Light and Optics: Shoplifter's Distance and Height

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SUMMARY

The discussion centers on a physics problem involving a shoplifter observed using a convex mirror. The image of the shoplifter appears 22.0 cm behind the mirror, which has a focal length of 24.0 cm. The calculations reveal that the shoplifter is positioned 2.64 meters away from the mirror. Additionally, using the magnification formula, the apparent height of the shoplifter is determined to be 14.0 cm, leading to the conclusion that the actual height can be calculated using the relationship between the image height and object height.

PREREQUISITES
  • Understanding of convex mirrors and their properties
  • Familiarity with the mirror formula: 1/do + 1/di = 1/f
  • Knowledge of magnification equations: M = hi/ho and M = -di/do
  • Basic algebra skills for solving equations
NEXT STEPS
  • Study the principles of convex mirrors and their applications in real-world scenarios
  • Learn how to derive object and image distances using the mirror formula
  • Explore the concept of magnification in optics and its significance
  • Practice solving similar problems involving mirrors and lenses
USEFUL FOR

Students studying physics, particularly those focusing on optics, as well as educators looking for practical examples of mirror equations and magnification concepts.

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Homework Statement


A shoplifter is spotted using a convex mirror, in which the image appears to be 22.0cm behind the mirror, which has a focal length of 24.0cm. HIs apparent height, in this image, is 14.0cm tall.
A)How far away is the shoplifter from the mirror?
B) How tall is the shoplifter?

Homework Equations


M=hi/ho
1/do + 1/di = 1/f
M= -di/do

The Attempt at a Solution


A) 1/22 + 1/do =1/24
do=2.64 m
 
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Taylor Mdi/ s said:

Homework Statement


A shoplifter is spotted using a convex mirror, in which the image appears to be 22.0cm behind the mirror, which has a focal length of 24.0cm. HIs apparent height, in this image, is 14.0cm tall.
A)How far away is the shoplifter from the mirror?
B) How tall is the shoplifter?

Homework Equations


M=hi/ho
1/do + 1/di = 1/f
M= -di/do

The Attempt at a Solution


A) 1/22 + 1/do =1/24
do=2.64 m
Remember that M=di/do=hi/ho
 

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