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Lens and convex mirror arranged so the image coincides with the object

This type of question, asked 2 times: 2021 Paper 19, 25 Jul 2022. All 2 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    2021 Paper 19

    29
    An object is placed at a distance of 12 cm12\text{ }cm from a convex lens. A convex mirror of focal length 15 cm15\text{ }cm is placed on other side of lens at 8 cm8\text{ }cm as shown in the figure. Image of object coincides with the object. When the convex mirror is removed, a real and inverted image is formed at a position. The distance of the image from the object will be ______ cm.

  2. Question 2

    25 Jul 2022

    119
    A convex lens of focal length 20 cm20\text{ }cm is placed in front of convex mirror with principal axis coinciding each other. The distance between the lens and mirror is 10 cm10\text{ }cm. A point object is placed on principal axis at a distance of 60 cm60\text{ }cm from the convex lens. The image formed by combination coincides with the object itself. The focal length of the convex mirror is ____\_\_\_\_ cmcm.