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Homework Statement
An object is 18 cm in front of a diverging lens that has a focal length of -12 cm. How far in front of the lens should the object be placed so that the size of its image is reduced by a factor of 2.0
Homework Equations
The thin lens equations:
(1/di)+(1/do)=1/f
The magnification equation
(hi/ho)=-(di/do)
f=focal length
di=image distance
do=object distance
hi=image height
ho=object height
The Attempt at a Solution
The first thing I do is plug in values for the thin lens equations and solve for di (do and f are given). I end up getting:
18/di=-2.5
di=-7.2 cm
So the distance of the image from the lens is -7.2 cm.
However, this is where I get confused. I could use hi/ho=-(di/do) but there are two unknowns (hi/ho).
The answer to this, by the way, is 48 cm. I don't know how to get to this, though.