Converging Lens Question

[collegelife101]

I was just wondering, can a converging lens ever have an image located at the focal point?

I'm asking because of this question: Which of the following describes the image formed in a typical human eye from light rays from an object 10 cm away?

This was part of a passage, where it mentions that the retina is roughly 2 cm away from the lens of the eye.

Solution: According to the second paragraph, the retina is about 2 cm away from the lens in most humans. Also, the light rays actually converge on the retina. That describes the formation of a real image. Thus, the image is real and is about 2 cm away from the lens.

I get this, but then it mentions not choosing an answering which said 2.5 cm: this would be the correct answer if the distance between the retina and the lens were the focal length, but this does not match the passage's description. The position of the light rays actually converging (or where they would be tracked back to converge, for a virtual image) is the image distance, not the focal length.

I don't get why the answer would be 2.5 if the distance was the focal length. Can someone please explain? Thanks!

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[DrknoSDN]

No, a converging lens can't have an image at the focal point. The image would be infinitely small. (or large if virtual).
In general, Converging systems (convex lens or concave mirror) cant make an image at the focal point because at that point all light is concentrated into a single dot and the image would have no height.

The 2.5cm comment is a textbook way of saying "you gotta know this lens equation".

1/f = 1/p + 1/q
1/(2cm apparently) = 1/10cm + 1/q

Solve: for image distance (q)... Basically if the focal length of your lens was 2 cm, and you looked at an object 10 cm away. The image would form 2.5cm from your lens (which would inevitably be 0.5 centimeters behind your retina making the image blurry). I hope that's what they were getting at. It is strange to think of a lens where object distance and image distance are constants with focal length being the variable.

Wolfram alpha for visuals:
https://www.wolframalpha.com/input/?i=(1/2)=(1/10)+(1/x)