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A convex lens is placed in contact with ...

A convex lens is placed in contact with a plane mirror. An axial point object at a distance of `20 cm` from this combination, has its image coinciding with itself. What is the focal length of the convex lens ?

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Shows a convex lens placed in object with a plane mirror. An axial point object is placed at `O` at a distance `OC = 20 cm`.

As the image `I` of the object coincides with `O`, the rays refracted first from the lens and then reflected by the plane mirror must be retracing their path. This would happen when rays refracted by the convex lens fall normally on the mirror i.e., the refracted rays form a beam parallel to principal axis of the lens. Hence the object `O` must be at the focus of the convex lens.
`:. f = CO = 20 cm`
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