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Question

# A concave lens has a focal length of 20 cm. At what distance from a lens a 5 cm tall object should be placed, so that it forms an image at 15 cm from the lens? Also, calculate the size of the image formed.

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Solution

## According to the question,Image distance, v=−15 cm (negative due to convex lens)Focal length, f=−20 cmLet the object distance be u.By lens formula:1v−1u=1f⇒1−15 cm−1u=1−20 cm⇒1u=120 cm+1−15 cm⇒1u=3−460 cm=−160 cm⇒u=−60 cmTherefore, object is placed at 60 cm away from the lens, on the same side as image.Now,Height of object, h1=5cmMagnification, m=h2h1=vuPutting value of v and u:Magnification, m=h25 cm=−15 cm−60 cm⇒h25 cm=14⇒h2=5 cm4=1.25 cmThus, the height of the image is 1.25 cm and the positive sign means the image is virtual and erect.

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