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Question
A convex lens is placed in contact with a plane mirror. A point object at a distance of 20 cm on the axis of this combination has its image coinciding with itself. What is the focal length of the lens?
Solution
Given, convex lens placed in contact with a plane mirror.
Image of the object coincides with the object.
So, the rays refracted from the first lens and then reflected by the plane mirror will 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 is at the focus of the convex lens.
Therefore, focal length, f = 20 cm
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