You place an object 21.0 cm in front of a diverging lens which has a focal lengt

Question

You place an object 21.0 cm in front of a diverging lens which has a focal length with a magnitude of 14.6 cm.  Determine how far in front of the lens the object should be placed in order to produce a new image that is 2.75 times smaller than the original image

Explanation / Answer

f = -14.6 cm h' = h/2.75 => h'/h = 1/2.75 => m = 1/2.75 => v/u = 1/2.75 => u = 2.75*v also, (1/v) - (1/u) = 1/f => (1/v) - (1/2.75*v) = -1/14.6 => 0.6364/v = -1/14.6 => v = -9.29 cm so, u = 2.75*v = - 25.5475 cm The object should be placed at a distance of 25.5475 cm to the left of the lens.

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