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    Question

    A thin converging lens of focal length 20 cm is placed

    at the origin. An object is placed at x = –30 cm. A plane mirror is placed at x = +40 cm. The final image formed after reflection is at:
    A x = +60 cm Correct Answer Incorrect Answer
    B x = +20 cm Correct Answer Incorrect Answer
    C x = +80 cm Correct Answer Incorrect Answer
    D x = –20 cm Correct Answer Incorrect Answer

    Solution

    We are given: • A converging lens (thin convex lens) placed at origin (x = 0) with focal length f = +20 cm. • An object is placed at x = –30 cm (i.e., to the left of the lens). • A plane mirror is placed at x = +40 cm. We are to find the final position of the image formed after reflection from the plane mirror. Image formed by the lens: Use the lens formula: where f = +20 cm, u = −30 cm (object is to the left of the lens, so negative). v = +60 cm So the first image (by the lens) is formed at x = +60 cm (to the right of the lens). Reflection from plane mirror: The image at x = +60 cm acts as a virtual object for the plane mirror at x = +40 cm. The mirror reflects this point image to the same distance behind it : Distance from mirror to image = 60–40=20 cm ⇒ Reflected image=40–20 = x = +20 cm So the final image is at x = +20 cm .

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