# A real,inverted image is I of an object O is formed by a convex lens. The object image of separation is d=40 cm,measured along the axis of the lens. The image is half the size of the object....

A real,inverted image is I of an object O is formed by a convex lens. The object image of separation is d=40 cm,measured along the axis of the lens. The image is half the size of the object.

Calculate the object's distance from the lens. Calculate the focal length of the lens.

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### 1 Answer

A real, inverted image of an object is formed by a convex lens. The object image of separation is d = 40 cm, measured along the axis of the lens. The image formed is half the size of the object.

If D1 is the object distance and D2 is the image distance, the magnification is given by M = (D2)/(D1)

D1 = 40 cm.

M = -0.5

D2 = 20 cm

If f is the focal length of the object, M = (f)/(f - D1)

=> -0.5 = f/(f - 40)

=> 20 - 0.5f = f

=> f = 20/1.5 = 40/3

The object's distance from the lens is 20 cm and the focal length of the lens is 40/3 cm.