Power eq P=1/(focal length), you'll find that lens power is very much increased. The same principal is applied to lenses in optics. You need powerful lenses to converge light. Acuity is the result of light that is highly focussed.
At distances shorter than the focal length the lens loses its ability to accomodate and will blur.
Hope that helps.
ps the light is bent more by a convex lens as compared to the less convex lens you see when the the ciliary muscles contract and "flatten" the lens. Do a drawing a prove it to yourself