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

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The correct formula for calculating the focal length of convex mirrors is indeed f = r/2, where r is the radius of curvature. A misunderstanding arose from a textbook that incorrectly stated f = 2/r, which led to confusion among students. The accurate relationship is expressed as 1/f = 2/r, clarifying that the focal length is negative for convex mirrors. This error was confirmed to be a typo in the solutions manual. Understanding the correct formula is crucial for success in tests covering mirrors and lenses.
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
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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