# A concave lens has focal length of 15 cm. At what distance should an object from the lens be placed so that it forms an image at 10 cm from the lens ?

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A concave lens has focal length of 15 cm. At what distance should an object from the lens be placed so that it forms an image at 10 cm from the lens ? Also, find the magnification of the lens.

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Here, focal length of concave lens, f = -15 cm.
object distance, u = ?, image distance, v = -10 cm, magnification of lens, m = ?
As (1)/(f) = (1)/(v) - 1/u, 1/u = (1)/(v) -(1)/(f) = 1/(-10) + 1/15 = (-1)/30 or u = -30 cm
Thus the object should be placed at a distance of 30 cm on the left side of the concave lens.
Linear magnification, m = v/u = (-10)/(-30) = 1/3.
The positive sign of m shows that the image is virtual and erect, and its size is (1//3) of the size of the object.