Calculating Object Distance from Lens with Magnification and Focal Length

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To find the object distance from a lens with a focal length of -15 cm and a magnification of ½, the relationship m = -q/p is used, leading to q = -(1/2)p. Applying the lens formula 1/p + 1/q = 1/f, substituting for q gives 1/p - 2/p = -1/15. Simplifying leads to -1/p = -1/15, resulting in p = 15 cm. The calculated object distance from the lens is confirmed as correct.
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Homework Statement


An object is in front of a lens with a focal length of -15cm. An image ½ the side of the object is formed. How far is the object from the lens?

Homework Equations


m - magnification
q - distance from image
p - distance from object
f - focal length

m = -q/p
1/p + 1/q = 1/f

The Attempt at a Solution


m = -q/p so q = -(1/2)p

1/p + 1/q = 1/f
1/p + 1/(-1/2p) = 1/-15cm
-1/p = 1/-15cm
p = 15 cm
 
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