Calculating the Focal Length of a Concave Mirror

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SUMMARY

The discussion focuses on calculating the focal length of a concave mirror using the mirror formula and magnification equations. The user provided the image size ratio (0.756) and the distance from the mirror to the screen (0.764 m) but initially calculated the object distance incorrectly as -1.01058 m. The correct focal length was calculated using the formula 1/do + 1/di = 1/f, leading to a focal length of 0.435 m. The user was advised to check their sign convention to ensure accuracy in their calculations.

PREREQUISITES
  • Understanding of concave mirrors and their properties
  • Familiarity with the mirror formula: 1/do + 1/di = 1/f
  • Knowledge of magnification concepts in optics
  • Ability to apply sign conventions in optics calculations
NEXT STEPS
  • Review the derivation of the mirror formula and its applications
  • Study the principles of sign conventions in optics
  • Explore practical examples of concave mirror applications in real-world scenarios
  • Learn about the differences between concave and convex mirrors
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Students studying optics, physics educators, and anyone interested in understanding the principles of concave mirrors and their calculations.

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concave mirror!

Homework Statement



The real image produced by a concave mirror is found to be 0.756 times the size of the object. If the distance from the mirror to the screen on which the image appears is 0.764 m , what is the focal length of the mirror?

Homework Equations



(a) 1 /do + 1/di = 1/f

(b) image height / object height=m = - di/do

(c) - object height / image height = do / di

The Attempt at a Solution


m= 0.756 = -hi / ho

so to use equation "c"

i inverted --- > -1/0.756
then set it euqal to rest of the equation so --> -1/.756 = do / .764
do= -1.01058 m

then i used equation "a"

(1/-1.01058) + (1/.764) = 1/f and solved for f

Answer was Wrong. Please tell me what I need to do. Thank you!
 
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I got the answer 0.435 m. Is it correct? If so check your sign convention.
 

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