TITLE: What is the actual significance of the focal point of a lens?
QUESTION [2 upvotes]: 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)
Concave lens

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.

and

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.

Convex 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?

REPLY [1 votes]: To answer this question, oneself or a group of learners needs to understand what is focal length and its importance. Thus, that it will give more clear insight if a learner knows how to differentiate and how to draw the diagrams of each lens like concave (diverging lens) and convex (converging lens).
However, lets define focal length. Focal length is the distance from the lens (vertex) to the focal point. The focal point is the point which enables light rays to parallel the axis.
The significance (important) of a lens to have a focal length is that;

It determines the image location after the object being reflected or refracted from the lens.

It shows the magnification of an image form from an object, whether it enlarges or diminished.

And also, it determines image height. This can be seen when the object was moved closer or further from or to the lens. Sometimes there is no image form when the object was placed on the focal point and there are times when the image form behind the mirror as the object was continually moved towards the lens.
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