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Silvered lens: equivalent mirror and the object position for an image on the object

This type of question, asked 4 times: 22 Jan 2025, 23 Jan 2025, 24 Jan 2025, 8 Apr 2026 S2. All 4 questions below, oldest first.

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  1. Question 1

    22 Jan 2025

    20
    Given is a thin convex lens of glass (refractive index μ\mu) and each side having radius of curvature RR. One side is polished for complete reflection. At what distance from the lens, an object be placed on the optic axis so that the image gets formed on the object itself?

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  2. Question 2

    23 Jan 2025

    17
    Given a thin convex lens (refractive index μ2\mu_{2} ), kept in a liquid (refractive index μ1,μ1<μ2\mu_{1},\mu_{1}<\mu_{2} ) having radii of curvature ∣R1∣\left| R_{1} \right| and ∣R2∣\left| R_{2} \right|. Its second surface is silver polished. Where should an object be placed on the optic axis so that a real and inverted image is formed at the same place?

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  3. Question 3

    24 Jan 2025

    12
    A thin plano convex lens made of glass of refractive index 1.5 is immersed in a liquid of refractive index 1.2. When the plane side of the lens is silver coated for complete reflection, the lens immersed in the liquid behaves like a concave mirror of focal length 0.2 m . The radius of curvature of the curved surface of the lens is :-

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  4. Question 4

    8 Apr 2026 S2

    5
    A thin biconvex lens is prepared from the glass ( μ=1.5\mu= 1.5 ) both curved surfaces of which have equal radii of 20 cm each. Left side surface of the lens is silvered from outside to make it reflect. To have the position of image and object at the same place, the object should be placed, from the lens at a distance of ____\_\_\_\_ cm.

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