The image (of a real object) formed by a concave mirror is twice the size of the object. The focal length of the mirror is 20 cm. The distance of the object from the mirror is (are)

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Given: Magnification ∣ m ∣ = 2 , focal length f = − 20 cm (concave mirror). For a real image, m = − 2 . Using m = − v / u , we get − 2 = − v / u ⟹ v = 2 u . Using the mirror formula 1/ f = 1/ v + 1/ u : 1/ ( − 20 ) = 1/ ( 2 u ) + 1/ u = 3/ ( 2 u ) . 2 u = − 60 ⟹ u = − 30 cm. The object distance is 30 cm. If the image is virtual, m = + 2 . 2 = − v / u ⟹ v = − 2 u . 1/ ( − 20 ) = 1/ ( − 2 u ) + 1/ u = 1/ ( 2 u ) . 2 u = − 20 ⟹ u = − 10 cm. The object distance is 10 cm. Therefore, the object distance can be 10 cm or 30 cm.

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JEE Main + Advanced (1 year 12th class)