Converging Lens and Mirror

1. The problem statement, all variables and given/known data

A small object is located on some distance from a converging lens. At some distant behind a converging lens lies a flat mirror. The resulting image is exactly at the same location as the small object. Why can we deduce that the object is located in the focal point of the converging lens?

3. The attempt at a solution

The first image created by the converging lens will be at infinity if the initial object is at the focal point of the lens. That image at the infinity is located in front of the flat mirror and when used as an object for the mirror, will produce another image at the infinity behind the mirror. This second image is then used as an object for the converging lens. Because this object is at infinity, the resulting image will exactly be on the focal length of the converging lens. Therefore the overall image is at the same place as the focal length.

Does this sound reasonable to you?

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