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A convex lens .L. and a plane Mirror .M....

A convex lens .L. and a plane Mirror .M. are arranged as shown in figure below. Position of object pin .O. is adjust in such a way that the inverted image .I. formed by the lens mirror combination, coincides with the object pin .O.. Explain how and when this happens.

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This happens when object is placed at the focus of the convex lens and after refraction from the convex lens the rays becomes parallel and after reflection from plane mirror it converges to focus.
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