I know how to find the focal length using the lens formulas, and I know where the focal point is on a diagram.
I've read a few definitions for the focal point such as (Cbakken.net)
Converging light rays striking a concave lens but headed towards a point on the other side can be bent until they emerge parallel to the axis. The point that causes this to happen is called the focal point.
The focal point of a concave lens is the point where light rays parallel to the axis seem to diverge from after passing through the lens. The distance from the lens to this point is called the focal length of the lens.
The focal point of a convex lens is the point where light rays parallel to the axis are brought to a point. The distance from the lens to this point is called the focal length of the lens. and
Diverging light rays striking a convex lens can be bent until they emerge parallel to the axis. The point where this happens is called the focal point.
But what hasn't clicked is why is the focal length significant or useful? If I had a lens, why would I care where the focal point is? Is it simply the point where the imagine (like in a telescope) goes into focus and becomes sharp?
Also, for a convex lens. If I have my eye at the focal point, would the image appear tiny? Since all the light rays converge there?