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When the focal length of a camera gets further, the object projected on the image gets larger. But would more or less of the object be projected on the image?

I know the answer is that less of the object would get projected on the image because just try it on a camera and I could see the effect. But I don't understand how is this so. I drew a quick diagram below to illustrate my thoughts:

enter image description here

The $f_1$, $f_2$ and $f_3$ are 3 different lengths of focal length from the the camera lens denoted by the small circle in the centre. The projected object on the image are the arrows. So it looks like the further the focal length, the larger the projected image gets. But this doesn't put on any restriction as to how much of the projected object on the image could be shown. In other words, it appears like whatever the lens could see of the object could be enlarged into the image if the focal length is increased without having the projected object being truncated on the image. What have I missed out?

I am assuming that the lens is a normal camera lens.

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Your diagram is not correct as far as camera is concerned.

Actually in a multifocus camera the focal length is actively changing, which causes the field of view to change.

enter image description here

As you can see from the image, a wide angle lens(having small focal length) has widest range while the reverse is true for telephoto lens.

enter image description here

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