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

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SUMMARY

The correct formula for calculating the focal length of convex mirrors is derived from the relationship 1/f = 2/r, where f is the focal length and r is the radius of curvature. This contrasts with the common misconception that f = r/2, which applies to concave mirrors. The discussion clarifies that the focal length for convex mirrors is negative, indicating that they diverge light. The confusion arose from a typographical error in a textbook that incorrectly stated the formula.

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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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