The equiconvex lens shown in the original figure is silvered on one side. Its μ and the radius magnitude of each curved surface is R. For what object distance from the lens will the image be formed on the object itself.
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Question

The equiconvex lens shown in the original figure is silvered on one side. Its μ and the radius magnitude of each curved surface is R. For what object distance from the lens will the image be formed on the object itself.

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G1 Physics · Accepted Answer

For the silvered lens, 1/ F e q F_eq F e ​ q = 1/ f m f_m f m ​ - 2/ f l . f_l. f l ​ . Using the lens and mirror powers for the shown geometry gives F = -R/[2(2μ-1)]. For object and image to coincide, |u| = 2|F|. Hence, |u| = R/(2μ-1).