A 2.5 dioptre lens forms a virtual image which is 4 times the object placed perpendicularly on the principal axis of the lens. Find the required distance (In cm) of the object from the lens.

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Given power P = 2.5 D, magnification m = + 4 (virtual image). Focal length f = 1/ P = 1/2.5 = 0.4 m = 40 cm. Magnification m = v / u = 4 ⟹ v = 4 u . Using lens formula: 1/ f = 1/ v − 1/ u . 1/40 = 1/ ( 4 u ) − 1/ u = ( 1 − 4 ) / ( 4 u ) = − 3/ ( 4 u ) . 4 u = − 120 ⟹ u = − 30 cm. The object distance is 30 cm.

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