Why does a lens have a focal length?

Question

Lenses

I mean, how does a beam of light reflected from an object at one distance from the lens differ from a beam from another distance.
I'm trying to understand why, when the camera or eye is focused at some distance, all objects in that plane get sharp edges, while everything outside that plane gets blurry edges.
I read about the conjugate focal length, which says that the distance from the object to the lens is always proportional to the distance from the lens to the image.
This is the answer to my question. But what this law is based on I cannot understand.
What is the difference between rays emanating from objects at different distances for a lens?
How does the lens "understand" where to refract this beam?

Answer 1

The lens, of course, does not understand anything. Everything is determined by simple refraction.
Imagine a small dot at some distance from the lens. Rays of light that hit this point are scattered, reflected in different directions.
Some of the rays hit the surface of the lens. And not one of these rays forms an image of a point on the other side of the lens (on the focal plane, that is, an imaginary screen), but all these rays must come to one point in order to form a clear image. Whether they will come to the same point on the selected plane depends on how far this plane is, what is the shape of the lens and what is the distance to the real point. If all these parameters are correlated in a certain way, then a clear image is formed. If the point is too far from the lens, then the rays will converge behind the selected plane. If too close, then in front. In both cases, the image on the imaginary (or real) "screen" or camera sensor will be blurry.
Due to the same effect, if you glue a small area of ​​the lens with an opaque material, the image will still be formed, because the rays that fall on the rest of the clean surface of the lens will reach the focal plane.

Answer 2

https://ru.wikipedia.org/wiki/%D4%EE%EA%F3%F1%ED%E...

Answer 3

Look on the Internet for a school physics textbook with pictures - it is drawn in which place which objects are focused. Everything will become clear.