Question

at what position of the object with respect to the focal length of the lens the image size seems to be equal object size.

Answer 1

It should be placed at centre of curvature i. e at distance f (focal length) from focus.

Answer 2

the image size seems to be equal object size. the corresponding image is formed at $2F_2$

Explanation:

When the object is placed at $2F_1$ of a lens, the image size seems to be equal object size. the corresponding image is formed at $2F_2$. At this point, the size of the image is same as that of object. The formed image is real and inverted wrt object. The ray diagram is shown in the attached figure.

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Ray diagram

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