Solving a 20-Year Puzzle: A Sports Car Enthusiast's Homework

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SUMMARY

The discussion revolves around a physics problem involving a sports car enthusiast examining a hubcap that acts as both a convex and concave mirror. The enthusiast observes his face reflected at distances of 34.0 cm and 9.4 cm behind the hubcap. Using the lens formula (1/f) = (1/p) + (1/q) and magnification equation m = -q/p, the problem requires determining the distance from the hubcap to the enthusiast's face. The challenge lies in identifying which reflection corresponds to which type of mirror and calculating the actual distance.

PREREQUISITES
  • Understanding of mirror equations in optics
  • Familiarity with convex and concave mirrors
  • Knowledge of image distance and object distance concepts
  • Basic algebra for solving equations
NEXT STEPS
  • Study the properties of convex and concave mirrors
  • Learn how to apply the mirror equation (1/f) = (1/p) + (1/q)
  • Explore practical examples of image formation in curved mirrors
  • Practice solving problems involving magnification and image distances
USEFUL FOR

Students studying physics, particularly those focusing on optics, as well as educators seeking to clarify concepts related to mirror types and image formation.

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Homework Statement


A dedicated sports car enthusiast polishes the inside and outside surfaces of a hubcap that is a section of a sphere. When he looks into one side of the hubcap, he sees an image of his face 34.0 cm in back of the hubcap. He then turns the hubcap over, keeping it the same distance from his face. He now sees an image of his face 9.4 cm in back of the hubcap.

How far is his face from the hubcap?

Homework Equations


(1/f) = (1/p)+(1/q)
m= -q/p

The Attempt at a Solution


Well, I recognize that there is some sort of theoretical way of solving this, but really...im drawing a blank. My AP physics teacher is a little goofy, and when someone asked him for help on the same problem today we(his students) realized that the answer to the problem he had written down for 20 years was incorrect. Please, anyone...I need your help.
 
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If one is a convex mirror, the other side is concave. Given the data, can we tell which image is for which type? The dist of the source is the same in both cases. Is there anything else common for both?
 

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