Determine equation for object distance

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SUMMARY

The discussion focuses on determining 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, the magnification equation N = -i/o, and the focal length f = R/2. The derived formula for object distance is o = ((1-N)/R)(1/2N), which was identified as incorrect by the participants. The correct approach requires careful application of the sign convention and manipulation of the equations.

PREREQUISITES
  • Understanding of mirror equations and sign conventions in optics
  • Familiarity with the concepts of focal length and radius of curvature
  • Knowledge of magnification in optics
  • Basic algebraic manipulation skills
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  • Review the derivation of the mirror formula and its applications
  • Study the sign conventions used in optics for mirrors
  • Explore the relationship between object distance, image distance, and magnification
  • Practice solving problems involving converging mirrors and image formation
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Students studying optics, physics educators, and anyone interested in understanding image formation using mirrors.

Barry Melby
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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?
 

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