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An object is placed at the distance of 200 cm from a lens which forms an erect image exactly one-fourth the size of the object. Find the focal length.

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Apply the lens formula and magnification formula together to get the answer.

From question Image height = 1/4 * Object Height

So, Magnification (m) = 1/4 = v/u

=> v = u/4

Putting the value of v in lens equation we get:

1/f = 1/v - 1/u

1/f = 4/u - 1/u

1/f = 3/u

f = u/3 = 200/3 = 66.6666cm

So, Focal length is 66.6666 cm

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