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An object is placed at a finite distance from a concave lens. Given are the two ray diagrams. Is the second ray diagram possible? If yes, that must be an enlarged, virtual and inverted image; if no, why not?

Ray Diagram 1:- Ray Diagram 1

Ray Diagram 2:- Ray Diagram 2

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No. The second diagram is not correct.

You did not diffract the ray away from the lens that is passing through F1 point. You just drew the ray along the normal to the surface which is where you got it wrong.

The ray will diffract from its path, away from the normal to the surface, and will probably pass somewhere from the lower plane surface of the lens. If you connect that ray to the first ray of the second diagram, you will get the image formed at the same point in diagram 1.

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In addition to the correct answer of @Spectra:

After removing the incorrect ray from $A$ to $F_1$, draw a ray from $A$ towards $F_2$. When that ray hits the lens, then it is refracted moving to the right parallel to the axis...

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