Confused about focal length and image distance

[Astra]

My understanding is the following:

Focal length: distance from the lens to the point where all of the light rays cross.

So why do these diagram differ?

http://hyperphysics.phy-astr.gsu.edu/hbase/class/imgcls/focallength.gif

http://hyperphysics.phy-astr.gsu.edu/hbase/class/imgcls/image2.gif

I memorized that 1/f = 1/0 + 1/i

I know what object distance is but I am having trouble understanding what exactly image distance is.

How do you tell where an image is going to be projected? because some diagrams show it as the point where the light rays intersect ( which I thought was the focal length)

https://www.ptgrey.com/Content/Images/uploaded/TAN-Images/TAN35/image006.png

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[BerkReviewTeach]

The focal point not where all the rays interest; it's where all incident parallel rays get refracted and then intersect at the focal point. In the first image you posted, all of the rays are parallel before striking the lens, so they all intersect at the focal point. In the second image you posted, notice that only one ray approaching the lens is parallel (perpendicular with respect to the midline of the mirror), and that that ray passes through the focal point. The nonparallel rays are not passing through the focal point, but are going on to intersect other rays and in doing so form an image.

 

[betterfuture]

Sorry to poke my nose into your thread @Astra118, but I had a question too about this topic since I am currently reviewing it.

So the incoming rays of light are parallel only when the object is far away? And the incoming light rays are non-parallel when the object is close to the lens? Is this correct? Because I too am having trouble understanding why some light would enter in as parallel and some parallel and some non-parallel.