Concave mirror positioning help

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SUMMARY

The discussion centers on the calculation of the distance from a concave mirror to a man's face, given a radius of curvature of 40 cm and an image magnification of 3.30 times the size of the face. The relevant equations used are the magnification formula (M = Si/S) and the mirror equation (1/S + 1/Si = 2/R). The correct distance from the mirror to the face is determined to be 13.94 cm after resolving initial calculation errors.

PREREQUISITES
  • Understanding of concave mirrors and their properties
  • Familiarity with the mirror equation (1/S + 1/Si = 2/R)
  • Knowledge of magnification concepts (M = Si/S)
  • Basic algebra for solving equations
NEXT STEPS
  • Review the principles of concave mirror optics
  • Practice solving problems using the mirror equation
  • Explore the concept of image magnification in optical systems
  • Learn about the applications of concave mirrors in real-world scenarios
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Students studying optics, physics enthusiasts, and anyone interested in understanding the behavior of concave mirrors and image formation.

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Homework Statement


A concave shaving mirror has a radius of curvature of 40 cm. It is positioned so that the (upright) image of a man's face is 3.30 times the size of the face. How far is the mirror from the face?


Homework Equations


M = Si/S 1/S + 1/Si = 2/R


The Attempt at a Solution


I have 2 equations with 2 unknowns. I isolated Si in the first one and substituted this expression into equation 2 to find S. I get an answer of 26.1cm.

The computer keeps telling me I'm wrong though. Could someone check my math or tell me if my equation setup is correct?
 
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oops never mind i got it... 13.94cm
 

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