What is the correct formula for calculating focal length in convex mirrors?

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Homework Help Overview

The discussion revolves around the calculation of focal length in convex mirrors, specifically addressing a perceived discrepancy between different formulas for focal length related to the radius of curvature.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to reconcile two different formulas for focal length, questioning the validity of the formula f = 2/r compared to the more commonly referenced f = r/2. Other participants inquire about the specific problem from the text and express concern about potential errors in the textbook.

Discussion Status

The discussion is ongoing, with participants exploring the possibility of a typo in the textbook. Some guidance has been offered regarding the interpretation of the formula, but no consensus has been reached on the correct approach or understanding.

Contextual Notes

There is mention of an upcoming test, which may heighten the urgency of clarifying the focal length formulas. The original poster has encountered consistent use of f = r/2 in their studies, leading to confusion when faced with the alternative formula.

kankerfist
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I'm studying for a test that is going to cover mirrors and lenses. I was under the impression that the focal length for any concave or convex mirror was half the radius of curvature:
f=r/2

but one of the questions in my book involving a convex mirror uses a different value for f, according to the solutions manuel. It says that:
f=2/r

of all the questions I've encountered while studying for this test, f has always been r/2. can someone help explain why f can be 2/r?
 
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That does seem like a typo. As r gets bigger, f will grow. Can you state the exact problem from the text?
 
So was that a typo? Test tomorrow...
 
kankerfist said:
So was that a typo? Test tomorrow...
Yes it was a typo. They meant to say 1/f = 2/r and that is the way they used it in the problem. The right hand side of the next to last line replaced the 1/f with -2/20yd
 

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