Finding object distance with only the focal length and magnification?

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To find the object distance using a diverging lens with a focal length of -13.0 cm and a magnification of +5.00, the magnification formula (magnification = v/u) is applied, where v is the image distance and u is the object distance. The lens formula (1/f = 1/v - 1/u) is also used, substituting the focal length. Rearranging these equations allows for solving the distances. The discussion emphasizes the need to manipulate the equations correctly to find the desired object distance. Understanding these formulas is crucial for solving similar optics problems.
Kristy92
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A magnifying glass has a diverging lens with a 13.0 cm focal length. At what distance from a toothpick should you hold this lens to form an image with a magnification of +5.00?

I simply have no idea what to do. I tied moving around the equations to make them work, but I can't figure it out.

Please help & thank you!
 
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Hi Kristy, Welcome to Physics Forums!you should have tried a bit more.

magnification = v/u = +5.

also, 1/f = 1/v - 1/u. f = -13cm for diverging lens.

solve.
 

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