Determine equation for object distance

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To determine the object distance (o) for a converging mirror that forms an image N times larger than the object, the relevant equations include the mirror formula 1/f = 1/o + 1/i and the magnification equation N = -i/o, with the focal length f expressed as R/2. The initial attempt at a solution led to the equation o = ((1-N)/R)(1/2N), which was later identified as incorrect. The discussion highlights the importance of correctly applying the sign convention and the relationships between object distance, image distance, and magnification. Accurate calculations are essential for deriving the correct object distance in relation to N and R.
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Homework Statement


You wish to use a converging mirror to form an image that is N times larger than the object. R is the radius of curvature of the mirror. At what distance o from the mirror should you place the object? Determine the object distance. Express your answer in terms of N and R. Follow the sign convention.

Homework Equations


1/f = 1/o + 1/i
N = -i/o
f = R/2

The Attempt at a Solution


N*o = 1 / (2/R + 1/o)
2N*o + N =1
o = ((1-N)/R)(1/2N)
This appears incorrect though.
 
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It is, in fact, incorrect. But what are your reasons for thinking so?
 
Thread 'Correct statement about size of wire to produce larger extension'

Thread 'Correct statement about size of wire to produce larger extension'

The answer is (B) but I don't really understand why. Based on formula of Young Modulus: $$x=\frac{FL}{AE}$$ The second wire made of the same material so it means they have same Young Modulus. Larger extension means larger value of ##x## so to get larger value of ##x## we can increase ##F## and ##L## and decrease ##A## I am not sure whether there is change in ##F## for first and second wire so I will just assume ##F## does not change. It leaves (B) and (C) as possible options so why is (C)...
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