How do I find the radius of curvature?

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The focal distance is determined to be 19.01868, and the relationship between focal length and radius of curvature is established, with the focal length being half of the radius. A virtual image indicates that the value of q should be negative, which initially led to an incorrect calculation. After reevaluating the problem, the revised answer for q is 127.55 cm. The discussion emphasizes the importance of understanding the relationship between focal length, radius of curvature, and image type in calculations. The final answer reflects the corrected understanding of these optical principles.
Hawking Jr
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Homework Statement
A concave makeup mirror is designed so that a person 29.3 in front of it sees an upright image at a distance of 54.2 cm behind the mirror.What is the radius of curvature of the mirror?
Relevant Equations
1/f=1/p + 1/q and 1/p +1/q = 2/R
I figured out that the focal distance is 19.01868
 
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And you want to know what? The radius of curvature? Do you know the relationship between the focal length and the radius of curvature?

And by the way, is the image real or virtual? And how did your answer to that question affect the way you did your calculation?
 
The focal length is half of the radius curvature. So I multiplied it by 2 and I still got it wrong. The image is virtual.
 
Hawking Jr said:
The image is virtual.

Correct. So what is the value of ##q##?
 
I think it is 54.2 cm
 
No. ##q## is negative when the image is virtual!
 
Oh! Give me a moment to do it over.
 
Okay I redid the problem and the answer I have now is 127.55 cm. Is it correct?
 

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