How to Calculate Image Position and Magnification for a Camera Lens?

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SUMMARY

The discussion focuses on calculating the image position and magnification for a camera lens with a focal length of 55mm and an object distance of 500mm. Using the lens formula \( \frac{1}{u} + \frac{1}{v} = \frac{1}{f} \), the image distance \( v \) is determined to be approximately 62mm. The magnification \( m \) is calculated as 0.124, indicating a reduction in size, and it is noted that the magnification should be expressed as -0.124 due to the image being inverted.

PREREQUISITES
  • Understanding of lens formulas, specifically \( \frac{1}{u} + \frac{1}{v} = \frac{1}{f} \)
  • Knowledge of object distance (u) and image distance (v) in optics
  • Familiarity with the concept of magnification (m) in lens systems
  • Basic principles of light behavior through convex lenses
NEXT STEPS
  • Study the derivation and applications of the lens formula in optical systems
  • Explore the implications of negative magnification in real-world imaging scenarios
  • Learn about different types of lenses and their focal lengths
  • Investigate the effects of varying object distances on image formation
USEFUL FOR

Students studying optics, photographers seeking to understand lens behavior, and anyone interested in the principles of image formation through lenses.

GoodOldLimbo
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Homework Statement



A camera lens has focal length 55mm and an object is 500mm away. Calculate the position of the image and the magnification (or reduction)


Homework Equations



1/u + 1/v = 1/f

u = Object Distance

v = Image Distance

f = focal length

m = magnification

The Attempt at a Solution



f = 55

u = 500

1/500 + 1/v = 1/55

1/55 - 1/500 = 1/v

55-1 - 500 -1 = 0.01618

ANS-1 = 61.79 so approximately 62mm

v/u = m

62/500 = 0.124M

Did I go with the right approach? Any help would be great.
 
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Looks OK to me.

The only things I can think of is that the magnification M = -0.124

1) magnification is supposed to be -ve because the image is usually upside down after the light rays go through a lens provided the object is outside the focal length

2) 0.124M should just be 0.124 since it is a dimensionless number.
 

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