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Question

# A convex lens has a focal length of 10 cm. At what distance from the lens should the object be placed so that it forms a real and inverted image 20 cm away from the lens? What would be the size of the image formed if the object is 2 cm high? With the help of a ray diagram, show the formation of the image by the lens in this case.

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Solution

## According to the question:Image distance, v=20 cmFocal length, f=10 cm (positive since convex lens)Let the object distance be uBy lens formula:1v−1u=1f⇒120 cm−1u=110 cm⇒1u=120 cm−110 cm⇒1u=1−220 cm=−120 cm⇒1u=−120 cm⇒u=−20 cmTherefore, the object is placed at 20 cm away from the lens, opposite to the image side.Now,Height of object, h1=2 cmMagnification, m=h2h1=vuPutting values of v and u:Magnification, m=h22 cm=20 cm−20 cm⇒h22 cm=−1⇒h2=−2 cmHeight of image is 2 cm, and the negative sign means the image is inverted.Thus, the image is real, inverted and same as the size of the object.The ray diagram shows the image formation.

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